Refined Zigzag Theory for Nonlinear Dynamic Response of an Axially Moving Sandwich Nano beam Embedded on Visco-Pasternak Medium Using MCST

Abstract

This paper develops the Refined Zigzag Theory (RZT) for nonlinear dynamic response of an axially moving functionally graded (FG) Nano beam integrated with two magnetostrictive face layers based on the modified couple stress theory (MCST). The Sandwich Nano beam (SNB) subjected to a temperature difference and both axial and transverse mechanical loads. The material properties of FG core layer depend on the environment temperature and are assumed to vary in thickness direction. The SNB is surrounded by elastic medium, which is simulated by visco- Pasternak model. The von-Karman nonlinear strain-displacement relationships are employed to consider the effect of geometric nonlinearities. In order to obtain governing motion equations and boundary conditions the energy method as well as Hamilton’s principle is applied. The differential quadrature method (DQM) is used for space domain and the Newmark-β method is taken into account for time domain response of the axially moving SNB. The detailed parametric study is conducted to investigate the effects of surrounding elastic medium, material length scale parameter, magnetostrictive layers, temperature difference, environment temperature, velocity of the SNB, axial and transverse mechanical loads and volume fraction exponent on the dynamic response of the SNB. Results indicate that the maximum deflection of the system can be controlled by employing negative values of velocity feedback gain values. In addition, the