Thermal, electrical and mechanical buckling loads of sandwich nano beams made of FG CNTRC resting on Pasternak’s foundation based on higher order shear deformation theory

Abstract

This research deals with thermo electro mechanical buckling analysis of the sandwich nano beams with face sheets made of functionally graded carbon nano tubes reinforcement composite (FG CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher order shear deformation beam theories (HSDBT). The sandwich nano beam with FG CNTRC face sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non classical nano beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.