Feasibility analysis of an active technology to improve acoustic comfort in buildings

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Building and Environment 42 (2007) 2785–2796 www.elsevier.com/locate/buildenv

Feasibility analysis of an active technology to improve acoustic comfort in buildings Berardo Naticchia, Alessandro Carbonari Department of Architecture, Construction and Structures, Faculty of Engineering, Polytechnic University of Marche, via Brecce Bianche 60131 Ancona, Italy Received 7 June 2006; received in revised form 5 July 2006; accepted 21 July 2006

Abstract In buildings, windows and glazed facades are often the preferred noise path for exterior disturbing noise towards the interior. Since passive means for improving sound transmission loss (STL) of glazed facades are very expensive and are effective only at high frequencies, an active controller that increases the STL in the low-frequency range is an attractive approach for reducing the noise level in buildings with glazed facades, guaranteeing the performance required by the 89/106/CEE European Directive, which made protection against noise a compulsory requirement for buildings. As buildings are often inserted in highly inhabited urban areas, near infrastructures and plants radiating high noise levels, the strategic importance of this task is increasing, together with the importance of acoustic comfort inside buildings. This paper concerns a feasibility study on the implementation of an active structural control system for glazed facades, in order to improve their STL at low frequencies. At present, applications for the reduction of noise level inside cars and planes are known. Relative to the use of active structural acoustic control (ASAC) systems, these systems are based on the reduction of structural vibrations through the use of actuators bonded on the vibrating surfaces, driven by an automated control system, whose task is minimizing those vibrations, and the radiated sound as a consequence. In this work, it is shown that actuators bonded on the vibrating surfaces, driven by an automated control system, are able to dramatically reduce those vibrations and, consequently, the radiated sound. The proposed technology is tested through experiments and numerical simulations, in order to compute the reduction of interior noise that could be pursued through the use of piezoelectric stack actuators. r 2006 Elsevier Ltd. All rights reserved. Keywords: Sound transmission loss; Active structural acoustic control; Curtain walls; Acoustic comfort; Piezoelectric actuators

1. Introduction This paper concerns a feasibility study of an automated control system, aimed at improving the sound transmission loss (STL) of glazed building facades. The 89/106/CEE European Directive has made protection against noise a compulsory requirement for buildings. As a consequence, the importance of a good design of building envelopes, which could provide the required acoustic comfort, was stressed by many researchers [1,2]. From an acoustic point of view, buildings’ envelopes have the task of reducing exterior noise to an acceptable level in the interior. In fact, Corresponding author. Tel.: +390712204397; fax: +390712204582.

E-mail addresses: [email protected] (B. Naticchia), [email protected] (A. Carbonari). 0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.07.040

glazed facades are the preferred path followed by disturbing noise from the exterior to the interior and are often not able to respect the strict limits required by standards and regulations, in spite of the adoption of very expensive passive means. The two main types of passive means for improving STL presently utilized are:

 

laminated glass technology, double glazing.

Both of them can be useful for reducing noise transmission at high frequencies, in particular, the laminated solution is used to shift the coincidence effect at frequencies higher than the audible range, in fact improving STL values in the range of acoustic waves higher than 1500 Hz, while determining no improvements at lower frequencies.

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Nomenclature STL R L T PZT D w W k t P h F a, b Kf E I DL V K

sound transmission loss sound reduction index noise level reverberation time piezoelectric Fac- ade’s sound transmission loss transversal displacement on a plate maximum vibration amplitudes on a plate Eigenvalue time modal pressure plate thickness and actuator height point force plate side lengths material-geometric constant modulus of elasticity momentum of inertia transmission loss due to fac- ade’s shape voltage stiffness

2m r win wa1 wa2 a p m n pe nT s f

at a distance of two meters reference window wall of type 1 wall of type 2 actuator plate first-order of modes second-order of modes piezoelectric normalized with respect to reverberation time shape flanking transmission

Greek letters r t o e

density ratio of the acoustic energy passing through an envelope to the amount originally striking it angular speed strain

Subscripts w e

wall element of a wall

On the other hand, in double glazing, the coupling between the glass panels and the air layer adds another resonance effect at frequencies lower than 500 Hz, while improving their STL in the range of frequencies limited between the resonance and coincidence effects. In this paper, the adoption of an active control system is suggested to solve the drop of acoustic performances of glass panels at low frequencies, showing how it is capable of controlling the vibrations of glazed panels and reducing the sound radiated as a consequence, while avoiding the use of very expensive glazed facades equipped with massive passive means effective only at high frequencies, whose adoption would rise also economic and technological problems for their installation on buildings. Presently, two main approaches are known for active control of sound [3]:

 

Active noise control (ANC), in which secondary waves interfere destructively with the disturbing noise. Active structural acoustic control (ASAC), in which the source of noise is controlled, through the reduction or modification of its vibration field.

