Size-dependent nonlinear dynamics of a non-uniform piezoelectric microbeam based on the strain gradient theory

Document Type: Research Paper


1 No. 3, golestan Street elahie Avenue, golha Street

2 Urmia university of technology



The nonlinear dynamics of an electrostatically actuated non-uniform microbeam equipped with a damping film and a piezoelectric layer is studied. The nonlinear behaviour of the system is modelled using von Karman geometrical strain terms. The strain gradient theory was utilized and the Hamilton principle was applied to obtain equations of motion and boundary conditions. Then the equations were reduced by the Galerkin method and they are solved by multiple scale methods. The size-dependent responses for primary, super-harmonic and sub-harmonic resonance were studied. The influences of beam width, thickness, and distance between electrodes on resonant frequency response along with nonlinearity of system were examined. The results showed that the static behavior and compulsory vibration of microbeams were strongly dependent on size. Also, The results demonstrated that along with the reducing effect of size, the hardness of the microbeam increases, which implies that if the thickness of the beam is smaller, then it results in the "hardening" of the system.