Parametrically driven morphing of thin piezoelectric surfaces

Summary. The possibility of exploiting the parametric resonance phenomena to perform morphing of piezoelectric surfaces is here investigated analytically and numerically. The case study consists of a PVDF beam subject to an in-plane pulsating strain applied through voltage variation. The dynamical excitation induces an out-of-plane parametric resonance of the beam which can be driven to excite desired individual modes or combination of them through nonlinear coupling. A nonlinear reduced order model for a piezoelectric thin Euler-Bernoulli beam is developed considering the multi-physics piezo-elastic coupling. The conservation of the electric charge is enforced in 3D while the equations of motion are expressed in 1D using the arclength parametrization along the beam centerline. The analytical treatment is based on the method of multiple scales and allows to obtain the region of the forcing parameters for which the parametric resonance is achieved. The analytical solutions are validated against numerical results provided by the finite element code ABAQUS through which a full 3D nonlinear model is addressed. The analytically obtained transition curves (representing the boundary between resonant and non resonant behavior in the space of forcing parameters) and the frequency response curves are compared to those obtained numerically achieving a good agreement. The voltage thresholds for which the parametric resonances are induced, and the robustness of the responses suggest that the investigated phenomenon is a promising strategy for surface dynamic morphing.