Study On Hybrid Control Method Of Structural Vibration Reduction With Viscoelastic Damper

In the field of structural vibration control,the hybrid control system with both passive and active damping devices has the comprehensive advantages of safety,economy and strong adaptability,and the related theoretical research and engineering application are increasing.In this paper,the viscoelastic damper,which is widely used as a passive damping device,is taken as an example to study the optimal control force design of additional active damping devices of related structures under earthquake.In this paper,the high-precision linearization method for solving the dynamic response of structures with viscoelastic dampers and the active control algorithm of linear equivalent structures are studied in turn,and the following innovative achievements are obtained.(1)To solve the nonlinear dynamic response of viscoelastic damper structure with fractional derivative model,an accurate direct numerical integration method is proposed by introducing Caputo fractional derivative and Adams-Moulton solution technology,and as an accurate reference solution,the calculation error of traditional fundamental frequency equivalent method is compared and investigated.(2)Based on the multi-order frequency correlation of viscoelastic damper performance,a high-precision linearization method for solving the dynamic response of structures with viscoelastic dampers,namely Sequential Modal Equivalence and Synthesis(SMES)method,is proposed.The quasi-orthogonal modal space is constructed,the additional modal damping ratio is determined,and the structural dynamic response is calculated by modal superposition.The calculation accuracy of this method is better than that of traditional fundamental frequency equivalent method,and the calculation efficiency is better than that of direct numerical integration method.Based on SMES method,a time-domain explicit method based on modal superposition scheme is further proposed,which can be used for efficient analysis of random seismic response of structures with viscoelastic dampers.(3)To solve the hybrid control problem of viscoelastic damper damping structure,firstly,the linear structural equivalence of viscoelastic damper damping structure is carried out by SMES method.Then,by considering the linear quadratic dynamic performance functional of earthquake excitation and control force aftereffect,the formula of optimal control force for active control is derived by using modal superposition method and time domain explicit method,which can realize high-precision feedforward control and feedback control.