Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Abstract

A theoretical framework is presented for analyzing the coupled nonlinear dynamic behavior of laminated piezoelectric composite plates subject to high thermoelectromechanical loadings. It incorporates coupling between mechanical, electric, and thermal governing equations and encompass geometric nonlinearity effects due to large displacements and rotations. The mixed-field shear-layerwise plate laminate theory formulation is considered, thus degenerating the 3D electromechanical field to 2D nodal variables, and an eight-node coupled nonlinear plate element is developed. The discrete coupled nonlinear dynamic equations of motion are formulated, linearized, and numerically solved at each time step using the implicit Newmark scheme with a Newton-Raphson technique. Validation and evaluation cases on active laminated beams demonstrate the accuracy of the method and its robust capability to effectively predict the nonlinear dynamic response under time-dependent combined mechanical, thermal, and piezoelectric actuator loads. The results illustrate the capability of the method to simulate large amplitude vibrations and dynamic buckling phenomena in active piezocomposite plates. The influence of loading rates on the nonlinear dynamic structural response is also quantified. Additional numerical cases demonstrate the complex dynamic interactions between electrical, mechanical, and thermal buckling loads.

Numerical and experimental investigation of the energy harvesting performance of electromechanically coupled piezoelectric prestressed beams subjected to nonlinear vibrations

“…The equations of motion of the piezoelectric laminate plate mandate that the work imbalance between internal and external forces Ψ u and internal and external electric charges Ψ e , during an arbitrary variation of displacements δu and electric potential δφ, should vanish at equilibrium, at any time t over the volume V of the laminated piezoelectric plate [29],…”

“…The coupled equations of motion are finally linearized and solved at each time step using the Newmark implicit time integration method in combination with the Newton-Raphson iterative technique. A previous developed numerical tool which formed the basis for the current model has been thoroughly described in previous works [28,29]. However, it does not include passive external electric circuits and only considers for open or closed-circuit conditions.…”

Time domain spectral finite element methods for the simulation of wave propagation in composite layered structures with active piezoelectric sensors

“…In 2009 a work by Varelis and Saravanos (2009) built a theoretical layerwise framework for analyzing the coupled nonlinear dynamic behavior of laminated piezoelectric composite plates subject to high thermo-electromechanical loadings. The discrete coupled nonlinear dynamic equations of motion are formulated, linearized and numerically solved at each time step using the implicit Newmark scheme with Newton-Raphson technique.…”