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SIMULATION OF A DAMPED NONLINEAR BEAM BASED ON MODAL DECOMPOSITION AND VOLTERRA SERIES

Abstract : This paper addresses the model order reduction and the simulation of a damped nonlinear pinned beam excited by a distributed force. The model is based on : (H1) the assumption of Euler-Bernoulli kinematics (any cross-section before deformation remains straight after deformation); (H2) Von Kar-man's assumptions which couples the axial and the bending movements, introducing a nonlinearity in the model; (H3) some viscous and structural damping phenomena. The problem is first described and its linearized version is analyzed. This is used to build a reduced order model based on a standard modal decomposition. Then, the nonlinear system is examined in the framework of the regular perturbation theory. It is solved based on a Volterra series approach : the vibration is decomposed into a sum of nonlinear homogeneous contributions with respect to the excitation. The convergence of the series and the truncation error are characterized. Finally, numerical experiments are presented and discussed.
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Submitted on : Tuesday, December 10, 2019 - 9:51:07 PM
Last modification on : Tuesday, April 28, 2020 - 4:02:12 PM
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  • HAL Id : hal-02403603, version 1

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Thomas Hélie, Béatrice Laroche. SIMULATION OF A DAMPED NONLINEAR BEAM BASED ON MODAL DECOMPOSITION AND VOLTERRA SERIES. 26th International Congress on Sound and Vibration, Jul 2019, Montréal, Canada. ⟨hal-02403603⟩

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