As will be shown in the following sections of this paper, the second approach is preferred by the authors because it may be more easily installed on buildings, and requires

low energy consumption and small equipment for working purposes. However, the first approach to be tested by researches was the ANC, even though there are few experiments on buildings. Back to the late 1980s, the first numerical simulations and experimental tests were carried out to show how ANC may be used for the minimization of harmonic enclosed sound fields [4,5]. The authors worked out optimal relative positioning of the secondary sources with respect to the disturbing one, and demonstrated that large noise reductions can be achieved only when the enclosure is excited on resonance; instead, low improvements were registered for off-resonance cases. Hence, it could be inferred that ANC performances are very dependent on the geometric and technical features of the active controlled room. Therefore, further research was devoted to develop a control system that could act at the noise source level, instead of inside disturbed rooms. The authors in [6] stated that ANC could be applied to double partitions by positioning loudspeakers inside the air gap between the two panels. From their investigation they found out that this kind of control can be a viable approach for the reduction of noise passing through double walls. Further, numerical and experimental results confirmed the validity of ANC approach [7,8] for the improvement of STL of double panels, addressing several configurations and sensor

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locations to drive the secondary noise source. However, further research was carried out in order to solve some technological problems that ANC control has when applied to buildings. Feedback controllers were considered more appropriate than feed-forward [9], thanks to the possibility of renouncing the use of sensors on the external surface of panels, placing them inside the air cavity itself. This solution does not seem suitable for any glazed facade, due to the conspicuous thickness of air layers, necessary to allow the insertion of sensors and loudspeakers inside them. An interesting application of feed-forward ASAC approach is presently known [10]. It boasts the utilization of patch actuators on the glass vibrating surface, overcoming the problem of thick air layers; however, sensor microphones are located on the exterior, making that configuration not feasible for installation on building facades. For that reason the authors of this paper suggest the use of a feedback ASAC control system, which will be deeply analyzed in the following, showing that it could represent a feasible strategy for improving STL of glazed panels. This paper is organized as follows: Section 2 summarizes the state of the art relative to passive acoustic means and ASAC control, whose best applications are known in the aeronautic and automotive fields of research. Section 3 details the features and the advantages of the ASAC solutions tested in this paper, compared with other approaches. Then, Section 4 is aimed at testing the technological feasibility of the system previously described, whose acoustic performances are analyzed in Section 5. Concluding remarks are presented in Section 6.

Fig. 1. Sound transmission loss curves for single, double and laminated glass panels [12].

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2. Passive and active approaches for sound transmission loss improvement 2.1. Passive means Passive means are presently in use for the improvement of sound transmission loss of glass panels. In Fig. 1, several stratifications of simply supported glass plates, which are widely available in the market, give back their corresponding STL curves, everyone characterized by weak lowfrequency STL [11,12]. The first critical point for a single glass panel is in correspondence of the resonance effect, registered at very low acoustic frequencies: the low damping of glass lets it vibrate with relatively high amplitudes. Above this value its STL increases with frequency until the critical effect causes another drop of STL. The matching between the wavelength of flexural vibrations propagating through the glass and the projection of the disturbing noise wavelength dramatically increases the overall radiation efficiency of the glass panel. The latter effect may be solved through the adoption of laminated glass panels with PVB layers, which decrease the overall flexural stiffness of laminated panels and shift up the corresponding critical frequency out of the audible range. But, no remarkable improvements are obtained at the resonance frequency, where the adoption of double glass panels is often needless. Even if that solution causes an average increment of STL (moreover in the middle frequency range): it generates another resonance frequency, due to the coupling between the two glass panels and the air cavity, whose position depends on the thickness and typology of the panels [11]. An illustrative example from measurements is presented in Fig. 2, based on Ref. [13]. Three double glass panels are compared to point out the importance of the air layer thickness with respect to the final STL.

Fig. 2. Sound transmission loss curves for double glass panels [13].

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Starting from a good double glazing (two 0.06 m thick glass panels with a 0.013 m air layer interposed), it is shown that even if the air layer is further widen, the low-frequency STL is low due to resonance dip that persists even if a much higher thickness of air, 0.05 m, is provided. Moreover, considering that traffic noise levels are usually very high in the low-frequency range [14], it follows that other solutions are required for guaranteeing acoustic comfort in buildings. According to the calculation method of the European standard EN 12354-3, the acoustic behavior of windows is very critical for the overall building facade performances. Acoustic performances of both walls and walls’ elements are expressed by means of their sound reduction indices Rw and Re that are directly linked to the fac- ade transmission loss between exterior and interior noise pressure level. Then, this value is normalized with respect to the reverberation time T, obtaining the transmission loss D2m,nT through the relation: D2m;nT ¼ Rw þ DLws þ 10 log

T , Tr

(1)

where DLws is the transmission loss due to the facade shape, T and Tr are, respectively, the actual and reference reverberation times, and Rw is computed by ! n m X X Rw ¼ 10 log te;i þ tf , (2) i¼1

f ¼1

where t is the ratio between acoustic energy transmitted through every element (e) or flanking path (f) out of the overall striking acoustic energy on the exterior surface of walls. The overall sound reduction index for a generic wall depends on the sound reduction indices of the elements it is made up of and from flanking transmission paths. Performing a parametric analysis where the features of flanking transmission paths are fixed and the wall is made up of an averagely insulating window and high insulating opaque parts, it can be noticed that the presence of the window makes the opaque part ineffective in improving the overall wall insulation index above a certain limit. Fig. 3 is thought to provide an example for the sake of clarity: as first case, let us assume a facade with the dimensions shown in Fig. 3a.

