Comprehensive effect of in-plane load and nonlinear thermal field on dynamic response of embedded bi-directional functionally graded tapered thick nanobeams

Abstract

This article presents a numerical model based on shear deformation theory in conjunction with Eringen’s nonlocal theory to investigate the thermo-elastic vibration behavior of bi-directional functionally graded nonuniform thick nanobeams supported on Pasternak's foundation. These beams are subjected to nonlinear temperature field along the thickness and uniform in-plane loading. Two directional variations in material properties are described by a power-law model across the thickness and as per the exponential function along the length. Employing Hamilton's energy principle, the governing equations are derived and then solved for frequency parameter via the generalized differential quadrature method for clamped, simply-supported, and combination of both the boundary conditions. A parametric study is carried out for understanding the vibration characteristic of considered beams, which shows that the combination of in-plane and thermal loadings with the foundation parameter is the most critical combination for bi-directional functionally graded nanobeams. Results are compared with the published work and found in good accordance. The results will be of great use in designing aerospace shuttles and scanning probe microscopes where nonuniform embedded nanobeams are subjected to compression in the thermal environment.

Keywords:

• Bi-directional functionally graded beam
• in-plane load
• nonlinear thermal load
• nonlocal vibration
• Pasternak’s foundation
• tapered beam