Green's functions for uniform Timoshenko beams

The vibration and control of distributed parameter systems is a topic of ongoing interest. The availability of closed form expressions for the Green's functions (or, equivalently, transfer functions) of individual elements facilitates the analysis of these systems. In this paper, a concise formulation is given for the Green's functions of uniform Timoshenko beams. It is shown that Green's functions for uniform Euler-Bernoulli beams, both with and without constant axial loads, can be expressed in the same form.