Explicit modal analysis of an axially loaded Timoshenko beam with bending-torsion coupling

Exact analytical expressions for the natural frequencies and mode shapes of a uniform bending-torsion coupled Timoshenko beam are presented. The beam is taken to be axially loaded, and for which cantilever end conditions appl y. A symbolic computing package (REDUCE) has been used, which simplifies th e analysis greatly. Results are presented for an illustrative example, whic h confirms the accuracy of the method, and provides a convenient benchmark for the validation of the finite element or other alternative approximate m ate methods. The approach offers the prospect of aeroelastic development, a nd is computationally efficient, thus holding out the promise of eventual o ptimization.