Study On The Analysis Method For Seismically Isolated Structures Considering The Non-classical Damping

As an effective strategy to enhance structural resistance to earthquakes,isolation techniques have been increasingly adopted in building structures and have achieved good isolation effectiveness.The damping distribution of the isolated structure has obvious non-classical properties,thus,the damping model of isolated structures have significant impacts on the accuracy of structural dynamic analysis algorithms,the reasonableness and applicability deserve attention.On the other hand,the widely used aseismic design methods in many codes are based on the assumption of classical damping,so that the widely used aseismic design methods is no longer applicable for seismically isolated structural systems.Thus,it is necessary to conduct further research on the seismic analysis method for isolated structures.In this paper,the seismic response of isolated structures is studied by theoretical modelling and numerical analysis.The research findings are drawn as follows:1.A new scheme is proposed for determining the damping matrix for isolated structures,and general expressions of the damping matrix of the superstructure and the damping constant of the isolation layer are presented.The influence of isolated structures is analyzed by considering different methods to construct the damping matrix of isolated structures,and the effectiveness of the proposed damping matrix is verified by comparing it with the existing damping matrix methods.The results show that the proposed method to form the damping matrix of isolated structures has been developed that can accurately reflect the damping properties of the isolated structure.Additionally,the direct use of the Rayleigh damping matrix of superstructures for isolated structures was found to cause an overestimation of the damping effect and consequently underestimate the deformation of the superstructure.Therefore,adopting the damping matrix method of the isolated structure proposed in this paper is suggested.2.The proposed damping matrix also can determine the equivalent load associated with the coupling damping between the structure and the support when the displacement-velocity input model is used.The analysis results are consistent with the acceleration input model by using the displacement-velocity input model,so the displacement-velocity input model should be used instead of the traditional displacement input model.The displacement input model generally overestimates the isolation deformation and underestimates the response of the superstructure.It is also found that the relative displacement results become more and more serious as the damping of the isolation bearing increases.3.Based on the proposed method to form the damping matrix of isolated structures,the applicability of the damping matrix proposed in this paper is analyzed in different response spectrum methods.On this basis,an improved complex response spectrum method(ICM-RSM)is introduced that integrates equivalent linearization with complex mode theories.A numerical investigation is conducted to demonstrate the feasibility and effectiveness of the proposed method.The results show that the proposed method has the advantages of simple calculations and high accuracy.Under the near-field and far-field ground motions,in contrast to the traditional analysis method,the proposed method still has good calculation accuracy of the BI structure under natural ground motion.4.A real-complex hybrid modal response spectrum method(RCHM-RSM)for the design of seismically isolated structures is proposed in this paper.In addition,an iterative analytical procedure is introduced that integrates equivalent linearization with real and complex mode theories.While accounting for the dynamic interaction between isolation bearing and superstructure during the calculation,thus,it can be better reflect the practical response of isolated structures.On the other hand,the seismic response of the isolation building is computed by applying the modal analysis to the superstructure only,which is typically considered as a classically damped system,avoiding the problems of large amount of calculation by complex modal analysis.The research results show that the use of the proposed RCHM-RSM can effectively improve the analysis accuracy of the base-isolated structure,which possesses the advantage of high performance,high efficiency,flexible and ease of use.5.The superstructure of the isolated structure can be idealized as distributed parameter systems.Based on Timoshenko and Bernoulli-Euler theory,the motion equations of the isolated structure are established.A distributed parameter system of isolated structures is developed to investigate the impact of the proposed method on the solution accuracy,by considering various damping characteristics of the isolation bearing and distributed-parameter models.In this study,a novel real-complex hybrid modal response spectrum method for the distributed parameter system of isolated structures is proposed based on Timoshenko and Bernoulli-Euler theory,which only applies the modal analysis to a superstructure,avoiding the complex boundary conditions for the isolated structure.In contrast to the traditional complex modal response spectrum method,the real-complex modal response spectrum is more effective and easier to understand.A model with a distributed parameter system of BI structures is developed to investigate the impact of the proposed method on the solution accuracy,by considering various damping characteristics of the isolation bearing and distributed-parameter models.Numberical results show that the proposed method demonstrated its advantages of simple calculations and a high accuracy,and therefore improves the analysis accuracy and reliability.The calculation accuracy of real-complex modal response spectrum had a high level for higher damping situations.