A random vibration study of structures under multi-component seismic excitations is presented in this paper. The pseudo excitation method proposed by J. H. Lin is employed and is further developed, from which a multi-component pseudo excitation method is formulated. Then, the random model and correlation for multiple ground motions are investigated. Based on the method, a computer program is developed and a random vibration study is performed for a double-layer spherical lattice shell to investigate its seismic performance under multi-component seismic excitations. It is found that a significant difference may occur between single and multi-component seismic excitations. The present study has shown that the developed method is a highly efficient and accurate CQC algorithm, in which all the cross-correlation terms between both participant modes and seismic excitations are involved. This method can easily be used for multi-component seismic analysis of structures that have closely spaced natural frequencies and coupled vibration modes.

Lattice shell is a type of spatial structure whose vibrations are dominated by both horizontal and vertical motion. In this paper, a multidimensional pseudo excitation method is developed for nonstationary random seismic analysis of structures under multi-support and multi-dimensional earthquake excitations, in which the phase lags between the excitations have been involved. Mathematical formulations are derived. A method of evaluating peak responses is recommended. Multi-dimensional seismic random models are discussed. A random vibration analysis is performed for a double-layer cylindrical lattice shell to investigate its seismic performance. It is shown that the developed method is a highly efficient algorithm, which can easily solve the nonstationary problem of large structures under multi-support and multidimensional earthquake excitations.