A DQEM for vibration of shear deformable nonuniform beams with general boundary conditions

Abstract

A differential quadrature element method (DQEM) for free vibration analysis of arbitrary non-uniform Timoshenko beams with attachments, i.e. concentrated mass and rotary inertia and resting on elastic supports is proposed. Using the Hamilton’s principle the governing equation and the natural compatibility conditions at the interface of adjacent elements are devised in a systematic manner. The differential quadrature (DQ) analogs to the governing equation, the compatibility conditions and the external boundary conditions implementations are explicitly formulated. The versatility, accuracy and efficiency of the presented DQEM for free vibration analysis of Timoshenko beams are tested against other solution procedures. The examples include; stepped non-uniform Timoshenko beams, non-uniform beams with attached heavy masses and supported elastically in transverse directions, and also non-uniform beams on elastic foundations. Accurate solutions are archived via few grid points for all the cases considered.