Energy-based dynamic analysis of secondary systems

A condensation procedure for the coupled analysis of multidegree- of-freedom primary-secondary (PS) structural systems is developed based on energy principles. It provides a simple and consistent approach to the response analysis of secondary systems in a vibrational environment for both tuned and detuned cases without explicit knowledge of the frequency characteristics associated with the combined PS system. In this method, a multidegree-of-freedom (larger than three degrees) P-system is always substituted by a three-degree-of-freedom system before condensing a 1S-3P model to a 1S-2P model based on the equivalence of the S-system energy. All the energy parameters in the 1S-2P and 1S-3P models are analytically calculated from closed-form expressions so that an increase in the number of degrees of freedom does not substantially increase the computational effort. Some of the solution properties such as its convergence as the mass ratio approaches a small value and the accuracy and efficiency of the solution procedure are discussed in some detail. Two numerical examples are presented to demonstrate these properties.