High Static Low Dynamic Stiffness Research Articles

On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness

Abstract The vibration isolation characteristics of a high-static-low-dynamic-stiffness (HSLDS) isolator, which has geometrically nonlinear stiffness, have been well established both theoretically and experimentally in the recent literature. However, the shock isolation characteristics of such an isolator subject to base excitation are not currently known. In this paper, these characteristics are determined for two illustrative inputs, which are a rounded step and a versed sine displacement, using a simple model of the isolator comprising a vertical spring coupled to two horizontal springs. The isolator is configured to reduce the dynamic stiffness of the isolator and hence increase the frequency range of isolation. The shock responses of the isolator are determined analytically for low levels of excitation, and numerically for high levels of excitation. It is found that when the shock amplitude is small, the nonlinearity is beneficial, and that the quasi-zero stiffness isolator has the best shock performance in terms of the smallest displacement and acceleration of the suspended mass.

Effect of the system imperfections on the dynamic response of a high-static-low-dynamic stiffness vibration isolator

The dynamic response of a high-static-low-dynamic stiffness (HSLDS) isolator formed by parallelly connecting a negative stiffness corrector which uses compressed Euler beams to a linear isolator is investigated in this study. Considering stiffness and load imperfections, the resonance frequency and response of the proposed isolator are obtained by employing harmonic balance method. The HSLDS isolator with quasi-zero stiffness characteristics can offer the lowest resonance frequency provided that there is only stiffness or load imperfection. If load imperfection always exists, there is no need to make the stiffness to zero since it cannot provide the lowest resonance frequency any longer. The reason for this unusual phenomenon is given. The dynamic response will exhibit softening, hardening, and softening-to-hardening characteristics, depending on the combined effect of load imperfection, stiffness imperfection, and excitation amplitude. In general, load imperfection makes the response exhibit softening characteristic and increasing stiffness imperfection will weak this effect. Increasing the excitation level will make the isolator undergo complex switch between different stiffness characteristics.

Dynamic isolation systems using tunable nonlinear stiffness beams

Vibration isolation devices are required to reduce the forcing into the supporting structure or to protect sensitive equipment from base excitation. A suspension system with a low natural frequency is required to improve isolation, but with linear supports the minimum stiffness is bounded by the static stiffness required to support the equipment. However, nonlinear high-static-low-dynamic-stiffness (HSLDS) mounts may be designed, for example by combining elastic springs in particular geometries, to give the required nonlinear force-displacement characteristics. Current approaches to realise the required nonlinear characteristics are often inconvenient. Furthermore, the weight of the supported equipment, the environment, or the structural stiffness may change. This paper investigates the design of HSLDS isolation mounts using beams of tunable geometric nonlinear stiffness. In order to obtain the nonlinear response required, we first study the case of generic beams subject to static loads that are able to tune their nonlinear force-displacement characteristics to ensure that the isolators have very low dynamic stiffness. Tuning is achieved by actuators at the ends of the beams that prescribe the axial displacement and rotation. Secondly, we study a composite beam with an initial thermal pre-stress, resulting in internal stresses that give the required nonlinear response.

A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation

The High Static Low Dynamic Stiffness (HSLDS) concept is a design strategy for a nonlinear anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount whilst maintaining the same static load bearing capacity. It has previously been proposed that an HSLDS mount could be implemented by connecting linear springs in parallel with the transverse flexure of a composite bistable plate — a plate that has two stable shapes between which it may snap. Using a bistable plate in this way will lead to lightweight and efficient designs of HSLDS mounts. This paper experimentally demonstrates the feasibility of this idea. Firstly, the quasi-static force–displacement curve of a mounted bistable plate is determined experimentally. Then the dynamic response of a nonlinear mass–spring system incorporating this plate is measured. Excellent agreement is obtained when compared to theoretical predictions based on the measured force–displacement curve, and the system shows a greater isolation region and a lower peak response to base excitation than the equivalent linear system.

Dynamic analysis of high static low dynamic stiffness vibration isolation mounts

The high static low dynamic stiffness (HSLDS) concept is a design strategy for an anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount, whilst maintaining the same static load bearing capacity. Previous studies have successfully analysed many features of the response by modelling the concept as a Duffing oscillator. This study extends the previous findings by characterising the HSLDS model in terms of two simple parameters. A fifth-order polynomial model allows us to explore the effects of these parameters. We analyse the steady-state response, showing that simple changes to the shape of the force displacement curve can have large effects on the amplitude and frequency of peak response, and can even lead to unbounded response at certain levels of excitation. Harmonics of the fundamental response are also analysed, and it is shown that they are unlikely to pose significant design limitations. Predictions compare well to simulation results.

설계 파라미터를 고려한 HSLDS 마그네틱 진동절연체의 실험적 성능평가

The isolation performance of a linear vibration isolator is limited to the ratio of stiffness to mass it supports. The stiffness of the isolator must be large enough to hold the weight. This results in the deterioration of the isolation performance. Recently, to overcome this fundamental limitation, the HSLDS(high-static-low-dynamic-stiffness) magnetic vibration isolator was introduced and its isolation characteristic was investigated theoretically. In this paper, the isolation performance of the HSLDS magnetic isolator is examined experimentally. Considerable amount of experiments are performed by carefully considering nonlinear characteristics. The experimental results verify the practical usability promisingly and agree with the theoretical studies, i.e. its performance is largely dependent on the key design parameter.

