Post-buckling and vibration of post-buckled rotating pre-twisted FG microbeams in thermal environment

Abstract

In this paper, comprehensive studies on the size-dependent thermal post-buckling and coupled bi-directional transverse-longitudinal free vibration behavior of post-buckled rotating pre-twisted functionally graded (FG) microbeams in thermal environment are presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction with mid-plane symmetric distribution, i.e., symmetric functionally graded (S-FG). At first, the discretized nonlinear post-buckling governing equations are derived based on the modified strain gradient theory (MSGT) in conjunction with the first-order shear deformation theory (FSDT) of beams under the von Kármán geometric nonlinearity assumptions using Hamilton's principle and Chebyshev-Ritz method. The resulting nonlinear equations under different boundary conditions are solved iteratively by employing Newton-Raphson's method. Then, using the same theories and solution procedure, the free vibration equations around the post-buckled configuration are derived and solved. After validating the approach, the effects of angular velocity, twist angle, length scale parameters, thickness-to-length ratio, hub radius, material gradient index and boundary conditions on the post-buckling equilibrium path and linear free vibration behavior of rotating pre-twisted S-FG microbeams are investigated. The results are prepared for both linear and nonlinear variations of the twist angle along the microbeam axis.