DYNAMIC RESPONSES OF STRUCTURES TO MULTIPLE SUPPORT SEISMIC EXCITATIONS - A RANDOM VIBRATION TIME HISTORY ANALYSIS

A modal state space random vibration analysis is presented to obtain the responses of a general multiple-degree-of-freedom (MDOF) system subjected to excitation at multiple support points.; The excitation, whether earthquake- or wind-type loading, is modelled as a colored, correlated, vector-valued, non-stationary random process. A new filter is used so that the excitation can have more than one predominant frequency and a wide range of spectral shapes. The time history of the root mean square (RMS) of the earthquake excitation at support points or the wind force at nodal points, which is the output of the filter, is prescribed directly. The corresponding input to the filter, a fictitious piecewise linear strength envelope, is estimated before engaging the filter with the actual system. In addition, for earthquake excitations the filter allows the support motions to be prescribed in terms of displacement, velocity or acceleration. Finally, the time history of the cross correlation between any two components of the excitation can also be prescribed.; A model state space time history random vibration formulation is utilized with exact analytical expressions for the elements of the state transition matrices. The transition matrix is used later to obtain the mean and covariance matrices for the modal system augmented by the filter equations. The concept of 'pseudo-static' displacement used by other researchers is avoided here by expressing the governing equation of motion in terms of absolute displacement along nodal degrees of freedom and by using the new filter prescribed above.; Exact analytical expressions are derived for the evolutionary mean and covariance matrices of a modal system augmented by the filter equations. The RMS time history of the absolute displacement, velocity and acceleration along the nodal degrees of freedom of the system are then computed using modal superposition. Furthermore, other responses of interest such as the components of the state of stress at a point, or the forces at nodal points of an element can be computed by expressing them as linear functions of responses with known statistics.; Finally, a ten-story frame subjected to multiple support excitations is analyzed to demonstrate the simplicity and the capability of the formulation. (Abstract shortened with permission of author.)...