Nonlinear vibration analysis of actively loaded sandwich piezoelectric beams with geometric imperfections

Modal analysis is developed for linear and nonlinear vibrations of deformed sandwich piezoelectric beams with initial imperfections. The beam is subjected to axial displacement and active voltage generated by the top and the bottom piezoelectric layers. The mathematical formulation is developed for the multimodal analysis. Using, the one-mode assumption, simplified relationships accounting for the active voltage, the imposed axial displacement and the amplitudes of imperfections are presented for the load–amplitude, the load–frequency and the nonlinear frequency–amplitude. The stability control of deformed beams is analyzed for various load and voltage levels. For statically deformed beams, a nonlinear frequency–amplitude relationship is presented with respect to positive and negative amplitudes. This formulation accounts for the piezoelectric, the imperfection and the load effects. Numerical tests are investigated for various voltage, load and amplitude levels. The under critical frequency behaviours related to deformed beams, showing the transition from softening to hardening effects, are presented for various levels of active voltage, static response and imperfection amplitudes of simply-supported sandwich piezoelectric beams.