Wave Analysis of In-Plane Vibrations of H- and T-shaped Planar Frame Structures

Abstract

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. An exact analytical solution is obtained using wave vibration approach. Timoshenko beam theory, which takes into account the effects of both rotary inertia and shear distortion, is applied in modeling the flexural vibrations in the planar frame. Reflection and transmission matrices corresponding to incident waves arriving at the “T” joint from various directions are obtained. Bending and longitudinal waves generated by a combination of point longitudinal forces, point bending forces, and bending moments are also obtained. Assembling these wave relations provides a concise and systematic approach to both free and forced vibration analyses of coupled bending and longitudinal vibrations in H- and T-shaped planar frame structures. Natural frequencies, modeshapes, and forced responses are obtained from wave vibration standpoint. The results are compared to results available in literature. Good agreement has been reached.