Modal parameter identification of RC frame under undamaged, damaged, repaired and strengthened conditions

Accepted Manuscript Modal Parameter Identification of RC Frame under Undamaged, Damaged, Repaired and Strengthened Conditions Ahmet Can altunı ş ık, Olguhan Şevket karahasan, Ali Fuat genç, Fatih Yesevi okur, Murat günaydın, Ebru kalkan, Süleyman adanur PII: DOI: Reference:

S0263-2241(18)30312-9 https://doi.org/10.1016/j.measurement.2018.04.037 MEASUR 5438

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

11 May 2017 14 March 2018 12 April 2018

Please cite this article as: A. Can altunı ş ık, O. Şevket karahasan, A. Fuat genç, F. Yesevi okur, M. günaydın, E. kalkan, S. adanur, Modal Parameter Identification of RC Frame under Undamaged, Damaged, Repaired and Strengthened Conditions, Measurement (2018), doi: https://doi.org/10.1016/j.measurement.2018.04.037

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Modal Parameter Identification of RC Frame under Undamaged, Damaged, Repaired and Strengthened Conditions Ahmet Can ALTUNIŞIK, Prof. Dr. [email protected] Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey Olguhan Şevket KARAHASAN, PhD. [email protected] Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Ali Fuat GENÇ, PhD. [email protected] Karadeniz Technical University, Department of Civil Engineering, Of Technology Faculty, 61080, Trabzon, Turkey

Fatih Yesevi OKUR, PhD. [email protected] Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Murat GÜNAYDIN, Asst. Prof. [email protected] Gümüşhane University, Department of Civil Engineering, 29100, Gümüşhane, Turkey

Ebru KALKAN, PhD. [email protected] Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Süleyman ADANUR, Prof. Dr. [email protected] Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Correspondence Address: Ahmet Can ALTUNIŞIK, Prof. Dr. Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, TURKEY. E-mail: [email protected]

Abstract

Structures are built on a design and then damaged in time by natural and manmade effects, repaired and strengthened for reusing. Determination of the structural behavior is very important to avoid future disaster. Operational Modal Analysis has been widely used recently to determine the inherent modal parameters of engineering structures and give significant information about the structural condition. Also, this method can be used to further studies such as model updating, damage detection and health monitoring. In this paper, it is aimed to investigate the changes of modal parameters considering undamaged, damaged, repaired and strengthened conditions using ambient vibration tests. For this purpose, a reinforced concrete frame model having two-floor with two spans in the longitudinal direction considering ½ geometric scales is built in laboratory. Four different cases are considered to emerge the efficiency of this procedure and the undamaged RC model is measured firstly to determine the initial modal parameters. Secondly, the lateral forces are applied to floor levels to obtain the damages, especially in beam-column joints. Thirdly, the damaged model is repaired using injection material and lastly strengthened with Carbon Fiber Reinforcement Polymer. It is also examined that what rate the dynamic characteristics return to back after repairing and strengthening studies by the comparison with undamaged condition? In addition to this the evaluation of carbon fiber reinforcement polymer effectiveness in strengthening for real applications is presented. It is seen that ambient vibration test is enough to identify the modal parameters of engineering structures for different conditions. The modal parameters are decreased distinctly with damages, and reverted almost initial condition with strengthening.

Keywords: Carbon Fiber Reinforcement Polymer, Damage, Modal parameter, Operational Modal Analysis, Reinforced concrete, Repair, Strengthening.

1. INTRODUCTION

Structures have been damaged over time due to some natural and human effects such as earthquakes, explosions, winds, floods, wars, vandalisms, lifetime expiration of materials, inconvenient use of the structures etc. Especially, earthquakes cause to destructive damages rather than others. These situations require to the strengthening of the structures. Two techniques are suggested to be used for strengthening in existing structures [1] such as applying external loads with prestressing and strengthening the constrained sections using high performance materials [2].

Suitable strengthening methods should be implemented for upgrading the existing structures and structural members, or attempting to restore them as closely as possible to their original form [3]. Besides the classic strengthening methods such as cement and epoxy mortar injections, innovative materials such as fiber reinforced polymers (FRPs) have been widely used to repair and strengthen the structures and their elements due to benefits and advantages such as high strength, rapid and easy application, low weight, corrosion resistance and durability [4-6].

