Free, periodic, large amplitude vibrations of small-scale piezoelectric beams by a modified couple stress theory

Abstract

With the goal of studying the evolution of their natural frequencies with the vibration amplitude, free, periodic vibrations of small-scale beams in piezoelectric materials are investigated. A modified couple stress theory is applied, in order to take the smallscale effects into consideration. The partial differential governing equations are transformed to ordinary differential equations by Bubnov-Galerkin's method. The latter equations are solved by the method of Multiple Scales. The results of this perturbation method are compared with solutions computed using a numerical method for boundary value problems, known as shooting method. The small-scale effects on the non-linear natural frequencies of piezoelectric beams are discussed.