A liquid-elastic active vibration isolation device and control method

Abstract

This invention discloses a liquid-elastic active vibration isolation device and control method, relating to the technical field of vibration isolation devices. A first cavity structure has an installation hole; a second cavity structure includes a channel section and a buffer section; the channel section is inserted into the installation hole, and a magnetorheological elastomer is sleeved between the outer peripheral wall of the channel section and the inner peripheral wall of the installation hole, the magnetorheological elastomer being equipped with a first magnetic field; a partition is installed inside the buffer section, the portion of the buffer section's inner cavity located on one side of the partition is connected to the channel section, and the portion of the buffer section's inner cavity located on the other side of the partition has a buffer structure, the buffering direction of the buffer structure being the same as the sliding direction of the partition; the magnetorheological fluid is equipped with a second magnetic field, the magnetic field direction of the second magnetic field being perpendicular to the flow direction of the magnetorheological fluid. By controlling the magnitude of the magnetic fields acting on the magnetorheological elastomer and the magnetorheological fluid respectively, the stiffness and damping of the entire device can be adjusted, thereby adjusting the vibration isolation frequency range and vibration isolation effect of the entire device to achieve the optimal vibration isolation target.

Description

Technical Field

[0001] This invention relates to the field of vibration isolation device technology, and in particular to a liquid-elastic active vibration isolation device and control method. Background Technology

[0002] Helicopters possess advantages such as vertical takeoff and landing (VTOL) and hovering capabilities, making them widely applicable in national defense, emergency rescue, and civilian sectors. However, vibrations generated by the helicopter rotor during flight are transmitted to the fuselage, causing structural vibrations that significantly impact passenger comfort, the lifespan and accuracy of onboard equipment, increase the likelihood of accidents, and even threaten passenger safety. Therefore, effective vibration isolation is a crucial design element for improving helicopter performance. However, vibration isolation platforms based on traditional materials can only effectively isolate vibrations within a specific frequency range. If changes in the external environment or structural operating conditions cause the excitation frequency to exceed the isolation frequency range, the vibration isolation performance will be greatly reduced. Therefore, developing adaptive active vibration isolation technology holds significant application potential. Summary of the Invention

[0003] The purpose of this invention is to provide a liquid-elastic active vibration isolation device and control method to solve the problems existing in the prior art. By controlling the magnitude of the magnetic field on the magnetorheological elastomer and the magnetorheological fluid respectively, the stiffness and damping of the entire device can be adjusted, thereby adjusting the vibration isolation frequency range and vibration isolation effect of the entire device to achieve the optimal vibration isolation target.

[0004] To achieve the above objectives, the present invention provides the following solution: The present invention provides a liquid-elastic active vibration isolation device, comprising a first cavity structure, a second cavity structure, and a magnetorheological fluid filled in the cavities of the first cavity structure and the second cavity structure;

[0005] The first cavity structure has mounting holes;

[0006] The second cavity structure includes a communicating channel and a buffer section. The channel is inserted into the mounting hole and communicates with the first cavity structure. At least one magnetorheological elastomer capable of adjustable stiffness under a magnetic field is sleeved between the outer peripheral wall of the channel and the inner peripheral wall of the mounting hole. The magnetorheological elastomer has a ring-shaped structure and is equipped with a first magnetic field for changing its stiffness. The buffer section is located outside the first cavity structure, and a partition for isolating the inner cavity of the buffer section is slidably and sealed inside it. The portion of the inner cavity of the buffer section located on one side of the partition is connected to the channel. The portion of the inner cavity of the buffer section located on the other side of the partition is provided with a buffer structure connected to the partition. The buffering direction of the buffer structure is the same as the sliding direction of the partition.

[0007] The magnetorheological fluid is equipped with a second magnetic field for changing its viscous damping, and the magnetic field direction of the second magnetic field is perpendicular to the flow direction of the magnetorheological fluid.

