Citation
Stahl, Karl John (1971) Dynamic Response of Circular Plates Subjected to Moving Massive Loads. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1R1H0G28. https://resolver.caltech.edu/CaltechTHESIS:04182018103519413
Abstract
Techniques are presented for studying the dynamic response of circular disks excited by moving loads. The loading system, consisting of a mass, spring, and dashpot, travels in a circular path concentric with the disk at constant angular velocity. For cases involving elasticallysupported rigid disks, the equations of motion for the disk and moving load may be written as a set of coupled Hill Mathieu equations, typical of moving mass problems. By applying relatively simple transformations the equations may be rewritten as a set of coupled linear differential equations with constant coefficients. The problem is then reduced to solving an ordinary eigenvalue problem.
When the eigenvalues are pure imaginary numbers, they correspond to the frequency components in the motion of the moving mass, and describe the disk motion as well. In certain regions the eigenvalues have positive real parts, corresponding to motions which are unbounded in time. There are three distinct regions of instability which appear in the rigid disk problem. A stiffness in stability region occurs immediately above the critical speed of the disk, and is caused by load stiffness. At higher speeds, a region of instability due to modal coupling appears. Finally, if the load speed exceeds a certain terminal velocity (determined primarily by the mass of the load), an unstable solution will always exist.
The dynamic response of circular elastic disk s with similar loading is investigated using the conventional eigenfunction expansion technique. The system of coupled HillMathieu equations obtained by applying this method r educes to an ordinary eigenvalue problem when certain transformations are made. Thus, many modes may be included in the solution, although it is generally sufficient to consider only a few modes. Solutions to the eigenvalue problem reveal regions of instability directly analogous to those observed in the rigid disk examples.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Applied Mechanics  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Applied Mechanics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  25 May 1971  
Funders: 
 
Record Number:  CaltechTHESIS:04182018103519413  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:04182018103519413  
DOI:  10.7907/1R1H0G28  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  10815  
Collection:  CaltechTHESIS  
Deposited By:  Tony Diaz  
Deposited On:  25 Apr 2018 23:53  
Last Modified:  21 Dec 2019 01:31 
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