The Fourier Spectrum Element Method For Vibration And Power Flow Analysis Of Complex Dynamic Systems

THE FOURIER SPECTRAL ELEMENT METHOD FOR VIBRATION AND POWERFLOW ANALYSIS OF COMPLEX DYNAMIC SYSTEMS byHONGAN XUMay 2011Advisor: Dr. Wen LiMajor: Mechanical EngineeringDegree: Doctor of PhilosophyA general numerical method, the so-called Fourier-Space Element Method (FSEM), isproposed for the vibration and power flow analyses of complex built-up structures. In a FSEMmodel, a complex structure is considered as a number of interconnected basic structural elementssuch as beams and plates. The essence of this method is to invariably express each ofdisplacement functions as an improved Fourier series which consists of a standard Fourier cosineseries plus several supplementary series/functions used to ensure and improve the uniformconvergence of the series representation. Thus, the series expansions of the displacementfunctions and their relevant derivatives are guaranteed to uniformly and absolutely converge forany boundary conditions and coupling configurations. Additionally, and the secondary variablesof interest such as interaction forces, bending moments, shear forces, strain/kinetic energies, andpower flows between substructures can be calculated analytically.Unlike most existing techniques, FSEM essentially represents a powerful mathematicalmeans for solving general boundary value problems and offers a unified solution to the vibrationproblems and power flow analyses for 2and 3-D frames, plate assemblies, and beam-plate