Out-of-plane vibration of a multi-span Timoshenko curved beam due to a moving load including the warping inertia of the beam

The governing equations for the out-of-plane motion of a multispan Timoshen ko curved beam are derived. The warping inertia and flexural moment of the cross-section of the curved beam are included. An analytical method is pres ented to calculate the modal frequencies and their corresponding sets of mo de shape functions for the out-of-plane motion of the curved beam. Further, the orthogonality of two sets of mode shape functions corresponding to any two distinct modal frequencies for the out-of-plane motion of the curved b eam is derived. The basic characteristics of strain energy density of the c urved beam due to a moving load are investigated.