The Memory Characteristic And Self-adaptivity Of A Mem-inerter

The replacement of linear elements with nonlinear passive elements with variable parameters has opened up a new way for the development of traditional passive suspensions.At present,nonlinear damper and spring elements have already been widely studied,but nonlinear inerters and their applications in suspensions are rarely reported.In this situation,two new nonlinear mem-inerter devices are designed in this paper,and the memory characteristics of them are analyzed through simulation.Also,the equivalence between the mem-inerter and the traditional linear inerter is established based on the energy method,and the analysis result indicates that the inerter can be equivalent to a semi-active inerter with an initial-displacement-control strategy,which reveals a self-adaptability of the mem-inerter.The suspension system is used as an example to demonstrate that this self-adaptability can improve the load adaptability of the suspension system,thereby further improve the ride comfort of the vehicle.Firstly,based on the triangular periodic table of elementary mechanical elements,the constitutive relations of linear elements and memory elements of various orders are deduced,and the general constitutive model of mechanical elements is established.Based on that,the memory characteristics of nonlinear memory elements are analyzed.It is pointed out that the mechanical memory element can "remember" the entire history of the changes of some specific physical variables,which clarifies the ideas for the later analysis of the adaptivity of the mem-inerter to the initial value of displacement.From the perspective of the memory elements,the energy method and the integral Lagrangian method which is suitable for the memory system are deduced,which lays the foundation for the establishment of the equivalence between the mem-inerter and the linear inerter and for the exploration of the influence of the mem-inerter on the load adaptivity of the suspension system.Secondly,two mem-inerter devices(one with variable cylinder inner diameters and the other with variable channel depths)are designed,and the mathematical models of them are established.Based on that,the memory characteristics of the two mem-inerters are calculated and analyzed.The results show that the characteristic curve of the mem-inerters in the relative velocity-momentum plane is a pinched hysteresis loop,indicating the memory characteristics of the two devices.Thirdly,based on the energy method,the equivalence between a mem-inerter and linear inerters is established,and the regulation that the equivalent linear inertance of the meminerter changes with the initial value of displacement excitation is found,revealing that the mem-inerter can be equivalent to a semi-active inerter with an initial-displacement-control strategy,indicating that the equivalent linear inertance of the mem-inerter is adaptive to the change of the initial displacement.Then,the mem-inerter is placed into the suspension system,and the quarter suspension model is established.The kinematic differential equation is established by using the integral Lagrangian method,and the simulation analysis is carried out.The results show that the adaptivity of the mem-inerter’s equivalent linear inertance to the initial displacement can bring load adaptability to the suspension system and thus improve the ride comfort of the vehicle.Finally,an engineering model of the mem-inerter device is established considering the dynamic viscosity of the fluid and the dry friction inside the device.Also,a prototype of the mem-inerter device is developed and a bench test is carried out on the INSTRON 8800 CNC hydraulic servo exciter.The test results show that the engineering model established in this paper is of high accuracy and can meet the needs of engineering applications.The characteristic curves of the damping part and the initial part for the device shows pinched hysteresis loops,which reveals the memory characteristic of the device.The result shows that the mem-inerter device is not only a mem-inerter providing initial force,but also a memdashpot providing damping force.