| Abstract: | Under multi-support earthquake excitation, the damping is proportional to the relative velocity in relative motion method, While the damping is proportional to the absolute velocity in method of direct solving absolute displacement, and the damping assuming difference may cause the calculation errors on structural responses. The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model, which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures. Based on probability theory, the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis, and some numerical examples are provided to verify the error analysis. At last, it is pointed out that the calculation errors between the two solving methods decrease with damping ratio, and it is negligible when the damping ratio of structure is less than 5%. |
