The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Schödinger equation (NNLSE) in the second approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the second approximation can describe the generally nonlocal soliton states of the NNLSE m...