Thermopiezoelastic nonlinear dynamics of active piezolaminated plates

Abstract

Nonlinear dynamics of active piezolaminated plates are investigated considering snap-through thermopiezoelastic behaviors. For highly deformed structures with small strain, the incremental total Lagrangian formulation is presented based on Hamilton's variational principles. A multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap-through phenomena, the implicit Newmark-beta scheme with the Newton-Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. To validate the new finite element formulation and code, dynamic analyses of nonlinear elastic plates are compared with published data, resulting in good agreements and better solutions. The bifurcate buckling and sling-shot buckling of the symmetric and eccentric structural models are first investigated and the characteristics of piezoelectric active responses are studied to find snap-through piezoelectric potentials and the load-path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap-through phenomena with several attractors are proved using the nonlinear time responses for initial conditions and damping loss factors. Present results show that the snap-through phenomena should be investigated with respect to nonlinear dynamics for shape control of piezolaminated buckled plates by using piezoelectric materials.

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