Eigenproperties of Nonclassically Damped Primary Structure and Oscillator Systems

Abstract

The calculation of the combined eigenproperties of a nonclassically damped structure and a supported equipment is of practical interest. Herein an approach is developed whereby these properties can be obtained, in terms of the eigenproperties of the structure and equipment, without a conventional eigenvalue analysis of the combined system. The eigenvalues are obtained as the solutions of a nonlinear characteristic equation, easily solvable by a simple Newton-Raphson scheme. Once the eigenvalues are known, the corresponding eigenvectors can be obtained from closed-form expressions. The approach can also be used effectively to obtain exact eigenproperties for very light as well as very heavy equipment supported on structures.