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

Thomas Hélie (1, 2) , Béatrice Laroche (3)

1 STMS - Sciences et Technologies de la Musique et du Son
2 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
3 INRA - Institut National de la Recherche Agronomique

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.

Mots clés: sound and vibration; partial differential equation; nonlinear systems; Volterra series; Convergence Analysis

Domaines: Systèmes Solubles et Intégrables [nlin.SI]; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Vibrations [physics.class-ph]

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⟩