Journal of Sound and Vibration (1987) 116(2), 199-219 PERTURBED COMPLEX EIGENPROPERTIES OF CLASSICALLY DAMPED PRIMARY STRUCTURE AND EQUIPMENT SYSTEMS L. E. SUAREZ AND M. P. SINGH Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A. (Received 13 March 1986, and in revised form 12 August 1986) In the dynamic analysis oflight equipmentsupported on structures, it sometimes becomes essential to consider the effectof the non-classicality of damping on the dynamic charac- teristicsand the equipment response, evenif the supporting structure is classically damped. This non-classical damping effect can be included in dynamic analysis through a state vector approach wherein damped and complex-valued eigenproperties are used. Herein a perturbation approach is developed to obtain such damped eigenproperties of the combined structure-equipment system in terms of the undamped eigenproperties of the supporting structure and the equipment. The closed form expressions are obtained for the eigenvalues and eigenvectors of both the detuned and tuned equipment. These can be used to obtain the dynamic response of equipment, such as seismic floor response spectra, which incorporate the non-classical damping effects and dynamic interaction between the two systems. The numerical results demonstrating the applicability of the proposed approach are presented. 1. INTRODUCTION For calculating the dynamic response of equipment supported on structures subjected to the dynamic effects of earthquake-induced ground motions, the modal properties of the combined equipment-structure system are required. These properties are often used in the development of the seismic floor response spectra which are commonly prescribed as the design inputs characterizing the seismic effect for the design of supported equipment. For a given equipment, the modal properties of the combined system can be obtained by a straightforward eigenvalue analysis of the analytical model of the combined system. However, such eigenvalue analyses can be beset with severe numerical problems and are also impractical. The numerical problems can occur when the supported equipment is very light compared to the supporting structure; in such cases the matrices of the combined system can become ill-conditioned and cause numerical problems. Although it is possible to overcome the numerical precision problem by employing extended precision eigenvalue analysis algorithms, such as IMSL double or quadruple precision subroutine packages, the whole procedure can become impractical if such eigenvalue analyses are to be performed repeatedly in a process. For example, in the process of generation of the seismic floor response spectra for a structure, one will have to carry out a new eigenvalue analysis each time the oscillator (or equipment) properties or its point of attachment to the primary structure are changed. Thus generating a set of floor response spectrum curves for different floors of a primary structure can become a prohibitively expensive proposition if one resorts to carrying out a straightforward eigenvalue analysis of the combined system. Thus in such cases where the primary structure remains the same, it is much more efficient 199 0022-460X/87/140199+21 $03.00/0 © 1987 Academic Press Limited