Methods Of Decouping In Real Spaces And Earthquake Action Calculation For Asymmetri Mass Matrix And Non-Classically Damped Structures And Its Application In Multilayer And High-Rise Isolated Structures

The isolation and other passive control structures have the long cycle and high damping performance, and they cannot meet the applicable conditions defined in the specification that the small damping met by the maximum inertia force generated in the process of seismic response of structure. Based on the equivalent standard of structural static effect and maximum dynamic effect, a new definition of the response of engineering structure based on the maximum displacement between the layers of the structure is proposed.The complex mode method is used to decouple the structure with asymmetric mass matrix and non-classical damping into an analytical expression of a series of equivalent SDOF systems. By means of solving the inter-story displacement of upper structure, TMD and other sub-structure relative to the main structure displacement or the relative displacement between the isolation layer and the ground displacement and the inter-story displacement of upper structure is written in a unified expression. By using random vibration theory, the mean-square values of structural displacement random response are decomposed of linear combination of mean-square values of displacement and velocity random response of serial standard oscillators according to the CQC modal combination, so that the problem of complex mode method use the analytical solution of random seismic response of the equivalent SDOF system only be taken into consideration in accordance with the principle of SRSS modal combination to solve the structure with asymmetric mass matrix and non-classical damping of the displacement response variance and seismic action is resolved.The decouping in real spaces and earthquake action calculation of the structures with asymmetric mass matrix and non-classical damping was proposed. The structural response equations with non-classical damping and asymmetric mass matrix are firstly decoupled exactly by complex mode method;Then, by configurating transformation of complex response and real response and using Laplace Transform,the exact decoupling method of asymmetric mass matrix and non-classically damped structure in real spaces is established,the structural displacement response are exactly decomposed of linear combination of displacement and velocity response of serial standard oscillators,all correlation characteristics of displacement and velocity response of serial standard oscillators are considered,the mean-square values of structural displacement random response are exactly decomposed of linear combination of mean-square values of displacement and velocity random response of serial standard oscillators,the exact solutions of structural collelation combination coefficients are given.Lastly, according to the mutual relationships between displacement maximum response of serial standard oscillators and response spectrum and based on the maximum displacement between the layers response of seismic action definition, the analytic solutions of displacement maximum between the layers response and earthquake action of structures with asymmetric mass matrix and non-classical damping basis on response spectrum are given. Through its application in the isolated structure, and examples are given, which vertify that the proposed methods are correct, so the complete analytical methods of decoupling in real spaces and earthquake action calculation for asymmetric mass matrix and non-classically damped structures are established. The proposed methods are general methods, and it takes only numerical solution structure of the complex eigenvalue and complex feature vector, the others all is analytic solution.The approximate real modal decoupling method is introduced into the analysis of isolated structure. The structural response equations with non-classical damping and symmetric mass matrix are firstly approximate decoupled by method of approximate decouping in real spaces,the structural displacement and velocity response are decomposed of linear combination of displacement and velocity response of serial standard oscillators. Then, by random vibration theory,the mean-square values of structural displacement random response are decomposed of linear combination of mean-square values of displacement and velocity random response of serial standard oscillators. Lastly, according to the mutual relationships between displacement maximum response of serial standard oscillators and response spectrum,the analytic solutions of displacement maximum between the layers response and earthquake action of isolated structures basis on response spectrum are given, so the approximate analytical methods of approximate decoupling in real spaces and earthquake action calculation for non-classically damped isolated structures are established. Results show that the approximate decoupling method has a clear significance and easy to master, and has a higher solution precision, and it is suitable for engineering applications.