Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory

This article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets.