Exponential Damping Model And Its Applications To Dynamic Analysis Of Reinforced Concrete Structures

ABSTRACT:Damping is one of the most important dynamic characteristics in a vibration system. During the last hundred years, various assumptions of damping models have been proposed for damping phenomena and each one has its own dynamic analysis method and application scope. In engineering practice, viscous damping model is widely employed to characterize damping properties of vibration systems for its mathematical simplicity. However, this model assumes that the damping force is dependent on the instantaneous generalized velocity and implies that energy dissipation per cycle is linearly proportional to the frequency. It can not truly represent the complicated damping dissipation characteristics in many engineering materials or structures. Therefore, further studying other damping models, which can better describe the damping characteristics of vibrate system, and its corresponding dynamic analysis methods would be a significant subject in civil engineering and other related areas.In this paper, aimming at solving the limitations offered by the classical viscous damping theory in describing damping characteristics of solid materials, a more suitable exponential damping model is introduced to describe the damping dissipation characteristics of concrete which is a weakly-viscoelastic material. Based on the further discussion on the damping dissipation mechanism of solid materials, dynamic equations with such exponential damping model are established through theory analysis, and fundamental techniques are developed for the analysis and identification of exponentially damped structural systems. Finally, through experiment research, the relaxation factor of concrete material is determined and the flexibility of exponential non-viscous damping model in describing the damping properties of concrete material is demonstrated. The main contents are included as:Firstly, the complex damping theory on describing energy dissipation characteristics of solid materials are studied with discussing its dynamic analysis methods and existing problems in mathematical description. Based on the dual principle of complex damping theory, a new direct time-history integration schemes are presented to solve the vibration systems with complex damping, which combines the Gauss quadrature with the calculation technique of matrix exponential function in the precise time-integration method. The stability condition of time-history method for complex damping systems is further studied. Secondly, the direct time-domain integration methods for exponentially damped systems are studied. Based on an unconditionally stable differential quadrature method, a new direct integration method for such non-viscously damped systems is proposed, which has the advantages of high efficiency high accuracy and extensive applicability.Thirdly, Frequency-domain analysis of linear systems with exponential damping is conducted. According to the Discrete Fourier Transformation (DFT), in which the pseudo-force approach is used for considering the non-zero initial conditions, the DFT method combined with Fast Fourier Transform (FFT) algorithms is effectively extended to the exponentially damped systems. The obtained frequency-domain analysis method is quite general for the exponential damping model.Fourthly, Based on quasi-variational principle, the equations of motion of exponentially damped systems are established through the theoretical derivation, which provides theory support for later proposed identification method of exponential damping parameters.Fifthly, aimming at the disadvantages of current identification methods of exponential damping model, a kind of exponential damping model with proportional damping coefficient matrices and a new iterative calculation method for its relaxation factor are proposed. Combined with the finite element model updating method, the validity of the proposed method is demonstrated by numerical experiment.Finally, vibration test of a group of reinforced concrete cantilever beams are studied. The damping parameters for concrete material are determined by using the identification method of exponential damping model proposed in the dissertation. The flexibility of the proposed exponential damping model in describing the damping mechanism of the concrete which is a weakly-viscoelastic material is demonstrated. Meanwhile, the validity and the correctness of algorithms in the chapters are also validated.