A general Solution for dynamic response of axially load non-uniform Timoshenko beams

A dynamic investigation method for the analysis of Timoshenko beams which takes into account the shearing deformation and the rotating inertia is proposed. The solution of the problem is obtained through the iterative variational Rayleigh–Ritz method and assuming as test functions an appropriate class of orthogonal polynomials which respect the essential conditions only. The procedure, applied to tapered beams for which a closed form solution is not known, is an alternative approach to the usual FEM methodologies used in literature. The small number of Lagrangean parameters needed for the analysis allows the use of strict symbolic calculation programs obtaining an high numerical accuracy with a relative short computer time. The work ends with the analysis of a few numerical examples and the results are compared with the ones obtained from other authors mentioned in bibliography.