Citation
Stumpf, Henry John (1960) Response of mechanical systems to random excitation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd07262006142737
Abstract
The Fourier Series and FokkerPlanck 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 twodegreeoffreedom system is considered which is excited by a nonstationary 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 multidegreeoffreedom 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, crossproduct 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 BernoulliEular beam excited by white noise, provided a finite cutoff frequency is used. In the other case involving random end motion, a oneterm 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 singledegreeoffreedom system over a rough surface is considered. It is shown that for an exponentional type of autocorrelation the mean square displacement is finite for unaccelerated motion and diverges when the system is accelerated.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Mechanical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1960 
Record Number:  CaltechETD:etd07262006142737 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd07262006142737 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2983 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  17 Aug 2006 
Last Modified:  26 Dec 2012 02:56 
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