A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams

摘要

The aim of the current work is to present a shear deformation theory which can model the free vibration of functionally graded nano-size beams made of two different types of materials (isotropic and anisotropic) resting on elastic foundation using a new shear strain shape function. The proposed model includes undetermined integral term and also contains both transverse shear and stretching effects. The size-dependent behavior of nano-size systems is captured via the nonlocal strain gradient theory. The governing equations of motion are obtained based on a virtual work of the Hamiltonian principle where an analytic technique based Navier series is established to solve the eigenvalue problem. From our knowledge, it is the first time that size-dependent dynamics of graded nanobeams made of anisotropic materials is investigated. The efficiency of the present model is verified by comparing the results of numerical examples with the different solutions found in the literature. It shows that the dynamic characteristics of the nanobeam are influenced by size effects, geometry, power-law index, exponential factor, and elastic foundation. Also, the possibility and accuracy of replacing a hexagonal model with isotropic one is investigated and discussed in detail.