Nonlinear vibration analysis of embedded smart composite micro-tubes based on modified couple stress theory

In this paper nonlinear vibration analysis of an embedded smart composite micro-tube is studied base on modified couple stress theory and Timoshenko beam (TB) model. The surrounded elastic medium is simulated as Pasternak foundation. The composite matrix which is made of polyvinylidene (PVDF) is reinforced by double-walled boron nitride nanotubes (DWBNNTs). Using von Karman geometric nonlinearity, Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the nonlinear higher order governing equations are derived. The differential quadrature method (DQM) is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency of micro-tube. The effects of Pasternak shear modulus, temperature change, small scale parameter, aspect ratio and volume percent of DWBNNTs are also studied in detail.

Keywords:

Nonlinear vibration , Couple stress theory , Pasternak foundation , Smart materials