| Abstract: | Closed-form expressions are obtained to calculate the approximate complex eigenvalues and eigenvectors of a system composed of a non-classically damped primary structure and a single degree of freedom oscillator. The expressions are obtained through a systematic second order perturbation analysis of a transformed eigenvalue problem of the combined system. The possibility of tuning between the structure and equipment is considered. The dynamic properties of the combined system are derived in terms of the complex eigenvalues and eigenvectors of the supporting structure and the frequency, mass and damping ratio of the equipment. Examples demonstrating the accuracy of the expressions for the eigenvalues and eigenvectors are presented. These eigenproperties are used for generation of floor response spectra for non-classically damped structures to incorporate the dynamic interaction effects between the structure and equipment. |
