| The purpose of this study is to compute the maximum responses of multi-degree-of-freedom (MDOF) secondary systems multiply connected to an MDOF primary system. The secondary system and its supporting primary system are treated as a single coupled system. Analysis of the coupled system accounts for many effects, not provided by uncoupled analyses of the two systems, including interaction effects--especially in tuned modes, nonclassical damping, correlations between responses from multiple supports, and straining effect introduced by the secondary system.;Numerical examples present several representative coupled systems subjected to various earthquakes to show the applicability and accuracy of the proposed methods.;The equation of motion of the coupled system is formulated in terms of normal (modal) coordinates of the uncoupled primary and secondary systems. Such formulation requires only limited information about the primary system. A perturbation method for evaluating complex mode shapes and frequencies of coupled systems is developed. The method applies even when the secondary system is not very light, and when the secondary system introduces static constraint on the primary system. A modal superposition method making use of complex mode shapes is developed. This method extends into a response spectrum formulation, in which a relative velocity spectrum is used in addition to the conventional displacement spectrum. The relationship between the two spectra is investigated. A procedure is also proposed to evaluate the velocity spectrum from the displacement spectrum. A general modal combination rule is established to combine the modal responses of systems with closely spaced frequencies as well as nonclassical damping. An instructure response spectrum (IRS) method including a majority of attributes of the coupled analysis is developed. The method can account for various coupling effects, which are not accounted for in the conventional floor response spectrum method. The method directly uses displacement and velocity spectra at the base of the primary system as seismic input without converting it into either compatible time history or a power spectral density function. |