Fig. 3. Test walls for calculation of the sound reduction index according to EN 12354-3:2000.

From Italian Standard UNI/TR 11175:2005 R values are provided relative to construction typologies typically adopted in the south of Europe. If we choose a window with Re ¼ 37 dB (Fig. 3b) and an opaque stratification with Rw ¼ 55 dB, then assuming that the facade shape transmission loss DL is null, the actual reverberation time is equal to the reference one (T ¼ T r ), the sound transmission loss given by Eq. (1) is equal to 46 dB in case there are no flanking transmissions (tf ¼ 0), which could be obtained by the interposition of resilient layers between the wall and its bearing structures. Anyway, its value is not meaningful for the purpose of our example. In the second case, where another opaque envelope with Rw ¼ 58 dB is chosen (Fig. 3d), no improvements are noticed in the overall value that is again computed through Eq. (1) and equals to 46 dB, because the window is too weak and acts as a preferred path for the sound. Therefore, the unique way to improve its overall acoustic performances lies in the increment of the window’s STL that most of the times is not feasible with passive means because they are very weak in the low-frequency range, and the use of active means becomes convenient.

2.2. Active means The concept of active noise control (ANC) was first introduced by Leug’s patent in 1936 (Fig. 4), relative to a system implementing active control of sound in a duct: the sound field is detected by a microphone, whose signal is passed through an electronic controller that drives a loudspeaker to produce a cancelling wave in a downstream duct. Superposition of the two waves, for the correct choice of control results in destructive interference of the primary or noise source wave. Another type of ANC was developed in 1953 [15]: the system was based upon detecting the offending sound with a microphone and feeding the signal back through a controller to a control loudspeaker located close to the microphone. Good local reductions at the microphone over a range of frequencies from 20 to 300 Hz were obtained. The first approach can be seen to be of feedforward type, as prior knowledge of the noise is obtained with an upstream microphone. In contrast, the second is a feedback arrangement, where the detection microphone is close to the active source. However, both approaches relate to the main concept of ANC, and have its drawbacks: when applied to buildings’ glazed facades, they need an

Fig. 4. Leug’s patent.

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external microphone for disturbance monitoring, and internal error sensors and loudspeakers for control purposes. For that reason, some attempts were made to insert all the system components inside the air cavity of double walls, but this task becomes too much difficult in the case of windows, due to their narrow air layers, as already stated in the introduction. Therefore, the ASAC system is preferred by the authors, because both reference sensors and actuators are placed on the same glazed panel, as required for the implementation of a feedback controller. Thus far in literature two main types of actuators are known (Fig. 5):

 

Piezoelectric (PZT) patch actuators providing bending actions to excite structures; PZT stack actuators providing point forces to excite structures.

The first type is usually bonded to a surface while the second needs a stiffening structures to fix it and make it vibrate for controling purposes. These actuators are available in a wide range of sizes (from few centimetres to some decimetres) and are able to generate high forces (with reduced displacements) inside a wide range of frequencies [16]. Even though they were shown to properly work for many applications there are no tested applications on glazed facades, and most of the experiments were carried out in the automotive and aeronautic fields of research. In [17] control experiments are performed in a test section comprising the aft portion of a furnished DC-9 aircraft, demonstrating the potential of ASAC in reducing cabin noise of aircraft structures. Using a typical feedforward controller arrangement driving two stack actuators as control forces, the researchers achieved global sound level reductions of up to 9 dB. In [18] an aluminum cylindrical test section with a removable floor structure was used to simulate an aircraft fuselage environment. PZT patch actuators were bonded directly to the cylinder surface and the system was excited acoustically with an exterior loudspeaker noise source. Using two microphones as error sensors, the ASAC system provided global attenuations of the order of 10 dB in the cylinder interior. Active control tests were performed by Fuller and Gibbs [19] in the cabin of a Cessna fuselage, a typical mid-sized business jet. PZT actuators bonded to the fuselage skin

Fig. 5. PZT patch (a) and stack actuators for glazed facades (b).

