Research On Isolation Mechanism And Performance Of Crank Train Inert Er Damper

Vibration control devices with inertial components,including inerters and inerter dampers,have the advantages of dynamic negative stiffness,mass amplification effect,local amplification effect for energy dissipating components and great stability.Thus,these devices have been widely studied in the field of structural vibration control and earthquake engineering.Traditional implementations of inerters or inerter dampers,by the ball-screw mechanism and rack-pinion mechanism for example,are disadvantageous due to the difficulties in adjusting the inertance and damping effect easily and asynchronously,making the devices’ parameters hard to adjust after installation.Moreover,it is unable to generate asynchronous control forces when these devices have large deformations.In order to solve the above problems and further enhance the isolation performance and application range of existing inerters and inerter dampers,Crank Train Inerters(CTIs),Crank Train Inerter Friction Dampers(CT-IFDs),Crank Train Inerter Eddy Current Dampers(CT-IECDs),and Crank Train Tuned Inerter Eddy Current Dampers(CT-TIECDs)are proposed based on the crank train and gear transmission mechanism.Their nonlinear dynamic mechanisms and isolation performances are studied using theoretical derivation,experimental verification,and numerical simulation methods.The main research contents are as follows:(1)The Crank Train Inerter(CTI)is proposed based on the crank train and gear transmission mechanism,and its mechanical properties are studied.The mathematical model of CTI is deduced,and the feasibility of the device and the accuracy of the mathematical model are verified by mechanical performance tests.The influence of different parameters of CTI on the inertial force is studied by using the mathematical model,and the geometric linearization of the linking rod is carried out.The parameter range and inertance expression of CTI can be approximated as linear inerter are given and verified by experiments.The results indicate that the experimental results are in good agreement with the theoretical results,so the accuracy of the mathematical model is verified.Short linking rods and cranks can cause nonlinear inertial forces in CTI.When the ratio of the length of the linking rod to that of the crank is greater than 6,the geometric nonlinearity can be ignored,and the applicable range of the crank rotation angle is within±60°.A shorter crank will equip the CTI with the ability to adjust its adaptive inertance(dynamic inertance is related to the deformation of CTI),and is adaptivity becomes better when external forces are large.When the ratio of the CTI deformation to the crank length is less than 0.312 and the ratio of the linking rod length to the crank length is greater than 1.803,the CTI can be regarded as a linear inerter.By changing the crank length,the inertance can be adjusted,and the tilting state of the linking rod under linear working state has little effect on the mechanical properties of CTI.(2)The nonlinear dynamics and vibration isolation performance of CTI are studied.Firstly,the mathematical model of a single degree of freedom(DOF)structure with CTI is established,and the nonlinear dynamic characteristics of CTI are derived and studied by harmonic balance method.The transmissibility of the system is derived,and the parameter analysis and linearization design are carried out.The amplitude-frequency response of CTI used in structural isolation layer is studied by a small shaking table test with a multi-DOF structure.Finally,the effect of CTI is evaluated by a seismic isolation case study,and the installation schemes of CTI for buildings and bridges are proposed.The results show that the geometric nonlinearity of CTI will cause the stiffness weakening and reduce the maximum transmissibility.When a CTI is used for the isolation layer of a multi-DOF structure,the resonance frequency of the system will be significantly reduced.For seismic excitation,CTI can reduce the seismic response of the traditional seismic isolation structure again(about 30%),and the CTI has better isolation effect than the traditional linear inerter for the same inertance-mass ratio.(3)Frictional energy dissipation devices with stable energy dissipation are advantageous as they are can be easily processed and not affected by temperature.Therefore,Crank Train Inerter Friction Dampers(CT-IFD)is developed by combing the frictional energy dissipation device and CTI.Based on a single DOF structure with CT-IFD,the relative nonlinear dynamics characteristics are analyzed,and the absolute transmissibility of the system is derived.The parameter analysis and linearization design are also carried out.The seismic response control effect of CT-IFD on the isolated structure is evaluated.The results show that the output force of CT-IFD has both geometric and frictional nonlinear characteristics.The increase of friction ratio will weaken the nonlinear characteristics caused by the inertance,and the existence of friction will cause a“locking" phenomenon of CT-IFD.The“unlocking”condition is met with the increases of frequency and excitation amplitude or the decrease of friction ratio.The geometric nonlinearity of CTIFD is beneficial to vibration isolation,especially for excitations with large amplitude,the maximum deformation of isolation layer can be reduced by about 27%.(4)Based on the principle of eddy current energy dissipation,the Crank Train Inerter Eddy Current Damper(CT-IECD)is proposed,which overcomes the disadvantages of poor stability and durability of traditional viscous dampers.The CT-IECD has the advantages of adjustable damping coefficient and high energy dissipation density.The output force of CT-IECD is obtained by theoretical calculation which is verified by mechanical properties test.The nonlinear dynamic characteristics of a single DOF structure with CT-IECD are analyzed by harmonic balance method.Based on the CT-IECD vibration isolation system,the transmissibility is derived,and the parameter analysis and linear design are carried out.The isolation performance of the CT-IECD is evaluated by taking a structure with seismic isolation as an example.The results show that the output force of CT-IECD has both geometric and damping nonlinear characteristics.It is found that increasing the structural damping ratio,inertance-mass ratio and CT-IECD damping ratio,or decreasing the excitation amplitude can weaken the geometric nonlinear characteristics of CT-IECD.The geometric nonlinearity of CT-IECD is beneficial to the isolation control,and its seismic response reduction effect is much greater than that of traditional FD.Compared with viscous damper(VD)and eddy current damper(ECD),CT-IECD can further reduce the seismic response by about 15%.(5)In order to further improve the vibration isolation performance of inerter dampers,the Crank Train Tuned Inerter Eddy Current Damper(CTTIECD)is developed by adding a tuning mechanism into the CT-IECD.The equation of motion of a single DOF structure with CT-TIECD is derived,and the amplitude-frequency response and the influence of parameter variation are analyzed by incremental harmonic balance method.The transmissibility of CTTIECD system is derived,and the optimal parameters of CT-TIECD are given in cases considering linearization or geometric nonlinearity.Further,the vibration isolation performance of CT-TIECD and the influence of parameter variation on its vibration isolation performance are studied.Finally,the control effect,output response and energy dissipation effect of CT-TIECD on an isolated structure are evaluated.The results show that CT-TIECD can be optimized according to the Tuned Viscous Mass Damper(TVMD)for a small excitation amplitude,while a larger stiffness ratio should be matched for a large excitation amplitude.For harmonic and seismic excitation,CT-TIECD has a better isolation control effect than that of Tuned Inerter Damper(TID),TVMD and CT-IECD,which can reduce 25%,5%and 22%of the structural response under strong earthquake,respectively.