Analytical Models for the Structural-Acoustic Response of Elastic Barriers Subject to Acoustic Forcing

Abstract

<p>Analytical models are developed for the structural-acoustic response of flexible panels to obliquely incident, planar harmonic acoustic waves. These models provide a detailed understanding of the complex effects of structural discontinuities on the reflection and transmission from both isolated and periodically connected panels bounded by two fluid half-spaces. This investigation demonstrates that boundaries and spatial discontinuities redirect part of the structural energy into reverberant structural waves having flexural wavenumbers different from the oblique wave forcing, creating deviations from specular reflection. The dominant mechanisms that characterize the acoustic scattering from the vibrating panels depend on the Mach regime of the structure-to-fluid in vacuo wave speed ratio. Super-critical reverberant flexural waves act as surface radiators that result in pronounced radiation lobes centered at the Mach Angles with localized spreading. The scattering from baffled sub-critical panels exhibit directivities that can be predicted by distributions of acoustic edge radiators, with significant energy redistribution occurring at structural resonances. These insights are both derived from and used to refine the analytical models developed for membranes and 2D plates. </p><p>The periodically connected panels interfaced with discrete discontinuities, and modeled by various boundary conditions, are analyzed with the method of Analytical Numerical Matching (ANM). The method is advanced to more efficiently model the influence of the structural discontinues and it is demonstrated that it improves the numerical accuracy and convergence rate of the structural-acoustic response. The ANM approach includes a novel way to handle difficulties associated with coincidence frequencies. The periodic configuration exhibits acoustic cut-off and a finite set of radiation angles dependent on structural and fluid properties.</p><p>In the pursuit of models suitable for broadband energy intensity based methods, radiation models for the baffled finite panels are developed by approximate means. The dominant effects of the fluid loading are characterized and introduced as modifications to the in vacuo flexural wavenumber of the structures. Simple, closed-form, far-field acoustic intensity directivity patterns and the corresponding power spectrums are analytically expressed for high frequencies. These approximate models are compared to the periodic configuration, and exhibit considerable agreement for limited fluid loadings and boundary conditions that eliminate structural coupling across bays. The approximate sub-critical models are refined using insight from the radiation mechanisms to improve the agreement to the periodic panels.</p><p>An exact benchmark solution for the structural-acoustic response of the acoustically driven baffled finite structure over a full range of parameters is developed and interpreted utilizing a new approach which is largely analytical. This hybrid modal-analytical solution is developed for homogeneous Dirichlet boundary conditions, and then generalized to arbitrary impedance conditions by isolating the influence of the boundaries. In addition to their availability for quantitative use, the benchmark solution offers a high degree of physical insight, and is used for verification and refinement of the approximate high frequency methods developed. Remarkable agreement between the approximate high frequency models and the benchmark solutions is demonstrated for both light and heavy fluid loading cases.</p>