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

Linear modal analysis of L-shaped beam structures indicates that there are twoindependent motions, these are in-plane bending and out of plane motions including bendingand torsion. Natural frequencies of the structure can be determined by finding the roots of twotranscendental equations which correspond to in-plane and out-of-plane motions. Due to thecomplexity of the equations of motion the natural frequencies cannot be determined explicitly.In this article we nondimensionalise the equations of motion in the space and time domains,and then we solve the transcendental equations for selected values of the L-shaped beamparameters in order to determine their natural frequencies. We use a numerical continuationscheme to perform the parametric solutions of the considered transcendental equations. Usingplots of the solutions we can determine the natural frequencies for a specific L-shape beamconfiguration.