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.
Harmonic shells: a practical nonlinear sound model for near-rigid thin shells
We propose a procedural method for synthesizing realistic sounds due to nonlinear thin-shell vibrations. We use linear modal analysis to generate a small-deformation displacement basis, then couple the modes together using nonlinear thin-shell forces. To enable audio-rate time-stepping of mode amplitudes with mesh-independent cost, we propose a reduced-order dynamics model based on a thin-shell cubature scheme. Limitations such as mode locking and pitch glide are addressed. To support fast evaluation of mid-frequency mode-based sound radiation for detailed meshes, we propose far-field acoustic transfer maps (FFAT maps) which can be precomputed using state-of-the-art fast Helmholtz multipole methods. Familiar examples are presented including rumbling trash cans and plastic bottles, crashing cymbals, and noisy sheet metal objects, each with increased richness over linear modal sound models.
Random Vibrations of a Nonlinear Elastic Beam
The theory of the Markoff process and the associated Fokker Planck equation is used to investigate the large vibrations of a hinged, axially restrained, elastic beam driven by white noise. An expression for the joint probability‐density function of the first N modal amplitudes is obtained and used to derive an approximate expression for the mean‐squared displacement. Numerical integration of the exact expression for the mean‐squared displacement indicates a reduction of this quantity as compared in the linear theory. Calculations also show a range of applicability of the derived approximate expression. Furthermore. computations show that the first node still gives a good estimate of the mean‐squared displacement but the coupling effects of the nodes are so strong, for sufficiently large deflections. that the effect of the higher modes must be taken into account when computing the mean‐squared value of the first mode.