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were used as control actuators to reduce interior noise due to harmonic structural disturbance applied at the engine mount. Using four actuator arrays, each consisting of four patches wired in series, and four error microphones, control was applied to acoustic resonance and offresonance cases. In the acoustic resonance case, noise reductions of up to 20 dB were reached. More recent successful experiments were performed to test the increment of performances in case actuators are bonded on both skins of a double wall instead of just on the internal one [20]. Similar tests were executed for noise reduction in helicopter cabins, by controling vibrations at low frequencies of sandwich panels usually used for their manufacturing [21]: applying a feedback control, improvements up to 6 dB were registered in the receiving room for a range of frequencies limited between 80 and 400 Hz. In this paper a feedback ASAC approach is adopted, but revised in such a way that it may be applied on glazed panels, considering the specific requirements that will be addressed in the following paragraph. 3. The ASAC approach analyzed in this paper Figs. 6 and 7 depict, respectively, the feed-forward and feedback arrangements of an ASAC configuration for glazed facades’ control. By the definition of the ASAC active control, we infer that in both cases, actuators are positioned on the vibrating surface, which is the source of disturbing noise in the receiving room and whose

Fig. 6. Feed-forward ASAC system for glazed facades.

Fig. 7. Feedback ASAC system for glazed facades.

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vibrations are reduced to rise its final STL. Unlike with ANC, ASAC can be easily integrated in buildings, as it does not require the use of loudspeakers or error microphones in the receiving environment; however, optimum positioning of sensors and PZT actuators on the vibrating surface must be pursued. Generally, various modes of vibration have different radiation efficiencies [22], and some are better coupled to the radiation field than others. This suggests two conclusions: only the most efficient modes need to be controlled, rather than the whole response; in some cases the relative phases and amplitudes of multi-modal response can be adjusted so that their radiated fields interfere destructively. The feed-forward control of Fig. 6 requires knowledge of the primary disturbance, which is derived by the use of a reference microphone: in the case of buildings this seems impractical, because it would require the installation of a microphone on the external of the window, which is not feasible for functional and esthetic issues. Therefore, the feedback type controller depicted in Fig. 7 seems to be opportune and is detailed in the following of this paper. The whole system is made up of the following components:

    

sensors to detect the vibration (e.g. strain gauges); electronic filters to analyze signals from sensors in order to check the vibration field induced by disturbance; one electronic controller to manipulate signals from the sensors and compute the most efficient control configuration at the actuators level; charge amplifiers to drive the secondary actuators on glazed panels according to the outputs sent by the controller; actuators to control the vibration field of glazed panels.

Once the signal comes from the sensors, it must be elaborated by charge amplifiers (converting voltage signals into physical variables like displacements, velocity and accelerations), and electronic filters that have the main task of separating the total vibration field into the one due to the primary disturbance from the other connected with the action of secondary sources. The controller, starting from the error signals, computes the radiated field in some positions of the receiving room, and computes the opportune voltage to be supplied to the secondary sources, whose electric power is provided by the amplifiers, in order to reduce the panel’s acoustic efficiency, by opportunely changing or reducing the vibration field of the radiating glass panel. In order to minimize the radiated sound with the use of few and small sensors and actuators that do not dramatically interfere with the possibility of looking through active controlled windows, several procedures have been developed. One of the most stable and robust is presented in [23]: it consists of two parts, the first dedicated to the determination of actuator size and location, the second to sensors. In both cases the core algorithm exploits the quadratic linear optimum control theory to work out

voltages to be supplied to actuators for every assumed location. The rest of the procedure minimizes an objective function applying the quadratic linear optimum control theory for several actuators’ locations, in order to find out the best actuator configuration, upon determination of constraints relative to plate’s geometry and design choices. That algorithm was applied for a bi-dimensional thin sheet metal surface, driven by PZT patch actuators. Instead, this paper is concerned with the investigation of the performances of ‘‘stack’’ actuators, considered much more feasible for glass panels, because of their small size. 4. Technological feasibility 4.1. Choice of actuator type As concerns the choice of actuators we refer to the previous work in [24], that will be summarized in this paragraph. From a literature survey it was found out that two main typologies of PZT actuators are presently available on the market: piezoelectric patches, successfully experimented in [25], and piezoelectric stack actuators, already tested in [17, 18]. As the first is a rectangular shaped patch, it may interfere with visibility (Fig. 8a); instead the second one is very small but need a stiffener to work properly (Fig. 8b). According to a validated analytical model to simulate the vibration field of simply supported rectangular plates [3], the general mathematical formulation is given by wðx; y; tÞ ¼

M X N X

W m;n sinðkm xÞ sinðkn yÞeiot ,

(3)

m¼1 n¼1

where km and kn are the eigenvalues of the plate, x and y its coordinate axes, Wm,n its vibration amplitudes that are given by W m;n ¼

Pm;n , rhðo2m;n  o2 Þ

(4)

where Pm,n is the modal pressure that may be computed, respectively, for patch and stack actuators by Pm;n ¼

4C 0 pe 2 ðk þ k2n Þp1 p2 , mnp2 m

(5a)

4F a sinðkm xf Þ sinðkn yf Þ, (5b) ab where r and h represent, respectively, density and thickness of the plate, o the disturbing wave angular frequency; m and n are the modal numbers of the plate along its two Pm;n ¼

Fig. 8. PZT patches (a) and PZT stack actuators (b) applied on a glass panel.

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axes; C0 is a term dependent with the material-geometric constant Kf, which in turn depends on the plate’s thickness, Poisson ratio and elasticity modulus of both the actuator and the plate [3], and is then computed by C0 ¼ EaI aK f .

