Linear modal analysis of L-shaped beam structures: parametric studies

摘要

Linear modal analysis of L-shaped beam structures indicates that there are twoudindependent motions, these are in-plane bending and out of plane motions including bendingudand torsion. Natural frequencies of the structure can be determined by finding the roots of twoudtranscendental equations which correspond to in-plane and out-of-plane motions. Due to theudcomplexity of the equations of motion the natural frequencies cannot be determined explicitly.udIn this article we nondimensionalise the equations of motion in the space and time domains,udand then we solve the transcendental equations for selected values of the L-shaped beamudparameters in order to determine their natural frequencies. We use a numerical continuationudscheme to perform the parametric solutions of the considered transcendental equations. Usingudplots of the solutions we can determine the natural frequencies for a specific L-shape beamudconfiguration.