Vibrations of Nonlocal Timoshenko Beams using Orthogonal Collocation Method

In this paper, orthogonal collocation method (OCM) is applied to solve the free vibration of nonlocal Timoshenko beams with various boundary conditions by using piecewise cubic Hermite polynomials (CHPs). In the numerical implementation, approximation solution and its space derivatives over the interval are approximated by the combination of the CHPs and unknown parameters. Through the generalized eigen-value problem analysis, the vibration frequencies of beams can be determined precisely. Form numerical analysis by using OCM sufficiently indicate that it has excellent convergence rate, and very close to analytical solutions.