Structural dynamic responses of linear structures subjected to Kanai-Tajimi excitation

Abstract

Aseismic design of building structures is desired to protect them from the disasters associated with earthquakes, which has caused serious casualties and huge economic loss to human society. In this study, an analytic method based on complex modal method (CMM) and pseudo excitation method (PEM), named as CM-PEM, is proposed to solve the spectral moments and variance of structural responses subjected to Kanai-Tajimi excitation. Kanai-Tajimi excitation is firstly represented by white noise excitation through the application of filtering equation, and the basic dynamic equation is decoupled into first-order differential equations with independent complex modal variables by using CMM. Then the unified explicit expressions of the both dynamic response and its power spectral density function (PSDF) are obtained by PEM and introducing generalized variables. Because the PSDF of structural response only contains variable term 1/(pi2 + ω2), which can be integrated to obtain closed-form expression of (0–2)-order spectral moments, when the variable term multiplies with ωi (i = 0, 1). Finally, in order to verify the accuracy and efficiency of the proposed method, a 6-storey structure is investigated by comparing with traditional PEM, with respect to PSDF of ground excitation, PSDF and spectral moments of dynamic responses.