A purely directional wave splitting for the homogeneous Timoshenko beam

A new wave splitting for the Timoshenko beam is derived, which partially remedies earlier problems with exponentially growing split fields and integral operator kernels. This allows for propagation of the split fields further along the beam and for longer time intervals. The elements of the transform and Greenʹs operator are derived in the Laplace domain and are computed by means of short and long time asymptotic expansions and contour integration. Numerical results are presented for the case of forced motion of the end of a semi-infinite beam and the cases of a point force and a point moment on an infinite beam.