“…Various numerical models have been established to acquire the coupling characteristics, amplitude-frequency characteristics, and structural properties of energy harvesters with different structures; develop calibration criteria and methods; and predict and characterize experimental results. 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.…”