Mathematical Handbook for Scientists and Engineers

Design of a quasi-zero stiffness isolation system for supporting different loads

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.

Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

Beneficial stiffness design of a high-static-low-dynamic-stiffness vibration isolator based on static and dynamic analysis

In recent years, negative stiffness vibration isolation device with nonlinear characteristic has become an emerging research area and attracted a significant amount of attentions in the community d...

https://journals.sagepub.com/doi/pdf/10.1177/1369433219900311

Negative stiffness devices for vibration isolation applications: A review:

This paper presents a novel quasi-zero stiffness (QZS) isolator designed by combining a disk spring with a vertical linear spring. The static characteristics of the disk spring and the QZS isolator are investigated. The optimal combination of the configurative parameters is derived to achieve a wide displacement range around the equilibrium position in which the stiffness has a low value and changes slightly. By considering the overloaded or underloaded conditions, the dynamic equations are established for both force and displacement excitations. The frequency response curves (FRCs) are obtained by using the harmonic balance method (HBM) and confirmed by the numerical simulation. The stability of the steady-state solution is analyzed by applying Floquet theory. The force, absolute displacement, and acceleration transmissibility are defined to evaluate the isolation performance. Effects of the offset displacement, excitation amplitude, and damping ratio on the QZS isolator and the equivalent system (ELS) are studied. The results demonstrate that the QZS isolator for overloaded or underloaded can exhibit different stiffness characteristics with changing excitation amplitude. If loaded with an appropriate mass, excited by not too large amplitude, and owned a larger damper, the QZS isolator can possess better isolation performance than its ELS in low frequency range.

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Theoretical Design and Characteristics Analysis of a Quasi-Zero Stiffness Isolator Using a Disk Spring as Negative Stiffness Element

This paper concerns the characteristics of a novel quasi-zero stiffness (QZS) isolator developed by parallelly combining a slotted conical disk spring with a vertical linear spring. The static characteristics of the slotted conical disk spring as well as the QZS isolator are presented. The configurative parameters are optimized to achieve a wide displacement range around the equilibrium position for which the stiffness has a low value and changes slightly. The overload and underload conditions are taken into account, resulting in a Helmoholtz-Duffing equation. The primary resonance response of the nonlinear system composed by a loaded mass and the QZS isolator are determined by employing the Harmonic Balance Method (HBM) and confirmed with the results of numerical simulation. The frequency response curves (FRCs) are obtained for both force and displacement excitations. The force transmissibility, the absolute displacement and acceleration transmissibility are defined and investigated. The study shows that the overloaded or underloaded system can exhibit linear stiffness, softening stiffness, softening-hardening stiffness and hardening stiffness with the increasing excitation amplitude. The response and the resonance frequency of the system are affected by the excitation amplitude and the offset displacement to the position at which the dynamic stiffness is zero. To enlarge the isolation frequency range and improve the isolation performance, the loaded mass and the excitation amplitude should be suitably controlled.

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Design and analysis of a quasi-zero stiffness isolator using a slotted conical disk spring as negative stiffness structure

The designed load of most quasi-zero stiffness (QZS) isolators is constant. The isolation performance will drop sharply once the load changes. A novel QZS isolator that can adapt to variable loads is proposed in this paper to improve the range of application of the isolator. The isolator is designed by paralleling the electromagnetic spring (ES), which provides negative stiffness, and the pneumatic spring (PS), which provides positive stiffness. The positive and negative stiffness can be adjusted by changing the pressure and coil current, which provides the possibility for the isolator to adapt to variable loads. This paper derived the conditions for the isolation system to obtain QZS characteristics, proposed the dynamic model of the isolation system, derived and verified the analytical expressions of the amplitude-frequency response and force transmissibility (FT), and discussed the change of FT and displacement transmissibility(DT) under different loads. Theoretical analysis shows that changing the pressure and coil current in the same proportion can maintain the superior low-frequency isolation performance when the load changes, thanks to the preservation of the QZS characteristics of the system after adjusting the pressure and coil current. Finally, the simulation results fg and isolation frequency band over the linear isolation system and PS isolation system. Furthermore, the proposed isolator can be adjusted online.

/pdf/design-and-analysis-of-a-novel-quasi-zero-stiffness-isolator-1wf62ztn.pdf

Design and Analysis of a Novel Quasi-Zero Stiffness Isolator under Variable Loads

The utility model discloses a stretcher support frame with an auxiliary carrying turning board. The stretcher support frame with the auxiliary carrying turning board comprises a support frame body, sliding grooves, a stretcher locking mechanism, a vibration separating device and the auxiliary carrying turning board. The support frame body is mounted on a floor of a carriage through the vibration separating device, the sliding grooves are fixed on two sides of the support frame body, the stretcher locking mechanism is mounted on the surface of the support frame body, and the auxiliary carrying turning board comprises support legs, sliding rods, sliding rod orienting grooves, pulling rods, a first-section turning board and a second-section turning board. The support legs are mounted on the floor of the carriage behind the support frame body, the upper end of the first-section turning board is movably connected with the top end of each of the support legs, the lower end of the first-section turning board is movably connected with the upper end of the second-section turning board, lock pins are arranged at the lower end of the second-section turning board, turning board sliding grooves are fixed on two sides of the first-section turning board and two sides of the second-section turning board, one end of each of the sliding rods is fixed on one of the support legs, the other end of each of the sliding rod is arranged in the sliding rod orienting grooves, and the sliding rod orienting grooves are fixed on the lower surface of the first-section turning board. The stretcher support frame with the auxiliary carrying turning board can be used to carry and transport the wounded and the sick on the stretcher, and meanwhile, the problem that the wounded and the sick are hard to be carried onto a vehicle and carried off from the vehicle with a stretcher is solved.

Stretcher support frame with auxiliary carrying turning board

A fuzzy PID control strategy for quasi-zero stiffness (QZS) isolator which connects the pneumatic spring (PS) and the electromagnetic negative stiffness mechanism (ENSM) in parallel to suppress low-frequency vibration is proposed in this paper. First, the restoring force of PS and the electromagnetic force of the ENSM are derived. Secondly, the static analysis of the isolation system is carried out, and the analytical expressions of stiffness and restoring force of the vibration isolation system is obtained. The possibility of the vibration isolator reaching the QZS state is explained. Then, to obtain a better isolation effect, the optimal current of the coil is found according to the designed fuzzy PID control strategy. Finally, the simulation result shows that the isolation frequency band of the isolation system under fuzzy PID control and PID control is widened, and the vibration isolation performance under fuzzy PID control reaches more than 85% under different excitation frequencies. Control effect and vibration isolation performance under fuzzy PID control are better.

Jinggong Sun

Papers

Theoretical Design and Characteristics Analysis of a Quasi-Zero Stiffness Isolator Using a Disk Spring as Negative Stiffness Element

Design and analysis of a quasi-zero stiffness isolator using a slotted conical disk spring as negative stiffness structure

Design and Analysis of a Novel Quasi-Zero Stiffness Isolator under Variable Loads

Stretcher support frame with auxiliary carrying turning board

Fuzzy PID Control of Nonlinear Vibration Isolator with Parallel Electromagnetic Negative Stiffness