[0008] Preferably, two magnetorheological elastomers are sleeved between the outer peripheral wall of the channel portion and the inner peripheral wall of the mounting hole, and the two magnetorheological elastomers are spaced apart along the insertion direction of the channel portion.

[0009] Preferably, a first electromagnetic coil providing the first magnetic field is provided between the inner peripheral wall of the mounting hole and the outer peripheral wall of the channel portion, and the first electromagnetic coil is electrically connected to a first power source that energizes it.

[0010] Preferably, the first electromagnetic coil is located between the two magnetorheological elastomers.

[0011] Preferably, the channel portion has an inertial channel connecting the first cavity structure and the buffer portion, and the second magnetic field covers the inertial channel.

[0012] Preferably, the flow cross-section of the inner cavity of the first cavity structure and the buffer part is larger than the flow cross-section of the inertial channel.

[0013] Preferably, the channel portion has a plurality of second electromagnetic coils that provide the second magnetic field, each of the second electromagnetic coils being electrically connected to a second power source that energizes it, and the second electromagnetic coils being spaced apart along the axial direction of the inertial channel, with the axial direction of the second electromagnetic coils being perpendicular to the axial direction of the inertial channel.

[0014] Preferably, an aluminum block structure separates two adjacent second electromagnetic coils.

[0015] Preferably, the buffer structure is a part of the inner cavity of the buffer section, and its interior is filled with air that can be compressed by the sliding of the partition.

[0016] A control method is also provided, which applies the following control equations:

[0017]

[0018] Where M is the mass of the lower liquid wall, m is the mass of the magnetorheological fluid in the inertial channel, R1 is the ratio of the cross-sectional area of ​​the upper liquid cavity to the cross-sectional area of ​​the inertial channel, R2 is the ratio of the cross-sectional area of ​​the lower liquid cavity to the cross-sectional area of ​​the inertial channel, x1 is the vertical downward displacement of the upper liquid wall, x2 is the vertical downward displacement of the lower liquid wall, c is the viscous damping of the magnetorheological fluid, K1 is the stiffness of the magnetorheological elastomer, and K2 is the equivalent stiffness of the lower buffer cavity.

[0019] The present invention achieves the following technical effects compared to the prior art:

[0020] Based on the variable damping characteristics of magnetorheological fluids and the variable stiffness characteristics of magnetorheological elastomers, this invention discloses a liquid-elastic active vibration isolation device. By adjusting the magnitude of the first and second magnetic fields, the damping and stiffness of the entire device can be changed, thereby achieving active adjustment of the vibration isolation frequency and vibration isolation performance. This allows the device to operate over a wider frequency range, greatly improving vibration isolation performance and expanding its application scenarios. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a cross-sectional view of one embodiment of the liquid-elastic active vibration isolation device disclosed in this invention.

[0023] Figure 2 The amplitude transmissivity curve of the liquid-elastic active vibration isolation device when the stiffness of the magnetorheological elastomer is changed according to the present invention;

[0024] Figure 3 The amplitude transmissivity curve of the liquid-elastic active vibration isolation device when the magnetorheological fluid damping is changed according to the present invention;

[0025] Among them, 1-first cavity structure, 2-magnetorheological fluid, 3-magnetorheological elastomer, 4-first electromagnetic coil, 5-second cavity structure, 6-second electromagnetic coil, 7-inertial channel, 8-aluminum block structure, 9-partition, 10-buffer structure. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The purpose of this invention is to provide a liquid-elastic active vibration isolation device and control method to solve the problems existing in the prior art. By controlling the magnitude of the magnetic field on the magnetorheological elastomer and the magnetorheological fluid respectively, the stiffness and damping of the entire device can be adjusted, thereby adjusting the vibration isolation frequency range and vibration isolation effect of the entire device, achieving the optimal vibration isolation target, and enabling the device to work in a wider frequency range.

