Vibrational behavior of rotating pre-twisted functionally graded microbeams in thermal environment

The vibration characteristics of rotating pre-twisted functionally graded (FG) cantilever microbeams are studied. The governing equations are derived based on the modified strain gradient theory (MSGT) of microbeams in conjunction with the first-order shear deformation theory (FSDT) of beams. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In addition to the initial stresses due to centrifugal forces, the initial thermal stresses induced by temperature rise are considered. The Chebyshev-Ritz method is employed to derive the algebraic eigenfrequency equations of the microbeams. After showing the fast rate of convergence and accuracy of the method, the effects of angular velocity, linear and nonlinear variation of the angle of twist along the beam axis, material length scale parameters, temperature rise and material gradient index on the free vibration of pre-twisted microbeams are studied. It is shown that the increase of the free end microbeam twist angle, the nonlinear variation of the twist angle along the microbeam axis, and also the temperature rise reduces the frequencies. On the other hand, by increasing the hub radius, the angular velocity and the length scale parameters, the frequencies increase.