On the Finite Deflection Dynamics of Thin Elastic Beams

Abstract

A dynamic theory of thin beams undergoing large deflection but small strain is derived. Geometric nonlinearities are preserved but the material is assumed to behave linearly. Contributions due to rotatory inertia, shear deformation, and axial stress resultants are included. The resulting equations are analyzed by characteristic techniques. Wave-propagation speeds, jump properties, and their physical significances are discussed. A simplifying assumption generates a modified Timoshenko beam equation which is valid for large deformation.