Nonlinear model of the longitudinal oscillations of a piezoelectric rod

Rainer Gausmann; Sven Koenig; Wolfgang Seemann

doi:10.1117/12.475215

10 July 2002 Nonlinear model of the longitudinal oscillations of a piezoelectric rod

Rainer Gausmann, Sven Koenig, Wolfgang Seemann

Proceedings Volume 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control; (2002) https://doi.org/10.1117/12.475215
Event: SPIE's 9th Annual International Symposium on Smart Structures and Materials, 2002, San Diego, California, United States

Abstract

Piezoelectric actuators usually are analyzed using finite element programs. These programs are often restricted to linear constitutive equations. Furthermore, the coupling with electrical element types is very problematical. Experiments showed, that even at weak electric fields the piezoceramics show nonlinear behavior, if the structure is excited near a resonance frequency. In many applications actuators are excited in resonance, for instance in ultrasonic motors and therefore these nonlinearities are important in practice. In this paper a nonlinear model for piezoelectric materials is presented. Nonlinear constitutive equations are derived from Hamiltons principle to calculate the longitudinal oscillations of a piezoceramic slender rod. The oscillations are excited by a harmonic electric potential at the electrodes of the rod, which is polarized in longitudinal direction. The resulting nonlinear partial differential equation is approximated using a Rayleigh Ritz ansatz. This leads to a set of ordinary nonlinear differential equations. In the present analysis, the displacement-functions used for the approximation are the eigenfunctions of the linearized system. The resulting nonlinear differential equation is solved by the harmonic balance method. This leads to a set of equations, that can be solved numerically to calculate the amplitude of the oscillations. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model. In future investigations the focus will be on the identification of the parameters of the nonlinear model.

Citation Download Citation

Rainer Gausmann, Sven Koenig, and Wolfgang Seemann "Nonlinear model of the longitudinal oscillations of a piezoelectric rod", Proc. SPIE 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, (10 July 2002); https://doi.org/10.1117/12.475215

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KEYWORDS

Dielectrics

Actuators

Differential equations

Ceramics

Ordinary differential equations

Ultrasonics

Electrical elements

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