Axial Vibration Reduction Of Shaft Structure Using Centrifugal Pendulum Absorber With Inerters

The vibration of shaft structure is one of the main vibrations of the engine.It will affect the life and the efficiency of the machine and even cause damage.Thus,how to effectively suppress the vibration of shaft structure is an important issue.In the present thesis,a centrifugal pendulum absorber with inerters is proposed to reduce the axial vibration of shaft structure.Firstly,an axial nonlinear dynamic equation of shaft structure subjected to external excitation is established.Based on low-amplitude vibration of the pendulum,an axial linear dynamic equation of shaft structure subjected to external excitation is further established.Then,for the cases that shaft structure is subjected to harmonic excitation and random excitation,the analytic method is used to analyze the axial vibration absorption of shaft structure using a centrifugal pendulum absorber with inerters,as well as the optimization of absorber parameters.In the situation of harmonic excitation,the optimization objective is to minimize the resonant amplitude of axial vibration of shaft structure.By using fixed-point theory,the optimal non-dimensional damping is analytically expressed.The tuning function has a significant effect on axial vibration,and maximum vibration reduction can also be achieved with a proper tuning function.Moreover,with the application of torsional inerters in an absorber,the tuning function can be easily adjusted.In the case of random excitation,the optimization objective is set as minimizing the mean square value of structural displacement of axial vibration of shaft structure.When the random excitation is Gaussian white noise,it is found that there are an optimal non-dimensional damping and optimal pendulum-dependent tuning function,and the inerter-dependent tuning function and mass ratio have a great influence on axial vibration reduction.While for wide-band noise excitation,the optimal inerter-dependent tuning function can be obtained,and the non-dimensional damping has a significant effect on axial vibration reduction.Furthermore,the effect of axial vibration absorption of the centrifugal pendulum absorber with inerters is compared with that of a dynamic vibration absorber,and it is illustrated that vibration reduction effect of the optimized centrifugal pendulum absorber with inerters is much better.In addition,numerical simulation method is applied to solve the axial nonlinear vibration equation of shaft structure using a centrifugal pendulum absorber under three kinds of excitations,i.e.,harmonic excitation,Gaussian white noise excitation and wide-band noise excitation,respectively.The resonant amplitude of axial vibration of shaft structure under harmonic excitation and the mean square value of the axial displacement of shaft structure under random excitation can be obtained.By comparing the numerical results of linear system and the nonlinear system,the validity of the linear system is illustrated.The valid ranges of the inertance and horizontal distance from the center of centrifugal pendulum to the pivot for the linear system are discussed in detail.