A Method for Reducing the Number of Degrees of Freedom in Mathematical Models of Damped Linear Dynamic Systems

1962 ◽  
Vol 84 (4) ◽  
pp. 418-421 ◽  
Author(s):  
S. E. Staffeld
Keyword(s):  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original System ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Limited Frequency ◽  
Damped Systems ◽  
Complex Coefficients ◽  
Better Than

A method is given for systematically operating on the equations of motion of a linear dynamic system to produce the equations of a new system of many fewer degrees of freedom. This reduced system has a multiterminal response as close as desired to the original system in a limited frequency range. The result will always be better than that obtained with the normal mode approach and application to damped systems does not result in complex coefficients.

Co-Ordinates Which Uncouple the Equations of Motion of Damped Linear Dynamic Systems

1958 ◽  
Vol 25 (3) ◽  
pp. 361-364 ◽  
Author(s):  
K. A. Foss
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Continuous Systems ◽  
Present Treatment ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Orthogonality Relations ◽  
Lumped Parameters

Abstract Orthogonality relations between the eigenvectors of damped linear dynamic systems with lumped parameters are derived; and from these relations co-ordinates are found in terms of which uncoupled equations of motion can be written. Methods are developed for determining transient stresses in terms of these co-ordinates. The present treatment is extended to systems involving transient damping and to continuous systems.

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