Free vibration analysis of cylindrical helical springs by the pseudospectral method

The pseudospectral method is applied to the free vibration analysis of cylindrical helical springs. The displacements and the rotations are approximated by the series expansions of Chebyshev polynomials and the governing equations are collocated. The number of collocation points is chosen to be less than the number of the expansion terms to handle the boundary condition. Numerical examples are provided for fixed–fixed, free–free, fixed–free and hinged–hinged boundary conditions. The results show good agreement with those of the transfer matrix method and the dynamic stiffness method. The formulation of the pseudospectral method is straightforward and shows an exponential rate of convergence with mesh refinement.