Finite element modeling of nonlinear vibration behavior of piezo-integrated structures

This paper aims at finite element modeling of nonlinear vibration behavior of piezo-integrated structures subjected to weak electric field. This nonlinear vibration behavior was observed in the form of dependence of resonance frequency on the vibration amplitude and nonlinear relationship between excitation voltage and vibration amplitude. The equations of motion for the finite element model is derived by introducing nonlinear constitutive relations of piezoceramics in Hamilton’s principle. Modal reduction is used to reduce the equations of motion. Thus obtained reduced equation of motion is solved by numerical integration. Experimental validation of the finite element model is also carried out.

► A new finite element approach to model nonlinear behavior of piezo-integrated structures.
► Constitutive relations are extended to include quadratic and cubic nonlinear terms.
► The equation of motion is derived by Hamilton’s principle.
► Solution by using the Newmark method with modified Newton–Raphson iteration.
► Validation of the finite element model with experimental results.