Spectral analysis and system of fundamental solutions for Timoshenko beams

We have found a unified method to analyse Timoshenko beams under various boundary conditions that occurred in practice. Explicit asymptotic expressions for the spectrum are obtained. Our method is very simple but effective because explicit formulas are obtained for the system of fundamental solutions, which are very useful for other purposes such as stability analysis. The eigenfunctions are also shown to form an orthogonal basis.