(6)

In addition, epe is the actuator’s unconstrained strain, p1 and p2 are two sinusoidal variable terms: p1 ¼ cosðkm x1 Þ  cosðkm x2 Þ,

(7)

p2 ¼ cosðkn y1 Þ  cosðkn y2 Þ,

(8)

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Table 1 PZT P-841 actuator main characteristics Feature

Value

Open loop travel Push/pull force capacity Torque limit at tip Unloaded resonant frequency Operating temperature range Weight Height Diameter

15  106 m 1000/50 N 0.35 N m 18 Hz 20 to +80 1C 0.02 g 0.03 m 0.013 m

where Fa represents the stack actuator’s point force: Fa ¼

d z VK . 1 þ ðK=K a Þ

(9)

Finally, xf and yf are the coordinates of application of such stack actuators, a and b the geometric dimensions of the plate, d is the strain constant of the actuator along the z direction, V the voltage supplied by the controller, K the stiffness of the stiffening system and Ka the actuator stiffness. By implementing this model in the MatLabTM environment and comparing the vibration field generated by a disturbing noise of magnitude 100 dB with the maximum force provided by both kinds of actuators driven at the maximum voltage of 100 V allowed for standard PZT actuators, it came out that single thin patches were not able to contrast vibrations induced by the chosen disturbance (Fig. 9), while it was feasible adopting the stack types [24]. In another contribution [25], it was shown that patch actuators in the laminated arrangement can provide such strong forces to excite glass plates, but they will not be considered in this work, due to their high thickness and size interfering with glass visibility. Therefore, in the following the effects of stack actuators (Fig. 8b) on glass panels will be investigated. Considering the low force intensities that PZT actuators must produce, simulations were led adopting the smallest

Disturbance 100 dB 8 PZTpatches

Vibration amplitude

commercially available actuators that least interfere with visibility: P-841 open loop PZT actuator produced by PI company [26]. Table 1 lists their main characteristics. It is an open loop actuator with small dimensions (0.03 m high) capable of providing strong forces and displacements up to 15  106 m in the range of frequencies lower than 300 Hz. A slight decrement of performances is registered for higher frequencies. 4.2. Actuator positioning on glass panels As previously maintained, there are two basic ways to decrease the radiation efficiency of vibrating glass panels [22]:

 

by decreasing the vibration amplitude of flexural waves (e.g. Fig. 10a); by changing the original vibration in order to obtain a vibration field where even modes dominate (e.g. Fig. 10b).

Every aforementioned alternative determines the corresponding choice for PZT positioning: in the first case the actuators must be installed on some points with maximum vibration amplitudes; in the second case they could be moved along the border lines, where they do not dramatically interfere with the function of looking though, but should be able to modify the vibration field. Fig. 11 shows three possible technological solutions:

26 PZT patches 1.19

1.05

1.12

0.91

0.98

0.84

0.7

0.77

0.63

0.49

0.56

0.42

0.28

0.35

0.21

0.14

0

-2.00E+01

0.07

0.00E+00

Amplitude (dB)

-4.00E+01 -6.00E+01 -8.00E+01 -1.00E+02 -1.20E+02 -1.40E+02 -1.60E+02 -1.80E+02 -2.00E+02

x-coordinate (m)

Fig. 9. Normalized amplitudes of vibration provided by disturbance and PZT patch actuators located along border lines.

1. stack actuators are installed on the maximum displacements to reduce vibration amplitudes, and are then stiffened through a metal profile, 2. stack actuators are installed along the borders and stiffened with an angular profile, 3. stack actuators are installed along the borders and stiffened with point reaction systems. The first and third solutions aim at generating point forces through the application of actuators stiffened by an externally constrained profile of the kind shown in Fig. 8b. The second case requires the use of the same actuators but stiffened with small angular profile glued on the glass to

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Fig. 12. Finite element models and cross sectional areas for the cases of interest.

Table 2 PZT stack actuators physical properties Fig. 10. Reduction of the overall acoustic radiation efficiency.

Fig. 11. Technological solutions suggested for the installation of actuators.

Symbol

Quantity

Units of measurements

Value

Epe npe rpe ha dz j Vmax

Modulus of elasticity Poisson coefficient Density Height Expansion constant Diameter Maximum voltage

