Radiation of sound into a cylindrical enclosure from a point-driven end plate with general boundary conditions

Abstract

The radiation of sound from a point-driven circular plate into a hard-walled cylindrical enclosure is investigated. Emphasis is given on studying the effects of the boundary conditions of the plate, which are modeled as a continuous distribution of edge springs acting against both the deflection and the rotation of the contour of the plate. With this model, both classical and intermediate boundary cases can be simulated by adjusting the elastic stiffness of the springs. A coupled acoustoelastic formulation is developed following a variational approach, with the use of hard-walled cavity modes. In the analysis, the full interaction between the structure vibration and the internal cavity sound pressure is considered. Numerical results indicate that a significant reduction in noise inside the cavity can be obtained for a relatively wide frequency range by completely relaxing the translational support (zero deflection stiffness) of the plate. This is mainly due to a weakening of the modal radiation efficiency of the flexural modes of the plate. With an increase of the deflection stiffness on the contour of the plate, this beneficial frequency range is shifted to higher frequencies. It is hoped that the findings of the present work will be useful for practical predictions of airplane cabin noise emitted by the rear pressure bulkhead, as well as for noise control in some aerospace structures and mechanical systems involving cylindrical-shaped cavities.

Acoustic characteristics of a sound field inside a cylindrical structure with excited end plates: Influence of excitation position on vibro-acoustic coupling

“…(2) for the plate mode shape into Eqs. (1), and are expanded over two sets of suitable trial functions [3,4]: An acoustic mode shape, which is represented by indexes p and q for the radial and longitudinal orders, is defined as…”

“…p is the structural damping factor of the plate, and F ns is a coefficient that is determined by the indexes n and s [3]. On the right-hand sides of the equations, the first and second terms express the point forces and coupling between each plate vibration and the sound field, respectively.…”

“…In the present study, the stiffnesses, which are set to be slightly higher for translational support than for sliding support (for instance, K b1 ¼ 0 and C b1 ¼ 10 8 ) for plate 1, and slightly higher for rotational support than for simple support (for instance, K b2 ¼ 10 8 and C b2 ¼ 0) for plate 2, are K b1 ¼ 10 2 , C b1 ¼ 10 8 and K b2 ¼ 10 8 , C b2 ¼ 10, respectively. When the excitation positions r 1 =a and r 2 =a are varied, the respective flexural displacements w 1 and w 2 at each point on the plates are evaluated based on average quadratic velocities V 1 and V 2 , which are calculated by integrating the displacement along the entire surface of each plate and are presented in dB referenced to 2:5 Â 10 À15 m 2 /s 2 ; this makes these parameters the products of complementary elements [3].…”

“…Although V 1 increases with r 1 =a, V 2 for r 2 =a ¼ 0:6 is as large as that for r 2 =a ¼ 0:8 and has a frequency range exceeding that for r 2 =a ¼ 0:8. In such an analytical model, the relationship between the circumferential orders of the plate vibration and the sound field has been reported to influence the coupling behavior [3]. Therefore, excitation frequencies of f ¼ 650 Hz and 1,090 Hz, which induce the (2; 0) and (1; 1) modes on plate 1, are discussed herein.…”

“…They concluded that the modal decay times of the system are related to the coupling coefficients, distribution of resonance frequencies, panel modal density, panel damping and panel radiation loss to the external space. Cheng and Nicolas investigated coupling between the vibration of the rear pressure bulkhead and the sound field of an airplane cabin in an attempt to control the noise inside the airplane [3,4]. They adopted a cylindrical structure, in which the rear pressure bulkhead at one end was assumed to be a circular plate, as an analytical model.…”