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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.

For a beam with uniformly distributed mass and stiffness, a linear mathematical model is derived that closely duplicates dynamic behavior through the two rigid-body modes and the first of two bending modes. The model has four terminals, transverse and angular displacement at each end, permitting it to be connected into assembly on a fixed-end basis. Eight degrees of freedom are used. It is shown that the response is superior to that obtained with the normal mode or lumped parameter approaches when a comparable number of degrees of freedom are used. Application of the results to a specific case involves only arithmetic operations.

No abstract