Three types of FRP materials such as glass fiber reinforced polymer (GFRP), carbon fiber reinforced polymer (CFRP) and aramid fiber reinforced polymer (AFRP) are generally used in structural strengthening. Usage areas of these materials are quite wide in structural industry. They have been used for almost all materials such as reinforced and prestressed concrete, masonry, timber, and steel structures [7]. As can be seen in literature that FRP strengthening increase the nonlinear response capacity, rigidity, load-carrying capacity, energy absorption, strength and environmental resistance, and reduce the seismic vulnerability and maximum displacement values [8-12]. These properties are directly related to modal parameters such as natural frequencies, period, mode shapes and damping ratios of structures.

In the literature, many researchers have studied about the FRP strengthening effect on the structural behavior of engineering structures or structural members. FRP strengthening effect is investigated experimentally considering reinforced concrete [13-20], steel-concrete composite [21-24], timber [25-28] and masonry materials [29-32]. Also, limited number of studies are available about the investigation of FRP effects using nondestructive experimental methods [3,7,13,33].

2. REINFORCED CONCRETE (RC) FRAME MODEL

The reinforced concrete (RC) frame model is constructed in laboratory condition to determine the initial modal parameters and investigate the damage, repairing and strengthening effect on the structural response, experimentally. The model has two-floor with two spans in the longitudinal direction considering ½ geometric scaling without material-oriented scaling. The frame model has two types’ columns with 15x20cm and 20x15cm dimensions and equal beams with 15x20cm dimension. The dimensions of spans and each floor height are selected as 140cm and 170cm, respectively. The raft foundation is considered to ensure the fixed base using 30cm slab thickness. The drawings including geometrical, sectional and reinforcement details are given in Fig. 1a. The view of RC frame model after construction is also presented in Fig. 1b.

(a) Drawing details

(b) After construction

Fig. 1 The drawing details and real views of the reinforced concrete frame

The using of low-strength concrete having 16MPa compressive strength is considered in order to represent the general material properties of building stock in Turkey. The amount of mixture produced on ready mixed concrete plant is given in Table 1.

Table 1 The amount of material mixture used in the RC frame model Component Aggregate (15-25 mm) Aggregate (7-15 mm) Aggregate (0-7 mm) Cement (C) Water (W) C/W Total

Foundation Concrete kg m kg m kg m kg m kg m 0.88 2392

Beam and Column Concrete kg m kg m kg m kg m kg m 0.86 2377

3. EXPERIMENTAL MEASUREMENTS

Ambient vibration tests are carried out to extract the modal parameters such as natural frequencies, mode shapes and damping ratios. In the ambient vibration measurements, a B&K 3560 data acquisition system with 17 channels, B&K 4507 and B&K 8340-type uniaxial accelerometers which have 10V/g sensitivity, uniaxial signal cables, PULSE [34] and OMA [35] software are used as the test equipment. Ambient vibration tests are carried out during 20 minutes considering 0-200Hz frequency range. The signals obtained from the accelerometers are accumulated in data acquisition system and then transferred into the PULSE and OMA software’s for signal processing. Then, modal parameters are extracted using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. It is very important to decide from which points to measure so that the experimental modal parameters are determined correctly. For this reason, finite element model of RC frame model is constituted in ANSYS program and modal analysis is carried out. The total of 22 measurement points are selected, which is bigger from the capacity of 17 channels data acquisition system, to extract the experimental mode shapes. So, the experimental measurements are divided into two sub-step and the reference accelerometer (location is not change during both measurements) is used to accumulate the vibration signals. This is one of the most important advantages to determine the modal parameters and give detail information for further studies such as damage identification and structural health monitoring. A representative model generated in PULSE software and accelerometers layout along with their directions are presented in Fig. 2.

Fig. 2 Accelerometer location during ambient vibration tests

3.1. Undamaged Model

Singular values of spectral density matrices (SVSDM) and the average of auto spectral densities (AASD) of the data set obtained by EFDD method for undamaged condition of RC frame model are given in Fig. 3. Fig. 4 shows the first three mode shapes of the RC frame.

