Dynamic analysis of Timoshenko beams by the boundary element method

A Boundary Element Method formulation is developed for the dynamic analysis of Timoshenko beams. Based on the use of not time dependent fundamental solutions a formulation of the type called as Domain Boundary Element Method arises. Beside the typical domain integrals containing the second order time derivatives of the transverse displacement and of the rotation of the cross-section due to bending, additional domain integrals appear: one due to the loading and the other two due to the coupled differential equations that govern the problem. The time-marching employs the Houbolt method. The four usual kinds of beams that are pinned–pinned, fixed–fixed, fixed–pinned and fixed–free, under uniformly distributed, concentrated, harmonic concentrated and impulsive loading, are analyzed. The results are compared with the available analytical solutions and with those furnished by the Finite Difference Method.