A systematic wave-based method for analysis of large planar frame structures based on Timoshenko waveguide theory

Abstract

This paper presents a new hybrid analytical/numerical systematic approach for continuous modeling of wave propagation in planar structural systems. To do so, a structure is considered as a number of waveguide elements that are connected to each other through different types of discontinuities. The wave propagation in waveguides is modeled using advanced Timoshenko beam theory to account for the rotary inertia, which provides accurate results for high-frequency excitations. The refraction matrices for different types of discontinuities such as change of material and cross section, various types of boundary conditions, and two- and three-member joints are presented using the existing literature, and the refraction matrices for a right-angled four-member joint is derived analytically for the first time. To provide a robust methodology for the analysis of large structural systems, a general new assembly procedure is introduced that is capable of assembling all of the propagation and refraction matrices in a single global system matrix. To insure the validity of the proposed methodology, detailed numerical examples are provided and their results are verified with finite element numerical method.