Modal Analysis of the Dynamic Response of Timoshenko Beam under Moving Mass

In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (eigenfunction expansion method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination, are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (discrete element technique) and the RKPM (reproducing kernel particle method).