Energy-conserving Modal Synthesis scheme for Vibrations of Thin Plates in Strongly Nonlinear RegimeReport as inadecuate




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1 ENSTA ParisTech UME - Unité de Mécanique 2 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles 3 University of Edinburg Edinburg

Abstract : Large-amplitude geometric nonlinear vibrations of plates are considered. The von Kármán equations are used as model for both unknowns : transverse displacement and Airy stress function. The key feature is the use of a modal approach for time-integrating the system with a very large number of degrees-of-freedom. The targeted application is the strongly nonlinear vibration of thin plates characterized by a turbulent state with a cascade of energy from the injection to the dissipative scale, involving a huge dimension of the phase space. More specifically, we are interested in the sound synthesis of cymbals and gong-like instruments, that show this wave turbulence regime when strongly beaten with a vigorous strike. A special emphasis is put on the derivation of an ad-hoc, conservative method. Thanks to symmetry properties of the nonlinear coupling coefficients, an energy-conserving scheme especially designed for the modal equations of the von Kármán perfect and imperfect plates is derived, for arbitrary boundary conditions.





Author: Cyril Touzé - M Ducceschi -

Source: https://hal.archives-ouvertes.fr/



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