Dynamic Analyses of Suspension Bridge Structures and Some Related Topics

• Main Author: Abdel-Ghaffar, Ahmed Mansour
• Format: Others
• Published: 1976
• Online Access: https://thesis.library.caltech.edu/10741/7/Abdel-Ghaffar_AM_1976.pdf; Abdel-Ghaffar, Ahmed Mansour (1976) Dynamic Analyses of Suspension Bridge Structures and Some Related Topics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Y1XR-WG52. https://resolver.caltech.edu/CaltechTHESIS:03012018-135434228 <https://resolver.caltech.edu/CaltechTHESIS:03012018-135434228>

<p>The thesis is divided into two parts. The first part develops a method of dynamic analysis for vertical, torsional and lateral free vibrations of suspension bridges, based on linearized theory and the finite-element approach. The method involves two distinct steps: (1) specification of the potential and kinetic energies of the vibrating members of the continuous structure, leading to derivation of the equations of motion by Hamilton's Principle, (2) use of the finite-element technique to: (a) discretize the structure into equivalent systems of finite elements, (b) select the displacement model most closely approximating the real case, (c) derive element and assemblage stiffness and inertia properties, and finally (d) form the matrix equations of motion and the resulting eigenvalue problems. The stiffness and inertia properties are evaluated by expressing the potential and kinetic energies of the element (or the assemblage) in terms of nodal displacements. Detailed numerical examples are presented to illustrate the applicability and effectiveness of the analysis and to investigate the dynamic characteristics of suspension bridges with widely different properties. This method eliminates the need to solve transcendental frequency equations, simplifies the determination of the energy stored in different members of the bridge, and represents a simple, fast and accurate tool for calculating the natural frequencies and modes of vibration by means of a digital computer. The method is illustrated by calculating the modes and frequencies of a bridge and comparing them with the measured frequencies.</p> <p>The second part contains two studies on the effect of differential motions of two foundations upon the response of the superstructure of a bridge. The first study deals with the dynamic response of a "long beam" model of a bridge to both steady-state and random excitations applied at the supports. The second study develops a method to analyze the dynamic soil-bridge interaction of a simple bridge model erected on an elastic half-space, and the input motion is in the form of incident plane SH-waves. The dynamic response of the bridge and the effect of the radiative damping in the half-space on the interaction of the bridge are also studied.</p>