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A Note on a Nonlinear Model of a Piezoelectric Rod
Author(s) -
Gausmann R.,
Seemann W.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310018
Subject(s) - nonlinear system , ansatz , harmonic balance , hamilton's principle , eigenfunction , ordinary differential equation , physics , mathematical analysis , duffing equation , resonance (particle physics) , ritz method , vibration , classical mechanics , nonlinear oscillations , nonlinear resonance , amplitude , differential equation , mathematics , boundary value problem , equations of motion , mathematical physics , eigenvalues and eigenvectors , quantum mechanics
If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model.