Pa — kg/m3 M m/V M V

6.3  1010 0.3 7650 0.003 0.000000000166 0.01 100

displacement) for a simply supported stiffener [29]: K¼

generate bending moments also. In this section, case a of Fig. 11 is analyzed, that is the basic and most straightforward type of technology. Positioning of actuators is dependent on the vibration filed that is due to boundary conditions, which in turn depend on the way of fixing the glass and on the material of the frame. In general, we can state that the stiffer the frame and the smaller are boundary strains. As shown in [27,28] modal shapes of a rectangular glass plate are strongly dependent with the chosen boundary conditions. However, the purpose of this contribution is to study the magnitude of vibration fields involved and the feasibility of acoustic active control. For that reason, it was decided to choose one particular boundary condition, like simply supported edges, considering that displacements and forces involved with glasses subject to the same acoustic phenomenon, even if installed in different ways, are of the same order of magnitude. The installation of PZT actuators requires the use of stiffeners to contrast their strain and allow the glass panel’s vibrations. The choice of the reaction profile for the first case in Fig. 11 must assure that its stiffness is comparable with the one of PZT actuators: at this stage the performances of a steel rectangular shaped profile were compared with the ones of an aluminum presently marketed profile for windows’ frames. A proper finite element model was developed for static analyses on stiffness computations (the magnitude of force necessary to produce a unitary

F . s

(10)

The extreme joints of the stiffener are supposed to be hinged to the window’s frame (Fig. 11a). First, the parameters of the finite element model were set in the case of Fig. 12a, by comparing its solution with the corresponding analytic well-known solution [29], and no differences were noticed in the two cases (in the middle point of the beam the same displacement of 2.68  105 m due to a 1 N force was recorded for section of Fig. 12c). Then the case object of the study in the numerical model of paragraph 5, having three actuators applied along the main axis (Fig. 12b), was analyzed, computing the stiffness provided by two reaction profiles with the two cross sections shown in Figs. 12c and 12d in correspondence of the points were actuators are applied. Assuming for PZT stack actuators, the characteristics listed in Table 2, Table 3 lists all the stiffness values obtained for the case of Fig. 12b, when equipped with the c type (Fig. 12c) or d type section (Fig. 12d). For safety reasons, actuators should be driven by low voltages. Therefore, it is necessary to provide a high stiffened reaction profile that could easily supply a strong reaction to the actuators. It can be noticed by Table 3 that the cross section of Fig. 12d is the suitable one, which can be easily produced with already available manufacturing processes. From a parametric study it came out that forces less than 0.5 N are necessary to contrast disturbing waves of about 80 dB: Table 3 shows that low voltages are required to drive that plate, thanks to the use of the stiffener in

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5.2. The finite element model

Table 3 Stiffeners’ computation results Profile

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Force positioning

Stiffness (N/mm)

Voltage to be supplied (V) for 0.5 N

F1 and F3 F2

0.30  108 0.22  108

40 52

F1 and F3 F2

2.20  104 1.56  104

4150 4150

Fig. 12d, while the other aluminum profile is too weak. In general, we can state that every time the reaction profile stiffness is comparable with the one of the actuators (the actuators of Table 2 have a stiffness of 1.63  108 N/m) and much higher than the controlled system’s one (the plate of glass used for experiments in the following has a stiffness in the centre of 8.80  104 N/m), it gives back opportune reaction forces. The choice of the reaction profile must be pursued according to the characteristics of the main frame of windows. Presently, the most commercially spread types of frame are made up of aluminum, PVC and wood. If we compare the last two types with the first one [29], it would come out that they are much weaker. Therefore, none of them can be used as reaction profile, in accordance with the outcomes reported in Table 3. But a generally valid solution could be using always a steel stiffening profile like in Fig. 12d, covered with the same (aluminum, PVC or wood made) coating which the frame of window is manufactured. 5. Estimation of STL improvement due to active control 5.1. Premise The development of an appropriate finite element model will be described in the following, preliminary to its application to a test case for an estimation of the acoustic improvements that could be determined by the application of such a system. By means of that approach, it will be shown that the magnitude of acoustic relief determined inside building rooms is appreciable for pursuing the acoustic comfort required by European standards and regulations like the 89/106 CEE European Directive. Experiments were performed in order to validate the numerical model presented in the next paragraph, utilized to simulate acoustic improvements provided inside a oneroom test case by the application of an active control system on a standard window (Subsection 5.3). The validation was carried out through comparison between natural frequencies computed by the finite element model and the ones supplied from experiments.

Previous to the numerical analyses that will be carried out in the following , it is necessary to setup a proper finite element model, relative to its subdivision into well-refined elements, to the inputted materials, geometric parameters and to its boundary conditions. As test case a rectangular (1.4  1.0) m glass plate, 0.006 m thick, simply supported along its edges was chosen for numerical and experimental analyses. A numerical model analysis was carried out, and used to set the parameters of the finite element model through a comparison with the corresponding experimental results. The model was implemented in ANSYS 8.0TM environment, subdivided into squared shaped finite elements of 0.02 m of side. Table 4 lists also some of the results computed for the first 25 natural modes of vibration of such a plate. The nomenclature is chosen according to the number of troughs along, respectively, the major and the secondary axes of the plate. The material-geometric parameters inputted for this analysis are: elasticity modulus E ¼ 6:9  1010 Pa; Poisson coefficient u ¼ 0:23; density r ¼ 2457 kg=m3 . We chose these values derived from an iterative refinement of that model, through comparison with experimental data: a rectangular window prototype (1.4  1.0) m large and 0.006 m thick (shown in Fig. 13) was built. Arranging a uniform tightening of the glass panel all along the border lines allowed to simulate a Table 4 Results from the numerical modal analysis The model

Mode shape

Frequency (Hz)

(1,1) (2,1) (1,2) (2,2) (1,3) (3,1)

22.35 45.00 66.80 89.36 141.00 82.79

Fig. 13. Prototype used for experiments.

