A modal superposition method for the nonlinear dynamic analysis of a structure subjected to multiple support motions is presented. The nonlinearities are due to clearances between the components and their supports. The finite element method is used to derive the equations of motion with the nonlinearities represented by a pseudo force vector. The displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. The modal superposition method is used to analyze the dynamic response of one loop of the nuclear steam supply system. This loop has nonlinear supports and is subjected to nonuniform seismic excitations at the supports. It is shown that the computational cost of the modal superposition method is lower than that of the direct integration.

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