Dynamic Analysis And Parameter Identification Of Exponential Damping Linear System

Damping,as an important factor to describe the energy dissipation of vibration systems,has been paid attention to by the theoretical and engineering circles.The rationality of damping models used in the process of structural dynamic analysis has a great influence on the accuracy and reliability of the analysis results.In these models,the viscous damping model has been widely used in engineering due to its simplicity of theoretical analysis and numerical solution and has matured;however,the energy dissipation calculated by this model is related to the external excitation frequency,which is not consistent with some experimental phenomena,thus the researchers put forward some new damping models on this basis to meet the needs of increasingly complex engineering materials and structure analysis in the engineering field.Due to the increasing research on the non-viscous damping model in recent years,this paper chooses to study the exponential non-viscous damping model,and the dynamic analysis and modal parameter identification of the model are studied systematically.The main contents and research results are as follows:(1)The mode-superposition method of exponential damping linear system is discussed.A general formula,for calculating seismic time history response of the exponential damping linear system,is deduced based on the algorithms of the complex superposition method and the state-space method.Meanwhile,the expressions of horizontal seismic action of the system at each mass point under each mode are developed based on the general formula,so that the traditional reaction spectrum analysis method can be extended from viscous damping system to exponential non-viscous damping system.The basic steps of response spectrum analysis of exponential damping linear system based above procedure,make the seismic design process of exponential damping system simplified,which is consistent with the design process of reaction spectrum of general viscously damped system.(2)A method of identifying modal parameters in exponential non-viscous damping systems on the basis of modal test is proposed.By solving a constrained optimization problem,the optimal modified damping coefficient matrix satisfying the system characteristic equation is obtained;and considering the non-completeness of the modal parameters obtained in the actual mode test,the damping coefficient matrix of the system can be accurately identified by using the limited low-order modes.Whereas with the gradual enhancement of the non-viscous characteristics of the system,the number of modes needed to accurately identify the damping coefficient matrix will gradually increase.(3)A method of updating the imaginary part of the complex mode-which can be greatly affected by noise in the modal test-is proposed to satisfy the characteristic equation of the exponentially damping linear system in this paper;and as a result,the damping coefficient matrix can be accurately identified by using the updated complex-modal imaginary part.Since the less research on the recognition of the relaxation parameter,the identification methods of relaxation parameter which is independent of the imaginary part of complex mode is proposed in this paper.(4)The cross tests of the pseudo-static and hammering vibration test are carried out in this paper for two cantilever beams with C35 concrete and high damping concrete respectively.Based on the frequency response function,the trends of the basic frequency and damping ratio of the high damped concrete cantilever beam with damage is studied;and the relationship between the dynamic characteristics and the damage of the cantilever beam is established.The results show that with the increase of control displacement,the basic frequency of the two cantilever beams decreases gradually,and the first order damping ratio increases at first and then decreases.The damping ratio of high damping concrete cantilever beam in inelastic stage is significantly higher than that of C35 concrete ones.The relationship between dynamic characteristics of concrete cantilever beam and damage is closely related to the cracks and plastic development of cantilever beam.By using the methods proposed in this paper,the exponential non-viscous damping coefficient matrices of the two test cantilever beams are identified;and the relaxation parameters are recognized;the damping properties of the two test beams are explored,and the applicability and rationality of the exponential damping model compared with the Rayleigh damping model are investigated.