Parameter Optimization And Dynamic Analysis Of Nonlinear Dynamic Vibration Absorbers

In the process of vibration control,dynamic vibration absorber is one of the commonly used methods,which has the advantages of simple structure,various realization forms,and convenient installation.Therefore,it is often used to reduce vibration in mechanical equipment and engineering structures,and has broad application prospects.The diversity of types,numbers,and installation positions of damping elements provides different design ideas for improving the DVA model.On the other hand,the selection of appropriate parameters is an important means for the dynamic vibration absorber to exert the best vibration reduction effect.In order to improve the vibration absorption performance of DVA,this thesis improves the existing dynamic vibration absorber model and optimizes the system parameters.The main research contents are as follows:(1)A dynamic vibration absorber model including lever,inerter and grounding stiffness is proposed.The optimal tuning ratio,the optimal stiffness ratio and the approximate optimal damping ratio of the system are solved obtained by applying the H∞ optimization criterion and the fixed point theory.On the premise of ensuring that the optimization results have physical meaning,the optimal working range of the inerter is analyzed.The correctness of the results is verified by comparing the numerical solution with the analytical solution.Under harmonic and random excitations,it is verified that the system has a good vibration reduction effect compared with the existing models.(2)The relationship between the main system response amplitude and excitation frequency of nonlinear vibration absorber with cubic stiffness is analyzed by harmonic balance method,and the monadic cubic equation about the amplitude of the main system is obtained after simplification.Based on the criterion of Cardan discriminant,an analytical expression for determining the multi-solution range of the system is obtained,and the correctness of the conclusion is verified by comparison with the numerical solution.Finally,the correlation between each parameter and external excitation in the NES and the vibration response of the main system is investigated by using the method of control variables.(3)Introducing amplifying mechanism,inerter and grounding stiffness into the traditional NES,a new type of leverage-type inerter-grounding stiffness NES is proposed.The unary cubic equation about the vibration response amplitude of the system is solved by using the harmonic balance method.Then,the number of multiple solutions of the system is judged according to the Cardan discriminant,so as to obtain the jump interval of the system.Using MATLAB to draw the amplitude-frequency response curves of the analytical solution and the numerical solution,the comparison proves the correctness of the conclusion.Then,under simple harmonic and random excitations,it was compared with the existing lever type NES to prove that the model has the best vibration reduction performance under the same conditions.The research content of this thesis is summarized at last,raising several unresolved issues and providing a reference direction for the follow-up research.