ICASE COUPLING BETWEEN PLATE VIBRATION AND ACOUSTIC RADIATION
A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far-field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far-field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance. 1Research was supported by NASA Langley Research Center under NAS1-19317. 2Research was supported by the National Aeronautics and Space Administration under NASA Contract Nos. NASl-18605 and NASl-19480 while the third author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 236810001.
A re-examination of the non-linear interaction between an acoustic fluid and a flat plate undergoing harmonic excitation
In a recent study Nayfeh and Kelly [1] employed a direct renormalization procedure to evaluate the structural and acoustic response resulting from resonant harmonic excitation of a flat plate. Such a problem had been solved earlier by a method that employs two co-ordinate strainings. The present investigation begins by showing that the finite amplitude acoustic waves are described by the same relations in the cases of resonant and non-resonant excitation. An explicit criterion for the location of a shock is obtained, and it is proven that shocks form along a series of straight lines. A quantitative example depicts various spatial and temporal responses; some of these responses have not been evaluated previously. The distortion effects are explained in terms of self-refraction phenomena, and the results of the dual renormalization method employed earlier are shown to be incorrect in the vicinity of the shock. †
Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates
Approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.