A study on the use of perturbation technique for analyzing the nonlinear forced response of piezoelectric microcantilevers

In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is consideredaccording to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbation approach, themultiple scales method is directly applied to the partial differential equation of motion. In the indirect approach, the multiple scales perturbation technique is applied to the discretized equation of motion. It is shown that, if the equation of motion isdiscretized using one non-uniform microbeam mode shape as a comparison function, then the results of indirect perturbation approach will be identical to those of thedirect perturbation approach. Moreover, it is observed that discretization using oneuniform microbeam mode shape as a comparison function results in a different output. The concept of non-uniform microbeam mode shape is the linear mode shape of the microbeam by considering the geometric and inertia effects of the piezoelectric layer.

کلیدواژه ها:

Direct perturbation ، Indirect perturbation ، Microcantilever ، Nonlinear vibration ، Shortening effect ، Piezoelectric