Alternative solution techniques for nonconservative, linear, dynamic systems

In this dissertation, three new numerical algorithms for analyzing nonconservative, linear, dynamic systems are proposed and evaluated in terms of accuracy, rate of convergence and computational expense. The problems considered are the moving mass problem, eigenvalue estimation and parametric stability analysis.; The moving mass problem describes the coupled dynamics of a rigid body transported across and coupled to a continuous medium. Two commonly used techniques to solve this problem are finite element method which suffers slow convergence and integro-differential equation which is computationally expensive. We propose a method using complex eigenfunction expansions which, to a certain degree, alleviate these two shortages. Understanding the linear dependence of complex eigenfunctions and constraining the solution so as to avoid numerical difficulties and ensure convergence is our key insight into this previously unsolved problem.; In some classes of eigenvalue estimation problems, Galerkin's method using complex eigenfunctions may be desirable. However, because of the linear dependence, the implementation of this technique is non-trivial, a fact that has not been well recognized. In this thesis, a new technique using Galerkin's method with complex eigenfunction expansions is proposed and compared to three other techniques. The new technique proposed here can be advantageous when large numbers of trial functions must be used.; Mechanical systems in which its stiffness varies harmonically are referred to parametrically excited systems. The design of these systems depends in part on their dynamic stability. The traditional numerical method for determining the stability is the transition matrix method, which is robust but computationally expensive. This dissertation presents a method using spectral collocation for parametrical stability analysis. The results indicate spectral collocation is competitive with the traditional transition matrix method.