Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures. An exact analytical solution is obtained using wave vibration approach. The classical Euler-Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling the flexural vibrations in planar frames. Reflection and transmission matrices corresponding to incident waves arriving at the “L” joint from various directions are obtained. A concise and systematic approach to both free and forced vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures is presented. Results are compared to the Euler-Bernoulli model results available in the literature. Good agreements have been reached.