Dynamics And Vibration Suppression Of Nonlinear Energy Sink Systems

Nonlinear energy sink has wide application prospect because of its simple structure,small additional mass and high absorption efficiency.In this thesis,several kinds of systems with NES are analyzed.The main contents are as follows.A two DOF dynamic system of main structure coupled with NES is established.Stability of fixed point and dynamics are analyzed by numerical simulation and Jacobi matrix based on complexification-averaging method.The influence of NES parameters on amplitude of main structure is researched.When system is without damping,amplitude of main structure increases monotonously as nonlinear stiffness strengthens and tends to a constant.Otherwise,a extremum appears and a appropriate nonlinear stiffness can be chosen to keep it away from the maximum or close to the minimum.Models of a linear oscillator with two NESs are established.Dynamics and stability of fixed point are analyzed by multi-scale method,numerical simulation and Jacobi matrix based on complexification-averaging method.Saddle-node bifurcation and Hopf bifurcation appear when NESs are connected parallel and damping coefficients are small,both Hopf bifurcation and period doubling bifurcation appear in in series connected NESs.Influence of the parameters of NESs on amplitude of main structure is analyzed,results show that strong stiffness and large damping coefficients help to vibration reduction when NESs are connected parallel.Strong nonlinear stiffness has advantages on vibration absorption in series NES system.Performance of NES coupled with impact damper is analyzed.The influence of three impact factors(mass ratio,clearance and coefficient of restitution)on the amplitude of main structure are researched by numerical simulation.Vibration of main structure can be reduced greatly under optimum mass ratio and clearance values.Percentage of initial energy dissipated in absorption equipment is analyzed.It is showed that appropriate clearance increases the number of collision and dissipates more energy at each collision.And small coefficient of restitution help to absorb energy comes from main structure.Further research shows that strong nonlinear stiffness is in favor of vibration absorption.A hypothesis is suggested that improving the efficiency of vibration absorption by adding number and changing connection type of NESs without increasing the mass.The response time,transformation of energy between oscillators(main system and NESs)and percentage of energy dissipated in NESs is analyzed under different initial conditions and connections.It is demonstrated that parallel multiple DOF NES helps to targeted energy transfer at large initial displacement,and the response time is shortened and percentage of energy dissipated in NESs is improved.Series two DOF NES actualize targeted energy transfer more effectively.Lastly,parameters of NESs are optimized under different initial conditions and different connections in two DOF NES.In series NES system,mass ratio of first degree NES should be enlarged,weak and strong stiffness can be adopted in large and small displacement respectively.Strong stiffness and same mass ratio should be adopted in parallel NES system.Capacity of both two NES systems is improved by this parameter optimization.