[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] First, it's important to clarify that magnetorheological fluid (MRF) is a smart liquid material whose damping can be adjusted by an external magnetic field. It consists of a non-magnetic matrix, magnetic microparticles, and additives. Without an external magnetic field, MRF exhibits the properties of a Newtonian fluid. When an external magnetic field is applied, the magnetic microparticles in the MRF align into chains along the direction of the magnetic field, and the solidified magnetic chains cause the MRF to exhibit solid-like yielding behavior. Under the influence of a magnetic field, parameters such as the yield stress and apparent viscosity of the MRF change dramatically with the change in the magnetic field. Currently, MRF is widely used in vibration control, power transportation, and precision machining. Magnetorheological elastomers (MEEs) are a novel type of magnetically controlled smart material, composed of an elastomer polymer matrix and ferromagnetic particles. By mixing and solidifying the elastic polymer matrix and ferromagnetic particles, due to the magnetorheological effect, the ferromagnetic microparticles form a chain-like structure under a magnetic field. Applying an external magnetic field can significantly alter the stiffness and other mechanical properties.

[0030] like Figures 1 to 3 As shown, this embodiment provides a liquid-elastic active vibration isolation device, including a first cavity structure 1, a second cavity structure 5, and a magnetorheological fluid 2 filled in the inner cavities of the first cavity structure 1 and the second cavity structure 5; the first cavity structure 1 has an installation hole; the second cavity structure 5 includes a channel portion and a buffer portion that are connected; the channel portion is inserted into the installation hole and is connected to the first cavity structure 1, and at least one magnetorheological elastomer 3 with adjustable stiffness under a magnetic field is sleeved between the outer peripheral wall of the channel portion and the inner peripheral wall of the installation hole. The magnetorheological elastomer 3 has a ring-shaped structure and is equipped with a first magnetic field for changing its stiffness. Specifically, the outer peripheral wall of the magnetorheological elastomer 3 is connected to the inner peripheral wall of the installation hole, and the inner peripheral wall of the magnetorheological elastomer 3 is connected to the outer peripheral wall of the portion of the channel portion inserted into the installation hole. In different embodiments, the outer peripheral wall of the magnetorheological elastomer 3 can be connected to the inner peripheral wall of the first cavity structure 1, or it can be directly connected to the inner peripheral wall of the mounting hole. Preferably, the mounting hole is circular, the radial cross-section of the portion of the channel inserted into the mounting hole is circular, the portion of the channel inserted into the mounting hole is coaxially arranged with the mounting hole, and the magnetorheological elastomer 3 is annular and coaxially sleeved between the inner peripheral wall of the mounting hole and the outer peripheral wall of the portion of the channel inserted into the mounting hole. Preferably, the magnetorheological elastomer 3 used in this invention is a solid structure with silicone rubber as the matrix and carbonyl iron powder dispersed therein. Utilizing the property that the stiffness of the magnetorheological elastomer 3 is adjustable under a magnetic field, and by adjusting the first magnetic field to adjust the stiffness of the magnetorheological elastomer 3, the frequency range of vibration isolation can be changed.

[0031] The buffer section is located outside the first cavity structure 1, and a partition for separating the inner cavity of the buffer section is installed inside it in a sliding seal. The part of the inner cavity of the buffer section located on one side of the partition is connected to the channel section, and the part of the inner cavity of the buffer section located on the other side of the partition is provided with a buffer structure 10 connected to the partition. The buffering direction of the buffer structure 10 is the same as the sliding direction of the partition. The magnetorheological fluid 2 is equipped with a second magnetic field for changing its viscous damping. The magnetic field direction of the second magnetic field is perpendicular to the flow direction of the magnetorheological fluid 2. Under the action of the second magnetic field, the magnetic particles in the magnetorheological fluid 2 will arrange themselves into chains along the direction of the magnetic field. When the magnetorheological fluid 2 flows, since the flow direction is perpendicular to the magnetic field direction of the second magnetic field, the particle chains will be broken, thereby generating a stable damping force. The magnitude of the damping force can be changed by controlling the strength of the second magnetic field. Changing the damping force is essentially based on the characteristic that the yield stress and apparent viscosity of the magnetorheological fluid 2 will change under the magnetic field. When the magnetorheological fluid 2 flows, it will generate a damping force on the wall of its flow path. Changing the magnitude of the second magnetic field will change this damping force. In summary, based on the variable damping characteristics of the magnetorheological fluid 2 and the variable stiffness characteristics of the magnetorheological elastomer 3, this invention discloses a liquid-elastic active vibration isolation device. By adjusting the magnitude of the first magnetic field and the second magnetic field, the damping and stiffness of the entire device can be changed, thereby achieving active adjustment of the vibration isolation frequency and vibration isolation performance. This allows the device to operate in a wider frequency range, which can greatly improve vibration isolation performance and broaden its application scenarios.

