An alternate numerical treatment for the nonlinear PDE models of piezoelectric laminates


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When piezoelectric laminates undergo large deformations exhibiting a non-linear behavior, and the axial vibrations are not neglected, linear models of piezoelectric laminates fail to represent and predict the governing dynamics. These large displacements are pronounced in certain applications such as energy harvesting.In this paper, first, a consistent variational approach is used by considering nonlinear elasticity theory to derive equations of motion for a three-layer piezoelectric laminate. The interactions of layers are modeled by the Rao-Nakra sandwich beam theory. The resulting infinite dimensional equations of motion form into an unbounded bilinear control system with nonlinear boundary conditions. The corresponding state-space formulation is shown to be well-posed in the energy space. With a particular choice of nonlinear feedback controllers, based on the nonlinearity of the model, the system dynamics can be stabilized to the equilibrium. Stabilization results are presented through the filtered semi-discrete Finite Difference approximations and these results are compared to the linear case.


Acoustics, Dynamics, and Controls | Applied Mathematics | Applied Mechanics | Control Theory | Dynamics and Dynamical Systems | Engineering Science and Materials | Non-linear Dynamics | Partial Differential Equations

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