Dynamic Response Algorithm Design And Analysis With Controllable High Frequency Dissipation Based On Discrete Control Theory

As an emerging test method,real-time hybrid test has received extensive attention in recent years due to its advantages of combining numerical simulation and test loading.The test technology combining test and numerical simulation also puts forward higher requirements on the test conditions: efficient and stable numerical integration algorithm,high-precision boundary condition simulation method,general test software and loading platform,etc.Based on the discrete control theory,an explicit and unconditionally stable numerical integration algorithm for structural dynamics was designed using the transfer format of an explicit algorithm,and the performance of the algorithm in real-time hybrid experiments was studied.The specific research work includes the following aspects:(1)This paper sorted out the research status of numerical integration algorithms for structural dynamics in recent years and the performance of a variety of commonly used dynamics numerical algorithms,introduced the importance of numerical algorithms for real-time hybrid experiments and their applications in hybrid experiments,summarized the content that needs to be further studied in the numerical integration algorithm of dynamics,and elaborated the purpose and significance of the research of this thesis.(2)The relevant principles of discrete control theory was introduced in numerical integration algorithm design and the main steps of discrete control theory algorithm design.Regarding the algorithm performance as the design purpose,two explicit transmission formats were selected,namely the displacement and velocity transmission formats of the CR(Chen and Ricles)method and the RST(Real-time Substructure Testing)method,and the zero amplitude attenuation rate,zero period extension rate and unconditional stability were used as the conditions for the algorithm derivation of an explicit new algorithm.This paper compared the two transfer formats,analyzed the accuracy and stability,and verified the performance of the algorithm through numerical simulation.The results show that the algorithm designed with the transfer format of the CR method has more advantages in performance such as accuracy,and the subsequent chapters will use the transfer format of the CR method to design the algorithm.(3)Based on the discrete control theory and the transfer format of CR method,an unconditionally stable explicit new algorithm with controllable numerical dissipation was designed.Algorithm derivation took controllable numerical dissipation as a known condition,derived algorithm parameters and poles through Z-transform and discrete transfer function characteristic equations,and introduced coefficient adjustment algorithm accuracy and nonlinear stability intervals.The parameters corresponding to multi-degree-of-freedom systems were derived.The results of theoretical analysis and numerical example analysis show that the new algorithm has good accuracy and stability,and its accuracy and stability are adjustable,and it can filter high frequency response well.When the appropriate coefficients are selected,the algorithm is equivalent to CR method.(4)The new algorithm designed in the previous chapter was used as a real-time hybrid test numerical algorithm,and compared with the real-time hybrid test Chang algorithm,the real-time hybrid test center difference method and the CR method.Considering the accuracy,linearity and non-linear stability,the influence of different nonlinearity,etc.,the performance of the four algorithms applied in real-time hybrid experiments was compared,and theoretical analysis and numerical simulation verification were carried out.According to the analysis results,suggested values for the coefficients of the new algorithm suitable for different systems were given.The results show that in the real-time hybrid test,the new algorithm and CR method are unconditionally stable for linear systems and nonlinear stiffness softening systems,while for nonlinear stiffness hardening systems,they are conditionally stable,and the stability limit is not affected by the structural damping ratio;both the real-time hybrid test Chang algorithm and the real-time hybrid test central difference method are conditionally stable for linear and nonlinear systems.At the same time,the new algorithm has obvious advantages in accuracy.