Access Type

Open Access Dissertation

Date of Award

January 2011

Degree Type


Degree Name



Mechanical Engineering

First Advisor

Wen Li


The Fourier Spectral Element Method (FSEM) was proposed by Wen Li on the vibration of simple beams (Li, 1999), and was extended to the vibration of rectangular plates (Li, 2004). This dissertation proposes a revised formulation on the vibration of rectangular plates with general boundary conditions, and extends the FSEM on the vibration of general triangular plates with elastic boundary supports. 3-D coupling formulation among the plates and beams is further developed. A general dynamic structure is then analyzed by dividing the structure into coupled triangular plates, rectangular plates, and beams. The accuracy and fast convergence of FSEM method is repeatedly benchmarked by analytical, experimental, and numerical results from the literature, Laboratory test, and commercial software.

The Key feature of FSEM method is that the approximation solution satisfies both the governing equation and the boundary conditions of the beam (plates) vibration in an exact sense. The displacement function composes a standard Fourier cosine series plus several supplementary functions to ensure the convergence to the exact solution including displacement, bending moment, and shear forces, etc. All the formulation is transformed into standard form and a set of stored matrices ensure fast assembly of the studied structure matrix. Since the matrix size of the FSEM method is substantially smaller than the FEA method, FSEM method has the potential to reduce the calculation time, and tackle the unsolved Mid-frequency problem.