Characterization of an Electromagnetic Vibration Isolator

A novel vibration isolator is constructed by connecting a mechanical spring in parallel with a magnetic spring in order to achieve the property of high-static-low-dynamic stiffness (HSLDS). The HSLDS property of the isolator can be tuned off-line or on-line. This study focuses on the characterization of the isolator using a finite element based package. Firstly using the single physics solver, the stiffness behaviours of the mechanical and magnetic springs are determined, respectively. Then using the weakly coupled multi-physics method, the stiffness behaviours of the passive isolator and the semi-active isolator are investigated, respectively. With the found stiffness models, a nonlinear differential equation governing the dynamics of the isolator is solved using the time-dependent solver. The displacement transmissibility ratios of the isolator are obtained. The study confirms that the isolation region of the isolator can be widened through off-line or on-line tuning.

HSLDS 마그네틱 진동절연체의 절연성능에 대한 설계 파라미터 분석

In general, the softer the stiffness of a linear vibration isolator the better the performance of isolation can be achieved. However, the stiffness of the isolator cannot be made too soft because it needs a sufficient stiffness to hold the load. This is the most critical limitation of a linear vibration isolator. Recently, a HSLDS(high-static-low-dynamic-stiffness) magnetic vibration isolator was proposed to overcome this fundamental limitation. The suggested isolator utilizes two pairs of attracting magnets that introduces negative stiffness. Previously, this new type of vibration isolator was merely introduced and showed a possibility of practical use. In this paper, detailed dynamics of the HSLDS magnetic isolator are studied using computer simulations. Then, the isolation performance is examined for various design parameters to aid the practical use.

A tunable high-static–low-dynamic stiffness vibration isolator

In this study, a novel vibration isolator is developed. The developed isolator possesses the characteristics of high-static–low-dynamic stiffness (HSLDS) and can act passively or semi-actively. The HSLDS property of the isolator is obtained by connecting a mechanical spring, in parallel with a magnetic spring that is constructed by a pair of electromagnets and a permanent magnet. The mechanical spring is a structural beam whose stiffness exhibits a hardening behavior. The stiffness of the magnetic spring can be positive or negative, depending on the polarity of the current to the electromagnets. A passive HSLDS isolator is obtained when the electromagnet current is zero. In the stiffness characterization study, the analytical model for each of the springs is established and the tuning parameters are identified. Using the stiffness models, the design optimization issues are investigated. In the experimental study, the effectiveness of the isolator for vibration isolation is tested. The analytical natural frequencies of the isolator are validated experimentally. The relationships between the displacement transmissibility and the exciting frequency are measured both under the passive mode and under the semi-active mode. The on-line tuning capability of the isolator is investigated.

Using nonlinear springs to reduce the whirling of a rotating shaft

Vibrations in rotating machinery cause many problems such as fatigue of the rotating components, excessive noise, or transmission of vibration to the supporting structure. A major source of this vibration is out-of-balance forces and this paper proposes that the rotor response is reduced by suspending the machine on nonlinear springs. In the field of vibration isolation, nonlinear mounts have been proposed which have the same static stiffness as an equivalent linear support, i.e. load bearing capability, but at the same time offer a low dynamic stiffness, i.e. a lower natural frequency. Thus the isolator is effective over an increased frequency range. These mounts are known in the literature as high-static-low-dynamic-stiffness (HSLDS) mechanisms. In this paper, the rotor is suspended on a hardening HSLDS spring to considerably reduce the critical speeds to values far away from the operating speed. The advantages of the nonlinear supports are demonstrated using a simple two degree of freedom rotating machine model consisting of a rigid disk, and shafts, bearings and supports that are flexible but have negligible mass. Following a linear analysis to highlight the benefits of a low dynamic stiffness, an approximate analytical solution of the nonlinear equation of motion is presented. A comparison between the linear and nonlinear response shows the effectiveness of the nonlinear supports. Finally, the problems that occur if the nonlinearity is too strong are highlighted.

On the design of a high-static–low-dynamic stiffness isolator using linear mechanical springs and magnets

The frequency range over which a linear passive vibration isolator is effective is often limited by the mount stiffness required to support a static load. This can be improved upon by incorporating a negative stiffness element in the mount such that the dynamic stiffness is much less than the static stiffness. In this case, it can be referred to as a high-static–low-dynamic stiffness (HSLDS) mount. This paper is concerned with a theoretical and experimental study of one such mount. It comprises two vertical mechanical springs between which an isolated mass is mounted. At the outer edge of each spring, there is a permanent magnet. In the experimental work reported here, the isolated mass is also a magnet arranged so that it is attracted by the other magnets. Thus, the combination of magnets acts as a negative stiffness counteracting the positive stiffness provided by the mechanical springs. Although the HSLDS suspension system will inevitably be nonlinear, it is shown that for small oscillations the mount considered here is linear. The measured transmissibility is compared with a comparable linear mass–spring–damper system to show the advantages offered by the HSLDS mount.