Abstract
In this chapter, a numerically efficient method, namely the Rayleigh–Ritz method is employed to investigate the dynamical characteristics of nanobeam embedded in the Winkler–Pasternak elastic foundation. Orthogonal polynomials such as Chebyshev polynomials, Legendre polynomials, and Hermite polynomials are used as shape functions in the Rayleigh–Ritz method. The main advantages of these polynomials are orthogonality, making the technique more computationally efficient, and avoiding ill-conditioning for higher values of polynomials. The governing differential equations of the present model are obtained by incorporating Hamilton’s principle, and the frequency parameters are computed for classical boundary conditions. Additionally, a comparative study has been carried out to justify the effectiveness and convergence of the present model or method for different polynomials.