Parameter Optimization Of A New Ball Type Dynamic Vibration Absorber Under Random Excitation

The new ball type dynamic vibration absorber does not need external power source,it can not only absorb vibration in multiple directions,but also overcome the influence of external excitation amplitude of the vibration absorption system on the natural frequency of the vibration absorber.The design parameters have a direct influence on the vibration absorption effect of the main system.The external excitation of vibration absorber can be divided into simple harmonic excitation and random excitation according to the function relation.Since the external excitation of mechanical equipment and engineering structure is mostly random in the actual working condition,the parameter optimization of the new ball type dynamic vibration absorber under random excitation is of certain practical significance to the development of dynamic vibration absorber.In this paper,the parameter optimization problem of the new ball type dynamic vibration absorber with external excitation as random excitation is studied.The main contents include:(1)The basic theories and methods of random vibration are discussed,such as the analysis of typical random processes and stationary processes through linear systems,and the response of single-degree-of-freedom systems to random excitation,etc.,which provide a foundation for the analysis of vibration absorption systems under subsequent random excitation.(2)Common optimization methods are discussed,such as analytic method,iterative method and intelligent optimization algorithm.The classical algorithm,Newton iteration method and particle swarm optimization algorithm are selected,and their basic principles and optimization process are learned,which provide references for subsequent selection and appropriate optimization algorithm.(3)The vibration absorption principle of the new ball type dynamic vibration absorber is introduced,and the motion equation of the vibration absorption system is obtained.When the external excitation is simple harmonic excitation,the maximum amplitude minimization of the main system is selected as the optimization objective,the damping of the main system is ignored,and the influence of various parameters of the vibration absorbing ball on the amplitude of the main system is analyzed.Considering the damping of the main system,the optimal numerical solution of the parameters is obtained by using the particle swarm optimization algorithm.(4)The external excitation of the dynamic absorber is regarded as the ideal white noise,and the minimum energy of the vibration absorbing system is selected as the optimization objective.When the damping of the main system is not considered,the optimal analytical solution of each parameter of the vibration absorbing ball is obtained according to the mathematical idea of extreme value,and the vibration absorbing effect is analyzed and compared with the optimal analytical solution under simple harmonic excitation.When the main system is damped,the optimal numerical solution of the parameters of the desorption ball is obtained by using Newton iterative method,and the effect of the damping of the main system on the vibration absorption of the system is analyzed and compared with that of the optimal numerical solution under simple harmonic excitation.