Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

Abstract

In this work, the nonlocal strain gradient theory is applied to study the free vibration response of a Timoshenko beam made of triclinic material. The governing equations of the problem and the associated boundary conditions are obtained by means of the Hamiltonian principle, whereby the generalized differential quadrature (GDQ) method is implemented as numerical tool to solve the eigenvalue problem in a discrete form. Different combinations of boundary conditions are also considered, which include simply-supports, clamped supports and free edges. Starting with some pioneering works from the literature about isotropic nanobeams, a convergence analysis is first performed, and the accuracy of the proposed size-dependent anisotropic beam model is checked. A large parametric investigation studies the effect of the nonlocal, geometry, and strain gradient parameters, together with the boundary conditions, on the vibration response of the anisotropic nanobeams, as useful for practical engineering applications.

Vibration analysis of cantilever FG-CNTRC trapezoidal plates

“…many authors to present numerical solution for one-dimensional and two-dimensional problems [42][43][44][45]. Values of a two-dimensional function like F(ζ,η) can be expressed in a matrix form as where N and M are number of grid points in ζ and η directions, respectively.…”