On the computation of moving mass/beam interaction utilizing a semi-analytical method

This article proposes a new orthogonal basis for the spatial discretization tracking the dynamic response of shear deformable beams. The corresponding initial boundary value differential equations of motion are dealt with focusing on Timoshenko and Reddy-Bickford beam theories. The presented technique takes advantage of a compatible trigonometric set of functions defining the rotation field in combination with orthogonal splines for the transverse deformation. A broad survey is conducted gaining the beam natural frequencies in free vibration; the forced vibration of the beam is attacked considering a traveling inertial body interacting with the base beam. For different beam end-fixity cases, the orthogonal basis could be straightforwardly constructed representing a rapid convergence. In this regard, a remedy is achieved for the inconvenient procedure of creating the shape functions in other competing methodologies.