Topics in seismic response of nonclassically damped systems

Two methods for evaluating the response of nonclassically damped multi-degree-of-freedom (MDOF) systems are reviewed. In the original and commonly used method, the responses are represented in terms of the relative displacement and relative velocity values of the modal equivalent single-degree-of-freedom (SDOF) systems. In the alternate canonical method a combination of the sine and cosine responses is used. It is shown that the two methods give identical response histories. The original method is preferred because it deals with the physical (relative displacement and relative velocity) values. The response spectrum version of the original method is also presented.;The time domain calculations of the relative velocity of the SDOF systems (needed for the nonclassically damped MDOF systems) give erroneous values in the high frequency range because the input acceleration is assumed to vary linearly between the data points, implying a limitless frequency content that is inconsistent with the accuracy of the measurements. A frequency domain calculation is, therefore, proposed. Various problems associated with such calculation are addressed and resolved. The new response calculation method is used to perform empirical studies on the response spectra and on various correlation coefficients needed for the combination of modal responses.;The problem of the high frequency response of nonclassically damped coupled primary-secondary systems is studied. A new formulation is proposed in which the degrees of freedom of the secondary system are represented related to the connecting DOF of the primary system and not to the base of the primary system. The higher frequency modes of the primary and secondary systems (that are not calculated) are represented by residual modal vectors.