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simply supporting constraint. As shown in Figs. 14a and b the glass was constrained between four cylindrical Teflon made bars, with a diameter of 0.01 m on the glass and other four bars under the glass: two bars were 1.4 m long and the others were 1.0 m long to assure the presence of the constraints all along the boundaries of the glass, both on and under the plate. An aluminum metal frame with a rectangular (0.13  0.05) m cross section (ALUSIC type produced by Sicomat s.a.s) was used to provide a uniform contact between Teflon and glass. Four equally spaced cap screws (0.008 m of diameter) on the longer side and other three equally distributed cap screws on the shorter side were screwed for stability of the whole system. Every screw fixing the glass panel in the window’s frame was subject to a torque equals to 0.1 N m, in order to guarantee a good and uniform contact between glass and Teflon. Before starting measurements, the whole system was positioned over dumping supports (Fig. 14c) to avoid the influence of external actions on the glass’s vibrations. Fig. 15 is devoted to show how experiments were performed in the Mechanical Measurement Laboratory of the Polytechnic University of Marche. The window was located horizontally at such a distance from the ceiling that it could be zoomed by the terminal of a Laser–Doppler vibrometer [30, 31], placed 3.30 m high from the floor by means of a steel bar-joint structure, allowing in this way a 3 m distance between that terminal and the tested window. The Laser–Doppler system is a high accuracy meter to

Fig. 14. Simply supporting constraint and dumping supports under the window frame.

(b)

(a)

(c)

measure vibration amplitudes of structures without contact (Figs. 15a and b): its theoretical foundations are based on Doppler effect and on interferometry, where the first is used to measure vibration velocities and the second frequencies of vibration. The whole system consists of a Polytec OFV 050 optical scanning head, an OFV 3000 vibrometer controller sending analogue signals to a PC (the measurement and control sub-system). This is equipped with a National Instruments AT-HIO 16E-10 board, which generates the signal to drive the scanning head to the vibrometer and to acquire the signal of the instantaneous position of the laser beam, a reference signal and the vibration signal. Finally, CADA-X software, from LMS International, is also used for the model analysis of the window prototype. Such system allows to measure the vibration displacements and velocity of a point through a low power beam (1 mW) focused on the surface of interest, up to frequency of 200 kHz, with a resolution of 8 nm in displacement and 0.5 mm/s in velocity. Through this experimental setup shown in Fig. 15a it was possible to perform the model analysis for the prototype of window object of this study: first the panel was excited by an impact hammer, which offers the possibility to input a force having a broad-band frequency spectrum (depending on the actual duration and shape of the force impulse), thus exciting all the natural frequencies of the window. The Laser–Doppler terminal has two oscillating mirrors mounted on it; they are used to obtain scanning of a surface over a regular grid. In this case it was chosen to monitor vibrations at the vertices of a squared grid of 0.1 m of side on the window prototype, carrying out the experiments inside the laboratory at standard environmental conditions (25 1C and 50% of relative humidity) and with no other sound waves or disturbing actions interfering with the utilized experimental apparatus. Then, those measures were elaborated to infer model shapes and frequencies, whose values are compared in the right side of Fig. 15 with the ones obtained by the numerical model: absolute shifts are generally very low, and when they seem to become a bit higher it can be noticed that the relative error is in every case lower than 6% (in the last two cases). Thanks to the overall agreement between numeric and

Mode

Freq. exp. (Hz)

Freq. num. (Hz)

Shift (Hz)

1,1

25.0

22.4

2.65

3,1

87.5

82.8

4.61

2,2

90.0

89.4

0.64

3,2

127.5

127.0

0.48

3,3

190.0

200.9

10.88

5,3

320.0

330.9

10.92

Fig. 15. Experimental apparatus for measurements (a), Laser–Doppler terminal (b), measure point on the glass (c) and comparison between numeric and experimental results (right side of this figure).

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experimental results, this model was considered suitable for further numerical simulations, detailed in the following paragraph. 5.3. Simulation of the active controlled window It is assumed that the aforementioned rectangular simply supported window is struck by a harmonic wave at 140 Hz, whose noise level is reasonably the one that could be generated by a lorry traveling at a speed of 70 km/h [14], that is 85 dB. Observing Table 4, it could be inferred that the mode [1, 3] is the most excited, with a bit of influence from the others. Figs. 16a and b sum up the harmonic motion generated in the uncontrolled and in the controlled case along the major and minor axes of symmetry of the glass plate. In the uncontrolled one, the plate’s maximum displacement reach the value of 1.73  106 m in the central troughs, whose value is very close to the other two ones. Fig. 16c depicts the locations for the controlling stack actuators that are supposed to act along the minor axis (like in Fig. 11a), to generate harmonic force amplitudes of 0.383 N at a frequency of 140 Hz. It can be noticed that there is a strong reduction of vibration amplitudes from the uncontrolled maximum value of 1.73  106 to 4.13  107 m that are the residual vibrations, due to the difference of shape between the vibration field induced by a disturbing wave and the other field induced by point forces. However, the release produced from an acoustic point of view may be estimated only analyzing the effects inside a cubic test room with 3 m side’s length. For that reason, the previously tested window was supposed to be installed on one wall of a test room having the following characteristics: plastered walls and ceilings, whose absorbance coefficient may be estimated equals to 0.04 and back stalls on moquette carpet floor, having an estimated overall absorbance coefficient equals to 0.7.

