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Dynamic Analyses of Suspension Bridge Structures.
Abdel-Ghaffar, A. M.
National Science Foundation, Washington, D.C., May 1976, 372 p.
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A method of dynamic analysis for vertical, torsional and lateral free vibrations of suspension bridges is developed that is based on linearized theory and a finite-element approach. It involves 2 steps: (1) specification of potential and kinetic energies of vibrating structure, leading to derivation of equations of motion by Hamilton's Principle, (2) use of a finite-element technique to: (a) discretize the bridge, (b) select displacement models, (c) derive stiffness and inertia properties, and (d) form matrix equations of motion. Stiffness and inertia properties are evaluated by expressing potential and kinetic energies of an element in terms of nodal displacements. Numerical examples are presented to illustrate the applicability of the analysis and to investigate dynamic characteristics of suspension bridges. The method eliminates the need to solve transcendental frequency equations, simplifies determination of energy stored in the bridge, and represents an accurate tool for calculating natural frequencies and modes by means of a digital computer. The method is illustrated by calculating modes and frequencies of a bridge and comparing them with measured frequencies.
Equations of motion; Vibration; Dynamic tests; Finite element analysis; Earthquake engineering; Resonant frequency; Bridge towers; Suspension bridges; Earthquakes; Dynamic structural analysis