Theoretical And Experimental Research On Parameter Identification And Time-history Analysis Of A Convolutionary Damped System

Damping is to dissipate the energy in a vibrating structure. The mechanism of structural damping is very complex, therefore it's often sketched and described by a simple mathematical model, and the parameters of the model are determined according to a certain principle of equivalent response in practice. During the last 100 years, many assumptions have been put forward for damping phenomena, and each one has its own merit and analysis methods. The viscous damping model has been widely applied in practical engineering and research field as it results in a simple equation of motion which can be conveniently analyzed. It is however, well known that the classical damping model is a mathematical idealization and it could not completely reflect the complex energy dissipation behavior of practical structure and new materials. Therefore, improving or further studying other damping models become an important subject of civil engineering related researches to make analysis of systems with different materials and structures possible.A convolutional type non-viscously damping model is studied in this paper. Firstly, an identification algothrim of the damping coefficient matrix about this damping model is derived, and subsequently, the dynamic time-history analysis of system with the non-viscous damping is studied. The performance test of a domestic viscoelastic material is carried out and the method for determining the parameters of the non-viscously damping model is given. Finally, through a shaking table test of two-story reinforced concrete frame, the above parameter identification and numerical analysis algorithms are verified. The main contents are included as follows:Firstly, the Laplace transform is applied to the viscous-damped and non-viscous damped multi-degree system respectively. By a complex modal analysis to the dynamic system, the formula of the mode frequency and mode shape of damped system are derived, and their connection to the characteristic parameters of the non-damped system is established. Finally, the identification methods of damping coefficients of the viscous-damped and non-viscous damped system are derived, respectively Secondly, the introduction of non-viscous damping model prevents the presnt dynamic analysis methods for viscous-damped system from application in non-viscous damped systems. The Taylor expansion method for the second type Volterra Integral Equations is introduced, and the response function of the system at each time point is approximated by Taylor series, which is substituted into convolutional kernel function of the non-viscous damping model to eliminate the integral part. By solving the derived time-varying linear equations, a discrete algorithm for time-history analysis of non-viscous damped system is obtained.Thirdly, based on the state space expression of equations of motion of non-viscous damped proposed by Wagner, the precise integration technique proposed by Wanxie Zhong is employed to numerically solve the state-space equation, and a higher accuracy time-recursive expression about the state vector is acquired. To avoid the error and ill-conditionness in the inverse matrix operation in precise integration technique, the Gauss-Legendre quadrature is introduced, then a modified precise integration technique without the inverse operation of matrix is obtained, which improves the practicality of the method.Fourthly, according to the rheological constitutive relation of the polymer materials and the physical meaning of non-viscous damping model, viscoelastic materials are selected as the object to which the damping model is applied. Based on the requirement for afterwards shaking table test, a number of small viscoelastic dampers are designed and fabricated by ZN-22 viscoelastic materials. More than 70 groups of sinusoidal cyclic loading tests are performed , and the mechanical properties of the material that varies with ambient temperture, exciting frequency and strain amplitude are determined. By mechanical relationship between the viscoelastic material parameters, the non-viscous damping coefficient and relaxation parameter in the non-viscous damping model is derived.Lastly, through the shaking table test of a 1:4 scale two-story reinforced concrete frame structure with viscoelastic dampers, the capability of convolution type non-viscous damping model in describing the damping mechanism of viscoelastic structures are demonstrated. The effectiveness and practicality of the methods proposed for model parameter identification and numerical dynamic respose analisys for the non-viscous damping system are validated.