Elasticity-based beam vibrations for various support conditions

The accuracy of common beam theories in determining resonant frequencies and mode shapes for various support conditions is investigated in this paper. This study analyzed the influence of three assumptions employed in the Euler–Bernoulli, Rayleigh, and Timoshenko beam theories by comparing their results to a three-dimensional, elasticity-based approximation for three different support cases: fixed-free, fixed–fixed, and simply-supported. Each of the theories of interest were applied to both isotropic and orthotropic beams of varying length and compared with elasticity-based solutions to study the influence of slenderness ratio and anisotropic properties. The discrepancies caused by each of these effects are discussed and suggestions for the applicability of the common beam theories are provided.