Nonlinear vibration analysis of pre-twisted functionally graded microbeams in thermal environment

The large amplitude free vibration behavior of pre-twisted functionally graded (FG) microbeams in thermal environment is investigated based on the modified strain gradient theory (MSGT) in conjunction with the first-order shear deformation theory (FSDT). The geometrical nonlinearity effects are taken into account in the sense of von Kármán nonlinear kinematic assumptions. The Chebyshev-Ritz method combined with harmonic balance method is employed to derive the nonlinear algebraic eigenfrequency equations of the microbeams subjected to different boundary conditions. The material properties are assumed to be temperature-dependent and graded in the thickness direction. After numerically demonstrating the fast rate of convergence and accuracy of the method, the effects of different geometrical and material parameters on the nonlinear free vibration behavior of pre-twisted FG microbeams are investigated. It is found that the effect of twist angle on the hardening or softening of the microbeams depend on the boundary conditions, and the largest and smallest values of nonlinear to linear frequency ratios belong to simply supported and fully clamped microbeams, respectively.