Error analysis of seismic response obtained by directly solving absolute displacement in frequency domain under multi-support earthquake excitations

Under multi-support earthquake excitations, nodal displacements were decomposed into pseudo-static and dynamic parts, respectively with the relative motion method, while the nodal displacements were solved directly with the absolute displacement solving method. The damping was proportional to the relative velocity in relative motion method, but the damping was proportional to the absolute velocity in the method of directly solving absolute displacement. The different damping assumptions may cause calculation errors on structural responses. The theoretical analysis based on random vibration showed that the structural response power spectral density errors obtained with the two solving methods are caused by mass damping, and affected by damping ratio and the ratio between excitation frequency and fundamental frequency of the structures with Rayleigh damping. The damping forces are determined by the nodal velocity difference with element damping model, and the nodal velocity difference are equal in the two solving method, so the calculation errors don't exist using element damping model.