Dynamic analysis of damping structures considering support stiffness

An analysis method for the random seismic response of viscoelastic damper structures with support is proposed. This method considers the influence of support stiffness and analyzes the dynamic characteristics associated with support stiffness. It also combines the advantages of the complex modal method (CMM) and the pseudo-excitation method (PEM), improving the complex integration operation in calculating the spectral moments and variances of random seismic responses. The support and the viscoelastic damper constitute the equivalent damper. The damper's constitutive relationship and structural dynamic equations are decoupled to calculate conveniently the frequency domain solution of the responses. Second, the quadratic decomposition of the power spectral density function (QD-PSDF) is applied to simplify the power spectrum and obtain the closed-form solution of spectral moments and variances. Finally, the structural dynamic characteristics and the influence of support stiffness on the vibration control effect of the equivalent damper are investigated based on the closed-form solution. The structural dynamic reliability is also discussed according to the first excursion failure criterion. The results demonstrate that the damper's control effect and structural reactions are reduced, while the dynamic reliability is also enhanced when increasing support stiffness. The performance of the structure and damper tends to stabilize when the support coefficient reaches a specific level.