Access Type

Open Access Dissertation

Date of Award


Degree Type


Degree Name



Mechanical Engineering

First Advisor

Hongan Xu


A general numerical method, the so-called Fourier-Space Element Method (FSEM), is proposed for the vibration and power flow analyses of complex built-up structures. In a FSEM model, a complex structure is considered as a number of interconnected basic structural elements such as beams and plates. The essence of this method is to invariably express each of displacement functions as an improved Fourier series which consists of a standard Fourier cosine series plus several supplementary series/functions used to ensure and improve the uniform convergence of the series representation. Thus, the series expansions of the displacement functions and their relevant derivatives are guaranteed to uniformly and absolutely converge for any boundary conditions and coupling configurations. Additionally, and the secondary variables of interest such as interaction forces, bending moments, shear forces, strain/kinetic energies, and power flows between substructures can be calculated analytically.

Unlike most existing techniques, FSEM essentially represents a powerful mathematical means for solving general boundary value problems and offers a unified solution to the vibration problems and power flow analyses for 2- and 3-D frames, plate assemblies, and beam-plate coupling systems, regardless of their boundary conditions and coupling configurations. The accuracy and reliability of FSEM are repeatedly demonstrated through benchmarking against other numerical techniques and experimental results.

FSEM, because of its exceptional computational efficacy, can be efficiently combined with the Monte Carlo Simulation (MCS) to predict the statistical characteristics of the dynamic responses of built-up structures in the presence of model uncertainties. Several examples are presented to demonstrate the mean behaviors of complex built-up structures in the critical mid-frequency range in which the responses of the systems are typically very sensitive to the variances of model variables.