transverse vibration for non-uniform timoshenko nano-beams

In this paper, eringen’s nonlocal elasticity and timoshenko beam theories are implemented to analyze the bending vibration for nonuniform nanobeams.  the governing equations and the boundary conditions are derived using hamilton’s principle. a generalized differential quadrature method (gdqm) is utilized for solving the governing equations of nonuniform timoshenko nanobeam for pinnedpinned, cled–cled, cled–pinned, cled–free, cled–slide, and pinnedslide boundary conditions. the nondimensional natural frequencies and the normalized mode shapes are obtained for short and stubby nanobeams where influences varying crosssection area, small scale, shear deformation, rotational moment of inertia, acceleration gravity and the selfweight of the nonuniform timoshenko nanobeam are discussed. the present study illustrates that the small scale effects are more significant for smaller size of nanobeam, larger nonlocal parameter and higher vibration modes. further, the compression forces due to gravity and the selfweight of the nanobeam also like the small scale effect are reduced the magnitude of the frequencies of the nanobeam.