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ICCM 2019
9th-13th July, Singapore, Singapore


A highly efficient and accurate analytical method for elastodynamic problems within the whole frequency range


Xiang Liu, Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, China School of Traffic & Transportation Engineering, Central South University, China
Email: xiangliu06@gmail.com


An efficient analytical spectral dynamic stiffness (SDS) method for exact dynamic analysis of elastodynamic problems is presented. The general solution satisfying the governing differential equation exactly is first derived by applying the proposed modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the exact general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The formulation is applicable to both dynamic response and wave propagation analyses; and the method is applied to elastodynamic problems with simple as well as complex geometries. When applied in modal analysis, the Wittrick-Williams algorithm is used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives exact solution with remarkable computational efficiency, covering low, medium and high frequency ranges. All results from the theory are accurate up to the last figures quoted to serve as benchmarks. This new method offers an idea tool for parametric and optimization studies of structures, especially in the vibro-acoustic analysis within mid- to high-frequency ranges.