Parametric resonances of nonlinear piezoelectric beams exploiting in-plane actuation

A nonlinear Euler–Bernoulli model of slender piezoelectric beams is employed to investigate parametric resonance motions driven by a pulsating voltage with DC component. The beam based on 3D electric charge conservation and 1D reduction the momentum balance laws assuming as space coordinate arclength along base line coordinate. constitutive relationships for material are specialized according ansatz transverse unshearability. piezoelastic problem parametrically excited directly attacked method multiple scales up fifth order overcoming modal projection drawbacks severe restrictions oscillation amplitude range. transition curves, separating regions stable unstable trivial solutions in frequency–amplitude plane, obtained various modes PVDF beam. onset resonances post-critical large motion investigated upon variations meaningful parameters such prestress amplitude. analytical outcomes compared those provided finite element code ABAQUS which yields numerical solution full problem. Moreover, frequency–response curves within computed applying pseudo-arclength algebraic equation. lowest few reveal new aspects can be exploited applications dynamic morphing thin surfaces.