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Magnetorheological elastomer (MRE) vibration isolation devices can improve a system’s vibration response via adjustable stiffness and damping under different magnetic fields. Combined with negative stiffness design, these MRE devices can reduce a system’s stiffness and improve the vibration control effect significantly. This paper develops a variable negative stiffness MRE isolation device by combining an improved separable iron core with laminated MREs. The relationship between the negative stiffness and the performance of the device is obtained by mathematical transformation. Its vibration response under simple harmonic excitation at small amplitude and the impact of the volume fraction of soft magnetic particles on the isolation system are also analyzed. The results show that the negative stiffness produced by the magnetic force is a major factor affecting the capacity of the isolation system. Compared to devices of the same size, the isolation system equipped with low-particle volume fraction MREs demonstrates better performance.

The isolation system has been widely used in high-precision measurement, automotive suspension, shipping shaft systems, and disaster prevention and reduction systems to reduce environmental disturbances [

Magnetorheological elastomers (MREs) are an intelligent composite material with actively controllable mechanical properties. The main ingredients of MREs are micron-sized soft magnetic particles and viscoelasticity polymer matrix. Micron-sized soft magnetic particles are dispersed directionally or distributed randomly in the polymer matrix curing without magnetic field or with that for higher material properties. The mechanical properties of MREs, such as damping feature, Young’s modulus, and shear modulus, may be transiently reversed under an external magnetic field. Being free of sedimentation and easily encapsulated, MREs are widely used in dampers, brakes, and deflection sensors [

Based on the magnetic force between an electromagnet and a permanent magnet, Mizuno et al. probed into the negative stiffness effects on the active isolation system [

The mechanical properties of MREs are sensibly influenced by the particle volume fraction, such as storage Young’s modulus, storage shear modulus, loss factors [

In this study, the performance of variable negative stiffness MRE vibration isolation systems is analyzed in theory; further work will be given in next part. After the introduction, the structure and workflow are detailed and expatiated. Second, the Fourier transformation is used to deduce the impact of the magnetic force that produced the negative stiffness on the MRE isolation system’s performance. In Section

The schematic diagram of the tunable negative stiffness MRE isolation device is depicted in Figure

Schematic diagram of MRE isolation system.

The alterable magnetic flux density can drive the two MRE layer blocks with variable stiffness

The theoretical stiffness

Operation chart of negative stiffness process.

An equivalent physical model of variable negative stiffness MRE isolation systems is illustrated in Figure

The phenomenological model.

From (

It can be obtained as follows:

If the displacement of the intermediate plate

From the equation mentioned above, the magnetic field force mainly falls into two parts: the first part is the displacement feedback part

The system’s isolation efficiency can be used to illustrate the capacity of the system’s energy dissipation. The system’s energy dissipation varies with damping ratio as shown in Figure

The vibration isolation capacity of the system.

Now suppose that an external excitation acts upon the above plate

Under an external magnetic field

If the displacements are small, the magnetic forces can be seen as linear functions of the relative displacement, and the resulting negative stiffness can be expressed as

Assuming that the stiffness values of the intermediate plate’s upper and lower support systems are equal,

Equation (

Chen et al. [

Transmissibility of the isolation system.

Transmissibility of the isolation system without negative stiffness.

Phase angle difference of the isolation system.

MREs prepared with a magnetic field character have a higher equivalent damping coefficient and energy dissipation than those prepared without a magnetic field [

The magnetic dipole moment can be expressed as

MRE stiffness can be expressed as a ratio of the product of its modulus and cross section area to unit thickness. According to the equations mentioned above, the stiffness of MREs can be obtained as follows:

Here, the magnetic flux leakage is neglected; from (

The impact of MRE particle volume fraction on the transmissibility is obtained from (^{2}, and the maximum displacement is 4 mm. It can be seen from the figure that an increased particle volume fraction results in an increased peak frequency; for isolation systems with identical size, the volume fractions had a remarkable influence on their natural frequencies. This can be explained because the particle volume fraction can affect the stiffness and modulus of MREs, and the system’s negative stiffness can lead to softened overall stiffness.

The impact of different volume fractions on the transmissibility.

According to (

This paper proposed an isolation system for MREs with negative stiffness whose separable iron core is replaced by a conventional cylindrical core, which provides negative stiffness for the conventional laminated MRE isolation core. To verify the effectiveness of the negative stiffness and the laminated MRE, the transmissibility with and without negative stiffness and that with different particle volume fractions were discussed; the following conclusions can be obtained:

The frequency and the system transmissibility decrease as the magnetic strength increases and there is lower transmissibility without negative stiffness.

The vibration isolation performance of the one equipped with MREs with a low volume fraction is better than the one with high particle fraction.

The negative stiffness effect produced by the magnetic force is conducive to the energy dissipation for the isolation system.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study was supported by the Jiangsu Province Science and Technology Support Program, China (Grant no. BE2012180), National Natural Science Foundation of China (Grant no. 51508237), Natural Science Foundation of Jiangsu Province (BK20140560), and Natural Science Foundation of Zhejiang Province (Y15E080043).

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