Free Vibration Analysis of Higher-Order Shear Elasticity Nanocomposite Beams with Consideration of Nonlocal Elasticity and Poisson Effect

摘要

Free vibration analysis of orthotropic beams with local and nonlocal formulation using the high-order theory including the Poisson effect is presented in this paper. The theory takes into account the transverse shear effects introducing a new displacement shape function and a parabolic distribution of the transverse shear strains through the thickness of the beam. Hence it is unnecessary to use shear correction factors. The governing equations are derived from the principle of virtual displacements. The couplings among the axial, torsion, and bending deformations are investigated in the one-dimensional beam model. The free vibration solutions are finally presented for the nonlocal higher-order beam/column models. The influence of the various geometrical and material parameters, thickness ratio, and number of symmetric and antisymmetric layers of the laminate material has been investigated to find the natural frequencies. The numerical results obtained in the present study for several examples are presented and compared to other models available in the literature.