Study On The Nonlinear Systems With Dry Friction

Due to the rapid development of China's military industry,traditional linear isolator can not meet the requirements in the fields of aerospace and others.In the perspective of new vibration control method,active vibration control and semi-active control can meet the requirements perfectly.However,the disadvantages of them are also very obvious: high prices,large volume,and external power supply.All of these limited the application of this technology.And the non-linear vibration isolator,such as metal rubber isolator,has the advantages of small size,great vibration isolation,and resistance to storage.All of these adavantages makes it become a profect alternative to linear isolator.However,due to the lack of corresponding analytical expressions in the mathematical equations of the nonlinear isolators,the development of nonlinear isolators is limited.Based on the actual demands,this paper explores the kinematic characteristics of three kinds of isolation system including dry friction damping and non-linear stiffness from a theoretical perspective.The first-order approximate analytical solutions of the three models are obtained by the average method.According to the obtained analytical solution,the influence of various parameters on the isolation effect and the motion state of the system are explored,and the stability domains of the corresponding system are analysised.According to the theoretical results,the optimization of three kinds of vibration isolators are completed.Finally,experiments are conducted to test the performance of the optimized isolators and verify the correctness of the theoretical model and inference.(1)Theoretically analyzing the motion characteristics of a single-degree-of-freedom nonlinear system with dry friction damping under the Coulomb model: this paper analyzes how the Coulomb damping influence on the motion of the system at low frequencies.And the feasibility of achieving no resonance is discussed.The effects of Coulomb's damping,non-linear stiffness and viscous damping on the non-resonance are also discussed.The optimal dry friction value for the non-resonance of the soft spring system is deduced,and a phemonemon called “residual resonance peak” in a hard spring system after realizing non-resonance is explained.By the way,the parameters of the GWF isolator are optimized based on the theoretical results.Experiments match well with the theoretical results and show that the optimized isolator has good performance.(2)Theoretically analyzing the kinematics of a single-degree-of-freedom nonlinear system with dry friction damping under a hysteretic loop model.Considering the elastic deformation of the friction plates before sliding friction emerged,and obtained the frequency-response functions before and after the emergence of sliding friction respectively.How the dry friction damping influence on the system motion at low frequency is discussed in the hysteretic loop model.The viability of realizing nonresonance is discussed respectly when the system is “locked” or “unlocked”.The influences of parameters,such as the stiffness of friction plates,dry friction damping,third-order nonlinear stiffness,and viscous damping on the effect of non-resonance are also discussed.In addition,based on the theoretical results,parameter optimization of the single-degree-of-freedom metal rubber isolator is completed.Experiments match the theory and show that the isolators work well.(3)Theoretically analyzing the motion characteristics of a two-degree-of-freedom nonlinear system with dry friction damping under the Coulomb model.The average method is used to obtain the frequency-response function of the system,and the relationship between the amplitude of the two moving objects in the model and the relationship between relative displacement and absolute displacement are obtained.The effects of Coulomb damping,nonlinear stiffness and other parameters on the effect of vibration isolation are discussed.In addition,according to the theoretical results,the design and parameters optimization of the two-degree-of-freedom metal rubber isolator are completed.The experimental results show that the vibration isolator has good vibration damping performance.This paper explores the motion characteristics and main features of three nonlinear dynamic models with dry friction damping from a theoretical perspective.The effect of parameters on its vibration isolation are deduced analytically.And the theoretical results are used to optimize three kinds of nonlinear vibration isolator.The research results in this paper can provide a theoretical reference for the design and optimization of nonlinear vibration isolator,shorten the design cycle,improve product quality,and can further promote the engineering application of nonlinear vibration isolator.