Fig. 3 SVSDM and AASD of the data set for undamaged condition

Fig. 4 The mode shapes obtained by EFDD method for undamaged condition

The modal parameters also identified using SSI method. The stabilization diagram and singular values for the first three modes are given in Fig. 5. The natural frequencies, mode shapes and damping ratios are calculated as stabile values. Fig. 6 illustrates the first three mode shapes. Modal parameters are summarized for undamaged condition in Table 2.

Fig. 5 The stabilization diagram and singular values for undamaged condition

Fig. 6 The mode shapes obtained by SSI method for undamaged condition

Table 2 Experimental natural frequencies of the undamaged RC frame Mode Number 1 2 3

Frequency (Hz) 13.898 39.907 123.84

EFDD Damping Ratio (%) 1.022 0.613 0.451

Frequency (Hz) 13.69 39.93 124.7

SSI Damping Ratio (%) 0.859 0.432 0.680

In this study, only geometrical scaling is considered. It is well known that when the geometry is changed, mass of structure is also changed. The first natural frequency of 1/2 geometrical scaled laboratory model (fm1) is obtained as 13.898Hz. To obtain the full-scale results, the Eq. (1) should be used as:

fp

1 γ m1 S γp

Ep E m1

f m1

(1)

where, fm1 and fp are expresses the first natural frequency values of scaled and prototype models, respectively. Because of the fact that only geometrical scaling is considered, it is accepted that γ m1 = γ p and E m1 = E p in Eq. (1). There is no scaling for weight per unit of volume and modulus of elasticity. The first natural frequency of full-scale model is calculated as:

fp

1 13.898 6.949Hz 2

(2)

To evaluate the scaling of material properties, same scale factor is considered for modulus of elasticity. The corresponding concrete strength is chosen as 8.0MPa for C16/20 concrete class. Modulus of elasticity is calculated according to the corresponding concrete strength as Em2=13293.60MPa.

E

4700 f c'

(3)

E 4700 8 E m2

13293.60N / mm 2

(4)

where, f c' is the characteristic cylinder strength at 28 days (in MPa) By using of geometrical scaled model (fm1=13.898Hz) as a reference parameter, the first natural frequency is obtained considering same scale factor for geometrical and material properties as:

f m2

1 γ m1 S γ m2

E m2 E m1

f m1

(5)

f m2 f m2

13293.60 13.898 18800 11.69Hz

(6)

where, fm1: frequency value of scaled model (geometric), fm2: frequency value of scaled model (geometric and material), Em1: modulus of elasticity of scaled model (geometric), Em2: modulus of elasticity of scaled model (geometric and material). By using of full-scale model (fp=6.949Hz) as a reference parameter, the first natural frequency can be also obtained considering same scale factor for geometrical and material properties as:

f m2

f m2 f m2

S

γp

E m2

γ m2

Ep

fp

13293.60 6.949 18800 11.69Hz 2

(7)

(8)

where, fp: frequency of actual (full-scale) model, fm2: frequency value of scaled model (geometric and material), Ep: modulus of elasticity of full-scale model, Em2: modulus of elasticity of scaled model (geometric and material). The flow chart of the scaling procedure and related formula is given in Fig 7.

Fig. 7 The flow chart of the scaling procedure and related formulas

3.2 Damaged Model In the damaged condition, it is aimed to constitute several damages on the frame model. One of the most important points is where the cracks may occur to reflect the real structural behavior using laboratory models as soon as possible. It is seen from the literature survey of real RC building models, dynamic model tests, and numerical analyses that the beam-column joints of the RC buildings are weakest points and that, in general, this is where cracks occur during an earthquakes.

Similar to the earthquake loads, lateral forces are applied to floor levels (beam-column joints) of frame model to obtain the cracks and damages, especially in beam-column joints (Fig. 8). The minor crack widths (<10 mm) and excessive diagonal crack widths (>10 mm) occurred around the first and second floor beam-column joints. Concrete cover splitting also occurred in some regions.

Fig. 8 Some views from damaged RC frame model

The ambient vibration measurements are conducted on damaged frame model to evaluate the changes of modal parameters. Fig. 9 shows the some photos from ambient vibration measurements performed on damaged RC frame model. Singular values of spectral density matrices (SVSDM) and the average of auto spectral densities (AASD) of the data set obtained by EFDD method for damaged RC frame model are given in Fig. 10. Fig. 11 shows the first three mode shapes of the damaged RC frame.

