Size-dependent behaviours of metal foam microbeams with three different porosity distribution models are studied in this paper. Based on the finite element model, a normal and shear deformation theory has been employed for first time to investigate their structural by using modified strain gradient considering effects variable material length scale parameter. The equations motion boundary condi...

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...

In this contribution, the variational problem for Kirchhoff plate based on modified strain gradient theory (MSGT) is derived, and Euler-Lagrange equations governing equation of motion are obtained. The Galerkin-type weak form, upon which finite element method constructed, derived from problem. shape functions satisfy homogeneous partial differential as extensions Adini-Clough-Melosh (ACM) Bogne...