Abstract

Linear modal analysis of L-shaped beam structures indicates that there are two
independent motions, these are in-plane bending and out of plane motions including bending
and torsion. Natural frequencies of the structure can be determined by finding the roots of two
transcendental equations which correspond to in-plane and out-of-plane motions. Due to the
complexity 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 beam
parameters in order to determine their natural frequencies. We use a numerical continuation
scheme to perform the parametric solutions of the considered transcendental equations. Using
plots of the solutions we can determine the natural frequencies for a specific L-shape beam
configuration.