Free vibration analysis of sandwich beams with carbon nanotube reinforced face sheets based on extended high-order sandwich panel theory

Free vibration analysis of a sandwich beam with soft core and carbon nanotube reinforced composite face sheets, hitherto not reported in the literature, based on extended high-order sandwich panel theory is presented. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded. In this theory, the face sheets follow the first-order shear deformation theory. Besides, the two-dimensional elasticity is used for the core. The field equations are derived via the Ritz-based solution which is suitable for any essential boundary conditions. Chebyshev polynomials multiplying boundary R-functions are used as admissible functions and evidence of their good performance is given. A detailed parametric study is conducted to study the effects of nanotube volume fraction and their distribution pattern, core-to-face sheet thickness ratio, and boundary conditions on the natural frequencies and mode shapes of sandwich beams with functionally graded carbon nanotube reinforced composite face sheets and soft cores. Since the extended high-order sandwich panel theory can be used with any combinations of core and face sheets and not only the soft cores that the other theories demand, the results for the same beam with functionally graded carbon nanotube reinforced composite face sheets and stiff core are also provided for comparison. It is concluded that the sandwich beam with X and V distribution figures of face sheets, no matter what the boundary conditions, has higher vibration performance than the beam with UD-CNTRC face sheets.