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%.