Analytic Methods Of Decouping In Real Spaces And Earthquake Action Calculation For Shear Beam Model Isolated Structures

In this paper, the partial differential equations for the middle-low isolated shear beammodel with an equal cross-section and a variable cross-section are established. By usingthe first mode expansion, the partial differential equations of the infinite degrees offreedom of the continuous system are converted into multi-degree-of-freedom equationsof motion of a discrete system. By using the real space, the equations are decoupled into aseries of single-degree-of-freedom equations of motion. Due to the highly non-classicalcharacteristics and non-ignorable higher modes of the isolated shear beam model with anequal cross-section and a variable cross-section, using the asymmetric and non-classicalstructural equations of motion expanded by multiple modes and the real-space decoupling,the structural seismic response analytical expression is obtained, and the originalmulti-degree-of-freedom isolated shear beam structure is broken down into a series ofequivalent single degree of freedom system.The relative ground displacement of isolation layer and superstructure shear functionare written in a unified expression. By using the random vibration theory, the analyticalexpressions of random response variance of the structure displacement and shear randomresponse variance are broken down into a linear combination of the displacement andvelocity random response variances of a series of standard oscillators, so that the problemis resolved; Finally, by using the corresponding relationship between the maximumresponse and response spectra of a series of standard oscillators, the analytic method forthe maximum response of the displacement and shear and their equivalent staticearthquake value of isolation shear beam model with an equal cross-section and a variablecross-section based on the acceleration response spectrum of the seismic code, so that thecomplete analytical solution for the real-space decoupling and response spectrum-basedearthquake value of isolated shear beam model with an equal cross-section and a variablecross-section considering higher modes is established. Meanwhile, the proposed method isfully applicable to the random wind-induced response and equivalent static wind loadvalues of building under the passive control. Finally, the analytical solution ofnon-classical damping structure under passive control based on the real-space decouplingmethod and its equivalent earthquakevalue has been fully resolved.