A combination of Fourier cosines series and polynomials (4 terms, 4th order) in Rayleigh–Ritz method is proposed to solve the vibration problem of a generally restrained beam. The characteristics of auxiliary polynomials, which actually are determined by homogeneous boundary conditions of the beam under consideration, can directly change the convergence properties and numerical instabilities of vibration results significantly. Fast convergence and reliability of the proposed polynomials are illustrated with numerical examples in comparisons with available results.
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