Resonance characteristics of connected subsystems: Theory and simple configurations

The dynamic properties of connected continuous subsystems are examined with use of analytical expressions for the modal properties. The analysis begins with a Lagrange multiplier formulation to develop a characteristic equation in terms of subsystem mobilities and impedances. The complexity of the problem is examined in terms of the order of the polynomial expressions in the characteristic equation. To obtain insight into the system's complicated dynamic characteristics, the complexity of the problem is reduced. It is shown that the reduction of complexity can be obtained only with a reduction of accuracy, but by retaining the dominant effects of the dynamics problem, the loss of accuracy is not excessive. The reduced problem is examined further to develop simple, yet powerful expressions for the modal properties which provide insight into the resonance characteristics of the connected subsystem problem. The results are useful as a complement to existing computational techniques for understanding and interpreting dynamic analysis results. In this paper, the theory and simplest configurations are examined, and in the companion paper, more general configurations are studied.