Harmonic motion simulation and resonance frequency determination for a piezoelectric strip-like actuator using high precision finite element method

The dynamic behaviour of a strip-like rectangular piezoactuator is simulated via finite element method using high order interpolation polynomials. The governing equations are considered in the frequency domain, where a harmonic solution has a much simpler form. The Laplace transform is applied in order to obtain the non-stationary solution in time domain. Gauss-Legendre-Lobatto polynomials are used as approximation and test functions. Two different boundary-value problems are analysed. In the first case it is assumed that the piezoactuator has stress-free boundaries, the electric potential has a certain value at the bottom surface of the actuator, the upper surface is ground, and the side surfaces are free of charge. The second problem has almost the same boundary conditions, except a surface load at the bottom boundary and the clamped left boundary, which means zero displacements. The system of linear equations includes the coefficients for displacement and potential functions at finite element nodes. The vector of unknowns is composed of the values of electric potentials and of bottom surface normal and tangential stresses at the nodal points according to the boundary conditions. The model developed is compared with the COMSOL Multiphysics model. A comparison of displacements, stresses, electric potential and electric displacements has been performed. The corresponding plots and tables demonstrating the maximum and minimum values of wave-fields are provided. The dependence of the actuator behaviour on various boundary conditions and harmonic oscillation frequency has been analysed. The resonance frequencies of the actuator have been calculated, and the corresponding eigenmodes have been studied.