Distortional eigenmodes and solutions for thin-walled beams

This paper presents a generalization of the classic theory for thin-walled beams by including distortional displacements. A condensed presentation of the novel finite-elementbased displacement approach in [1,2] is given, where specific distortional displacement fields, which decouple the differential equations for generalized beam theory (GBT), are determined via a semi-discretization procedure. The distortional displacement fields are found as solutions to a distortional homogeneous eigenvalue problem which produce distortional displacement eigenmodes. Using the distortional modal matrix found for the homogeneous system the final uncoupled set of distortional differential equations including the load terms are presented and the full solution is given, including an illustrative example. This new approach is an alternative to the traditional first order GBT method.