“…Such models include the high-precision lumped parameter model, 26 finite element method multimode analytical model, 27 unimode cantilever enclosed frequency-varying functional model, 8 disorderly loosely-coupled resonator model, 28 nonlinear model based on Hamilton’s principle 29 and its electromechanical coupling dynamic model, 30 and shearing piezoelectric cantilever electromechanical coupling model. 31 In particular, for nonlinear processes in which different geometric features, material constructions, and damping are considered, the strain gradient theory, 32 Timoshenko model, 33,34 and Hamiltonian principle 35,36 are effective in analyzing free vibration, bending, and electric potential effects, 37,38 thermal effects, 39 humidity, 40 and multiphysics loads 41 on sandwich transducers. Further, under varying geometric features, 42 material composition, 43 and additional damping, 44 studies on the nonlinear motion processes have demonstrated the effectiveness of this method.…”