The response characteristics of beams and flat rectangular panels excited by specific acoustic fields are analyzed mathematically. Acoustic-structural coupling-coefficient (joint acceptance squared) frequency spectra indicate a marked sensitivity to changes in the spatial-correlation distribution. Panel mode shapes progressively lose their wavelength selectivity as spatial correlation decreases.
The response characteristics of beams and flat rectangular panels excited by specific acoustic fields were analyzed mathematically. The acoustic-structural coupling coefficients developed by A. Powell and others for general systems were modified and extended to beams and flat rectangular panels with free, simply supported, and clamped boundary conditions. A variable, exponentially decaying spatial-correlation distribution, which allows an analytical approximation of expected near-field characteristics, is an added feature. Numerical results of the acoustic-structural coupling-coefficient frequency spectrum indicate a marked sensitivity to changes in the spatial correlation, a measure of the force-distribution coherence over the structural area. The panel mode shapes progressively lose their wavelength selectivity as the spatial correlation decreases and, hence, respond at all frequencies. An IBM 7090 FORTRAN computer program was written to perform the numerical calculations for single beams and panels with specified boundary conditions and particular plane-wave acoustic fields. An analytical method extending the analysis to an array of beams and/or panels is developed. An approximation for irregular wavefronts is also treated along with the problem of a plane wave traveling at an angle θ with respect to a panel edge and angle φ with respect to the panel plane.
The primary state-of-the-art laboratory method for the evaluation of the response and fatigue characteristics of skin panels exposed to intense noise is the progressive-wave or parallel incidence test facility. This method obtains the highest sound-pressure levels per unit input power by minimizing the cross-sectional area of the duct and also maintains a relatively flat frequency response. However, many of the current configurations provide excessive radiation damping to the panel in its lower modes. This paper summarizes analytical and experimental investigations of the radiation damping of panels mounted in progressive-wave test sections. The results are presented in generalized form, which give the dependency of the radiation damping on the ratio of the panel area to test duct cross-sectional area and pertinent panel parameters. In addition, the paper reviews an analytical study of the response of panels to variable incidence progressive waves and to a reverberant field. These results demonstrate the possible future importance of reverberant fields as a replacement for progressive-wave tests.
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