Abstract
This paper describes an analytical and numerical continuous wave-based approach for the forced vibration analysis of large waveguide systems. With Timoshenko beam theory as the basis for modeling wave propagation in the waveguides, the refraction of waves at discontinuities is studied analytically. Within this context, the refraction of waves at multi-member joints is formulated. In addition, a joint-based procedure is introduced to assemble analytical joint equations in the global system matrix. The joint-based approach is mathematically equivalent with the existing element-based approaches but has the advantage of accounting for the effects of a rigid joint region explicitly. The method is used to find the response of a large frame subjected to steady-state dynamic loadings with a wide range of frequency excitations. The fidelity of the methodology is verified using finite element simulations. The main advantage of the new approach is that it can analyze arbitrary waveguide systems for a wide range of frequencies, which makes it suited for studying the behavior of complex large systems using a single global matrix with a very low computational cost.
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