Fig. 9 Some views from ambient vibration measurements for damaged model

Fig. 10 SVSDM and AASD of the data set for damaged condition

Fig. 11 The mode shapes obtained by EFDD method for damaged condition

The modal parameters also identified using SSI method. The stabilization diagram and singular values for the first three modes are given in Fig. 12. The natural frequencies, mode shapes and damping ratios are calculated as stabile values. Fig. 13 illustrates the first three mode shapes. Modal parameters are summarized for damaged condition in Table 3.

Fig. 12 The stabilization diagram and singular values for damaged condition

Fig. 13 The mode shapes obtained by SSI method for damaged condition Table 3 Experimental natural frequencies of the damaged RC frame Mode Number 1 2 3

Frequency (Hz) 7.269 23.263 69.293

EFDD Damping Ratio (%) 2.28 0.985 0.686

Frequency (Hz) 4.441 23.6 62.65

SSI Damping Ratio (%) 15.32 9.463 6.887

3.3. Repaired Model

The damaged RC frame model is repaired using epoxy injection and cracks are closed. The ambient vibration measurements are conducted on repaired frame model to evaluate the changes of modal parameters. Firstly, the cracks generated by lateral forces gradually to the beam-column joints are marked and epoxy injection is applied to crack regions. Some technical specifications of the used Concresive 1302 injection material [36] are given in Table 4. Before injecting, the powder layer on the frame is cleaned with a wire brush. In the injection application, marked cracks areas are drilled by drill and packers are compressed by crushing the injection pumps (10x60 mm) in the holes. Subsequently, the injection material is injected into the cracks from the packers by adjusting the pressure by means of the pump. Some views from epoxy injection are given in Fig. 14. The ambient vibration measurements are performed after injection application (7 days). Fig. 15 shows the some photos from ambient vibration measurements performed on repaired RC frame model.

a) Drilling of the injection packer holes

b) Crushing and compressing of the packers into the holes

c) Injecting of injection material into cracks by pressure Fig. 14 Some views from injection application

Table 4 Some technical specifications of Concresive 1302 epoxy injection material Material Structure Concresive 1302 Component A

Epoxy Resin

Concresive 1302 Component B

Epoxy Hardener

Mixture Density

1.06±0.05 kg/lit

Viscosity

200-350 N/mm s

Adhesion Strength (to Concrete) (7 day)

>2.0 N/mm

Application thickness

Minimum 0.2 mm-Maximum 1.0 mm

Using Duration

25 minutes

Total Curing Time

7 days

Fig. 15 Some views from ambient vibration measurements for repaired model

Singular values of spectral density matrices (SVSDM) and the average of auto spectral densities (AASD) of the data set obtained by EFDD method for repaired RC frame model are given in Fig. 16. Fig. 17 shows the first three mode shapes of the repaired RC frame.

Fig. 16 SVSDM and AASD of the data set for repaired condition

Fig. 17 The mode shapes obtained by EFDD method for repaired condition

The modal parameters also identified using SSI method. The stabilization diagram and singular values for the first three modes are given in Fig. 18. The natural frequencies, mode shapes and damping ratios are calculated as stabile values. Fig. 19 illustrates the first three mode shapes. Modal parameters are summarized for repaired condition in Table 5.

Fig. 18 The stabilization diagram and singular values for repaired condition

Fig. 19 The mode shapes obtained by SSI method for repaired condition

Table 5 Experimental natural frequencies of the repaired RC frame Mode Number 1 2 3

Frequency (Hz) 9.895 30.27 115.6

EFDD Damping Ratio (%) 2.178 1.783 1.375

Frequency (Hz) 9.573 30.09 114.8

SSI Damping Ratio (%) 99.55 6.627 2.159

3.4. Strengthened Model

Two mainly alternatives can be considered for damaged structures either demolishing and rebuilding in accordance with related standards and regulations or strengthening it. The selection of each alternative based on the magnitude of damage and economic factors. When the structural strengthening is decided, one of the commonly used techniques can be chosen such as shear wall addition, column/beam jacketing for cross-sectional growth, steel reinforcement and reinforcement with the composite materials.

