Explicit Modal Analysis of an Axially Loaded Timoshenko Beam With Bending-Torsion Coupling

Abstract

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 apply. A symbolic computing package (REDUCE) has been used, which simplifies the analysis greatly. Results are presented for an illustrative example, which confirms the accuracy of the method, and provides a convenient benchmark for the validation of the finite element or other alternative approximate methods. The approach offers the prospect of aeroelastic development, and is computationally efficient, thus holding out the promise of eventual optimization. [S0021-8936(00)01002-3]