On sound transmission into a heavily-damped cylinder

Journal of Sound and Y&&on (1978) 57( 1) 155-l 56

LETTER ON SOUND

TRANSMISSION

TO THE EDITOR INTO A HEAVILY-DAMPED

CYLINDER

1. INTRODUCTION III the context of the transmission of airborne noise into an aircraft fuselage, the author recently presented [l] a mathematical model for sound transmission into a thin monococque cylindrical shell. The specific problem studied was that of an oblique plane wave incident upon a flexible thin cylindrical shell (see Figure 1). The solution obtained was used to study sound transmission under “flight conditions”, i.e., under conditions of external air flow past the cylinder at flight altitude.

Figure 1. Geometry of the problem studied.

The adding of damping materials to the fuselage to aid in controlling vibration has long been common. Interest in the use of damping to control sound transmission has been receiving growing interest as both the noise environments and the desire to control internal cabin noise have increased. In view of these trends, the author used the above model to generate curves of cylinder transmission loss (TL) for heavily-damped cylinders. This was accomplished by varying the parameter, 9, the loss factor of the shell material. 2. DISCUSSION OF RESULTS Numerical results were generated for various plane-wave incidence angles for a typical narrow-bodied jet fuselage made from aluminum, with radius a = 1.83 m (6 ft), and wall thickness h = 0.159 cm (l/16 inch). The values of q used were q = 0.01, 0.10, 0.50, 0.75 and l-00. Figures 2(a)-(e) show the effect of damping for incidence angles of 30”, 45”, 60”, 75” and 90”. Inspection of Figures 2(a)-(e) for q = 0.01 shows that the cylinder transmission loss has dips at fR(cylinder ring frequency) and fc (critical frequency). Below fR,the TL tends to be stiffness-governed, except where cylinder resonances are present. The cylinder resonances occur when the trace wavelength and frequency match with a model having the appropriate number of waves around the circumference. Between& andf,, the transmission loss follows a mass law which is of the order of 5-6 dB/octave, depending on where the slope is measured. In Figures 2(a)-(e), the frequency has been non-dimensionalized by division by the critical frequency. The figures show that as the damping (i.e., loss factor) is increased, dips due to cylinder resonances are reduced and eventually disappear when q becomes large enough. High values of q also appear to reduce the size of the dip at the ring frequency and at coincidence. It is also 155 0022-460)3/78/0308-0155

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0 1978 Academic Press Inc. (London) Limited

156

LETTER TO THE EDITOR

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Figure 2. Transmission loss of heavily-damped cylinder. (a) 13= 30”; (b) 0 = 45”; (c) 0 = 60”; (d) 0 = 75”; (e) 0 = 90”. q = loss factor of structural material; FR = cylinder ring frequency.

interesting to observe that increased damping also provides a modest increase in TL in the mass-law region, ranging from 5 dB (0 = 30”) to 7 dB (0 = 75”) as q is increased lOO-fold from ?#I= 0.01 to q = 1.00. ACKNOWLEDGMENT

The work reported here was supported by NASA Langley Research Center under NASA Grant NSG-1050. L. R. KOVAL Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A. (Received 26 October 1977) REFERENCE 1. L. R. KOVAL 1976 Journal of Sound and Vibration 48,26527.5.

cylindrical

shell under “flight conditions”.

On sound transmission

into a thin