Fiber Reinforced Polymer (FRP) composite materials are bonded to the surfaces of structural members in different methods, shapes and directions. This application is practical, fast and reliable method for strengthening that has been commonly used during recent years. Some good and successful examples can be found in the literature about the strengthening with FRP composite materials on some structures such as bridges, tunnels, dams, bulkheads, large diameter pipes used in water and gas transmission lines. In order to investigate the FRP composite strengthening effect on modal parameters, RC frame model is strengthened by wrapping with FRP composite material. The modal parameters are extracted before and after strengthening to compare the results and emerge the efficiency of FRP composite material. In the strengthening, Mbrace Fiber CF 230/4900 type carbon fiber reinforced polymer produced by BASF [36] is used. Some technical properties are given in Table 6. Epoxy consisted of two components, namely, epoxy resin and epoxy hardener primer (BASFMBrace Primer) is applied to the element surfaces as a first step of strengthening application. Before proceeding to the next step, the lining material is waited three days to complete the curing, and then the carbon fiber reinforcement polymer fabric is wrapped and the structural elements are strengthened. Wrapping is carried out in such a way that the beam-column joints where the damages are available intensively, the column and beam sections without squeezing of the stirrup reinforcements, and the zones where the columns are combined with foundation. FRP composite material is wrapped in the fabric form, length of 50cm and 3 layers on the specified element surfaces. Epoxy-based special adhesive is used to ensure adherence between the FRP fabric and the concrete surface which has two components, high strength. Adhesive is spread thoroughly the primed element surfaces and the all fabric surfaces. Thus, the bonding operation is completed. Some technical properties of the Mbrace Fiber Saturant adhesive are given in Table 7. Some views from the strengthening with polymer fabric are given in Fig. 20. The detailed FRP strengthening scheme is given in Fig. 21.

Table 6 Some technical properties of carbon fiber reinforced polymer fabric Properties Modulus of elasticity (MPa) Tensile Strength (MPa) Design Cross-Section Thickness (mm) Total Fiber Weight (g/m Elongation at Break (%) Width (mm)

Mbrace Fibre CF 230/4900 200 g/m 230000 4900 0.111 210 2.10 500

Table 7 Some technical properties of Mbrace Fiber Saturant adhesive Material Structure Mbrace Fibre Saturant Component A Mbrace Fibre Saturant Component B Color Mixture Density Viscosity Compression strength (7 days) (TS EN 196) Bending Strength (7 days) (TS EN 196) Adhesive Strength (to concrete-7 days) Applicable Soil Temperature Re-coatability Duration(+20°C) Usage Time Total Cure Time

Epoxy Resin Epoxy Hardener Blue 1.02 kg/lit 1500-2500 mPa.s >60 MPa >50 MPa >3 MPa +5°C + 30°C Minimum 48 hours-Maximum 7 days 30 minutes 7 days

a) Preparation of lining material and application

b) Preparation of FRP fabric

c) Epoxy based adhesive material and removal of roughness

d) Wrapping FRP fabric to the elements and final view of the frame Fig. 20 Some views from strengthening application with FRP fabric

a) Edge axis wrapping detail on the base-column and beam-column joints

b) Central axis wrapping detail on the beam-column joints

Fig. 21 The detailed FRP strengthening scheme The ambient vibration measurement (Fig. 22) is performed after 7 days of FRP composite reinforcement application. Some measurement properties are considered with undamaged, damaged and repaired conditions. Singular values of spectral density matrices (SVSDM) and the average of auto spectral densities (AASD) of the data set obtained by EFDD method for strengthened RC frame model are given in Fig. 23. Fig. 24 shows the first three mode shapes of the strengthened RC frame.

Fig. 22 Some views from ambient vibration measurements for strengthened model

Fig. 23 SVSDM and AASD of the data set for strengthened condition

Fig. 24 The mode shapes obtained by EFDD method for strengthened condition

The modal parameters also identified using SSI method. The stabilization diagram and singular values for the first three modes are given in Fig. 25. The natural frequencies, mode shapes and damping ratios are calculated as stabile values. Fig. 26 illustrates the first three mode shapes. Modal parameters are summarized for strengthened condition in Table 8.

