Computer analysis techniques in structural dynamics

Abstract

The purpose of this thesis is to utilize analytical digital computer techniques to solve Structural Mechanics problems in the field of Elasto-Dynamics. The work is divided into two parts. In the first section, the development of a one degree of freedom mathematical model which illustrates in a simplified manner, the complex problem of the static buckling of axially-compressed, thin, cylindrical shells is considered. The resultant system is analyzed for stability both statically and dynamically. Critical buckling loads and rotations are determined for the perfect system, for the system with initial load eccentricity, and for the system with initial geometric imperfection. Potential functions and corresponding phase-plane diagrams for the perfect system are constructed using the CALCOMP PLOTTER system.

In the second section, the stability, modal shapes, and frequencies of the vibrating beam-column are investigated. Using the kinetic method, the Bernoulli-Euler differential equations of motion are obtained and the general dynamic stiffness matrix is constructed. From the classical Eigen-value-Eigenvector problem, the critical buckling loads, resonant frequencies, modal shapes are obtained. Using iterative numerical techniques, the roots of the resulting transcendental equations are obtained together with the associated Eignvectors. Plots of the stable and unstable states of dynamic equilibrium are constructed.