This paper concerns wave reflection, transmission, and propagation in Timoshenko beams together with wave analysis of vibrations in Timoshenko beam structures. The transmission and reflection matrices for various discontinuities on a Timoshenko beam are derived. Such discontinuities include general point supports, boundaries, and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices can be combined to provide a concise and systematic approach to vibration analysis of Timoshenko beams or complex structures consisting of Timoshenko beam components. The approach is illustrated with several numerical examples.
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.
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.
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