Fig. 25 The stabilization diagram and singular values for strengthened condition

Fig. 26 The mode shapes obtained by SSI method for strengthened condition

Table 8 Experimental natural frequencies of the strengthened RC frame Mode Number 1 2 3

EFDD Frequency (Hz) Damping Ratio (%) 13.14 1.500 43.12 1.085 113.9 0.910

Frequency (Hz) 15.53 39.65 113.7

SSI Damping Ratio (%) 51.730 0.964 0.816

4. COMPARISON OF MODAL PARAMETERS

In this paper, four different cases (undamaged, damaged, repaired and strengthened) are considered for RC frame model to show the changes of modal parameters in each cases using nondestructive experimental measurement. The obtained results are summarized and compared with each other in Tables 9 and 10 for EFDD and SSI methods, respectively. It is seen that natural frequencies decreased distinctly with damages. The maximum difference is calculated as 48%. After repairing procedure, the natural frequencies increased 36% for first mode, 30% for second mode and 67% for third mode. It is thought that this is a sign of repairing success. Also, the minimum and maximum differences between the natural frequencies of repaired and strengthened conditions are 2% and 43%, respectively. As a result of FRP composite strengthening, the modal parameters revert almost initial (undamaged) condition

Table 9 Comparison of EFDD results for each case EFDD Frequency (Hz)

Mode Number

Undamaged

1 2 3

13.898 39.907 123.84

Diff. (%) -47.70 -41.71 -44.04

Damaged 7.269 23.263 69.293

Diff. (%) 36.13 30.12 66.83

Repaired 9.895 30.27 115.6

Diff. (%) 32.79 42.45 1.47

Strengthened 13.14 43.12 113.9

Table 10 Comparison of SSI results for each case Mode Number

Undamaged

1 2 3

13.69 39.93 124.7

Diff. (%) -65.56 -40.89 -49.76

SSI Frequency (Hz) Diff. Damaged Repaired (%) 4.441 115.56 9.573 23.6 27.50 30.09 62.65 83.24 114.8

Diff. (%) 62.23 31.77 0.96

Strengthened 15.53 39.65 113.7

5. CONCLUSIONS

In this study, it is aimed to investigate the changes of modal parameters under undamaged, damaged, repaired and strengthened conditions for RC frame model using ambient vibration tests and show the FRP composite strengthening effect in returning success of modal parameters. At the end of the study following conclusions can be drawn. The dynamic characteristics obtained as a result of the ambient vibration measurements applied to the undamaged state of the reinforced concrete frame model according to the EFDD and SSI methods are very close to each other. This shows that the results obtained for both methods are in harmony. The mode shapes obtained from the experimental measurements (EFDD and SSI methods) are in harmony with each other. However there is no correlation between the damping ratios. Differences between the natural frequencies obtained from undamaged and damaged conditions are 41-48% for EFDD and 40-50% for SSI methods. The natural frequencies obtained from the ambient vibration measurements applied to the repaired state of the RC frame are 9.895Hz, 30.27Hz and 115.6Hz respectively for EFDD, 9.573Hz, 30.09Hz and 114.8Hz respectively for SSI. There is clear agreement between EFDD and SSI results for repaired situation. Differences between natural frequencies obtained from damaged and repaired conditions are 36-67% for EFDD and 27-116% for SSI methods. The natural frequencies obtained from the ambient vibration tests applied to the strengthening state of the RC frame are 13.14Hz, 43.12Hz and 113.9Hz respectively for EFDD, 15.53Hz, 39.65Hz and 113.7Hz respectively for SSI. The frequency values are obtained closely for EFDD and SSI method.

Differences between natural frequencies obtained from repaired and strengthened conditions are 1-43% for EFDD and 1-63% for SSI methods. After the CFRP strengthening of the RC frame, differences between natural frequencies obtained from undamaged and strengthened situations of the RC frame are 5-8% for EFDD and 1-13% for SSI. It is seen from the results that the structure had caught the pre-damage state. Finally it can be seen from the study that the repairing and strengthening applications are very effective tools and reverted to modal parameters almost initial (undamaged) condition.

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