Structural dynamic responses of building structures with non-viscous dampers under Kanai–Tajimi spectrum excitation

Abstract

Non-viscous dampers are commonly used in building structures for seismic energy dissipation. In this study, a concise analytical method based on the pseudo-excitation method (PEM) was proposed to obtain closed-form solutions of the structural responses of a non-viscous damper system subjected to the Kanai–Tajimi spectrum excitation. For this purpose, first, the ground motion equation of the non-viscous damper system was decoupled using the complex model method (CMM), and the solution expressions for the dynamic responses were unified using the PEM. Second, the power spectral density function (PSDF) of the Kanai–Tajimi spectrum was quadratically orthogonalised using the residue theorem, which was combined with a quadratically orthogonalised frequency response eigenvalue function (FREF) to obtain a quadratic orthogonalised PSDF (QO-PSDF) of the dynamic responses. Subsequently, a concise closed-form solution of spectral moments and variances of the dynamic responses were successfully obtained using the QO-PSDF. Finally, a comparative study was conducted with three test cases to compare the results of the direct frequency response method, traditional PEM, and proposed method, which proved the applicability of the QO-PSDF and the accuracy of the quadratically orthogonalised PEM (QO-PEM). Moreover, the calculation time required in the proposed method was found to be approximately th one-third at of the traditional PEM.