Fig. 16. Active control of a window subject to harmonic disturbance.

Fig. 17. Harmonic acoustic field generated by a lorry (a) and reduction due to the active control intervention (b).

Assuming the same harmonic disturbing wave of 85 dB level and propagating at 140 Hz, like in the previous study, the resulting acoustic harmonic disturbance inside the room will be equal to the one depicted in Fig. 17a, whose average level is 66 dB, the minimum is 34 dB and the maximum is 78 dB. In case the window is controlled by the three stack actuators of Fig. 16c, with a consequent decrement of vibrations until the course shown in Figs. 16a and b, a strong decrement of acoustic pressure level is obtained, as shown in Fig. 17b: the maximum peaks drops from 78 to 63 dB, thanks to the reduction of vibration amplitudes generated by the actuators, with a final drop of 15 dB. The average and minimum values drop to 53 and 32 dB respectively. 6. Concluding remarks Thanks to the application of an active structural acoustic control system, it is possible to strongly improve the STL of window panels in the low-frequency range: the presence of actuators drops dramatically the noise transmitted from the exterior to the interior, even when the disturbing noise frequency is near its resonance effect. Coupling this system with laminated technology, that are effective at high frequencies, would allow to obtain good insulation properties all over the range of audible acoustic frequencies, determining an increment of transmission loss performances for all the wall where such active controlled windows are inserted. In the particular case considered in this paper, where a relatively complex mode was excited, it was possible to obtain a sound reduction of the highest value up to 15 dB inside the chosen test room. Moreover, it was shown that several technological solutions are available for its installation on windows and that its functioning requires the use of very low voltages and cannot be considered dangerous for users.

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At this stage, it is possible to conclude that the ASAC system is a feasible and effective solution for the improvement of acoustic comfort inside buildings. Therefore, further research will be conducted to produce a first prototype of that active controlled window. In particular, further experiments will be performed to test experimentally the reliability of stack actuators on glass panels (as they have already been tested on panels of other kinds) and to design an adequate controller to drive those actuators. Acknowledgments We would like to thank the staff of the Mechanical Measurement Laboratory of the Polytechnic University of Marche for their helpful support. In addition, we thank the anonymous reviewers for comments that improved this paper. References [1] Oral GK, Yener AK, Bayazit NT. Building envelope design with the objective to ensure thermal, visual and acoustic comfort conditions. Building and Environment 2004;39:281–7. [2] Kruger EL, Zannin PHT. Acoustic, thermal and luminous comfort in classrooms. Building and Environment 2004;39:1055–63. [3] Fuller CR, Elliott SJ, Nelson PA. Active Control of Vibration. 2nd ed. San Diego-London-Boston-New York: Academic Press; 1997. [4] Bullmore AJ, Nelson PA, Curtis ARD, Elliot SJ. The active minimization of harmonic enclosed sound fields, Part II: a computer simulation. Journal of Sound and Vibration 1987;117(1):15–33. [5] Elliot SJ, Curtis ARD, Bullmore AJ, Nelson PA. The active minimization of harmonic enclosed sound fields, Part III: experimental verification. Journal of Sound and Vibration 1987; 117(1):35–58. [6] Sas P, Bao C, Augustinovicz F, Desmet W. Active control of sound transmission through a double panel partition. Journal of Sound and Vibration 1995;180(4):609–25. [7] Bao C, Pan J. Experimental study of different approaches for active control of sound transmission through a double wall. Journal of the Acoustical Society of America 1997;102(3):1664–70. [8] Pan J, Bao C. Analytical study of different approaches for active control of sound transmission through a double wall. Journal of the Acoustical Society of America 1998;103(4):1916–22. [9] Kaiser OI, Pietrzko SJ, Morari M. Feedback control of sound transmission through a double glazed window. Journal of Sound and Vibration 2003;263:775–95. [10] Zhu H, Rajamani R, Steltson KA. Active control of glass panels for reduction of sound transmission through windows. Mechatronics 2004;14:805–19. [11] Harris CM. Handbook of Acoustical Measurements and Noise Control. 3rd ed. New York: McGraw-Hill; 1984. [12] Spagnolo R. Manuale di acustica, UTET Libreria, 2001. [13] Harris CM. Noise Control in buildings. New York: McGraw-Hill; 1994.

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