Non-Stationary Synthesis of Multi-Dimensional and Multi-Point Seismic Waves

To better understand the realistic spatial behaviour and the multi-dimensionality and non-stationary nature of seismic ground motions, the trigonometric-series method was used to generate and synthesize the multi-dimensional and non-stationary seismic waves in the present work. Firstly, the design response spectrum was converted to an equivalent power spectrum. The power-spectrum density matrix was then extended from one dimension to three dimensions to account for the multi-dimensionality of the seismic ground motions. Subsequently, the envelope function and the trapezoidal window connection were employed to consider the non-stationary nature of the seismic ground motions and a Fourier transform was used to generate the time history of the spatial seismic waves. The response spectrum of a newly generated wave was compared with the target response spectrum at every excitation direction to revise the amplitude of the generated wave in the frequency domain. Finally, the fitted and the designed spectrum were compared to verify the accuracy of the synthetic seismic waves. Some important conclusions have been drawn from the comparison that the error in the fitted spectrum partially exceeds 10.00% (maximum 16.68% ); however, the overall error of fitting is not beyond 8.00% (18.00% without modification).