Response of Mechanical Systems to Random Excitation

Citation

Stumpf, Henry John (1960) Response of Mechanical Systems to Random Excitation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NJSA-T820. https://resolver.caltech.edu/CaltechETD:etd-07262006-142737

Abstract

The Fourier Series and Fokker-Planck Methods, the available techniques for solving vibration problems when the exciting force is a stochastic process, are reviewed and several detailed examples are given. In particular a two-degree-of-freedom system is considered which is excited by a non-stationary input and which possesses a general type of viscous damping. Several typical engineering problems involving stochastic processes are considered. In the case of fatigue it is shown that a criterion for fatugue failure in multi-degree-of-freedom systems may be established using Miner's cumulative damage hypothesis and the number of zero crossings per second. In the earthquake problem it is shown that when certain inequalities involving the natural frequencies of the building are valid, cross-product terms may be neglected in computing mean square displacements. Two problems involving beams are considered. In one case it is demonstrated that a convergent expression for the mean square bending moment may be obtained for a Bernoulli-Eular beam excited by white noise, provided a finite cutoff frequency is used. In the other case involving random end motion, a one-term approximation to the mean square bending moment may be obtained, when the correlation time is not too small. The isolation problem is considered and the concept of the "white spectrum fragility curve" is established as a criterion for adequate isolation. Finally the motion of a single-degree-of-freedom system over a rough surface is considered. It is shown that for an exponentional type of auto-correlation the mean square displacement is finite for unaccelerated motion and diverges when the system is accelerated.

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