[0032] In one specific embodiment, two magnetorheological elastomers 3 are sleeved between the outer peripheral wall of the channel and the inner peripheral wall of the mounting hole. The two magnetorheological elastomers 3 are spaced apart along the insertion direction of the channel. By adjusting the first magnetic field, the stiffness of the two magnetorheological elastomers 3 can be adjusted simultaneously, thereby expanding the frequency change range of vibration isolation.

[0033] In one specific embodiment, a first electromagnetic coil 4 is provided between the inner peripheral wall of the mounting hole and the outer peripheral wall of the channel to provide a first magnetic field. The first electromagnetic coil 4 is electrically connected to a first power source that energizes it, so that the first power source supplies power to the first electromagnetic coil 4, thereby generating a first magnetic field for adjusting the stiffness of the magnetorheological elastomer 3. The first power source can change the magnitude of the current supplied to the first electromagnetic coil 4, thereby changing the strength of the first magnetic field and thus changing the stiffness of the magnetorheological elastomer 3.

[0034] In this embodiment, the first electromagnetic coil 4 is preferably located between the two magnetorheological elastomers 3. Since the magnetorheological elastomer 3 has a ring-shaped structure and is a solid, it is connected between the outer peripheral wall of the channel and the inner peripheral wall of the mounting hole, and forms a blockage between the channel and the mounting hole. After the first electromagnetic coil 4 is installed between the two magnetorheological elastomers 3, the first electromagnetic coil 4 can be fully protected from external interference.

[0035] In one specific embodiment, an inertial channel 7 is provided inside the channel section, connecting the first cavity structure 1 and the buffer section. The second magnetic field covers the inertial channel 7. Under the action of the second magnetic field, the magnetic particles in the magnetorheological fluid 2 flowing inside the inertial channel 7 will arrange themselves into chains along the direction of the second magnetic field. When the magnetorheological fluid 2 flows, since the flow direction is perpendicular to the direction of the second magnetic field, it will break the particle chains, thereby generating a stable damping force. Changing the damping force is essentially utilizing the characteristic that the yield stress and apparent viscosity of the magnetorheological fluid 2 will change under the magnetic field. When the magnetorheological fluid 2 flows, it will generate a damping force on the wall of the inertial channel 7. Changing the magnitude of the magnetic field will change this damping force.

[0036] In one specific embodiment, the flow cross-sections of the inner cavities of the first cavity structure 1 and the buffer section are both larger than the flow cross-section of the inertial channel 7. Since the inertial channel 7 connects the first cavity structure 1 and the inner cavity of the buffer section, the damping force of the magnetorheological fluid 2 inside the entire device can be adjusted by adjusting the damping force of the magnetorheological fluid 2 in the inertial channel 7. There is no need to set up a second magnetic field with a wider coverage, and the effectiveness of adjusting the damping force of the magnetorheological fluid 2 is fully guaranteed.

[0037] In one specific embodiment, the channel section contains multiple second electromagnetic coils 6 that provide a second magnetic field. Each second electromagnetic coil 6 is electrically connected to a second power source that energizes it. The current in the second electromagnetic coil 6 is controlled by the second power source to change the magnitude of the damping force of the magnetorheological fluid 2. The second electromagnetic coils 6 are spaced apart along the axial direction of the inertial channel 7, and the axial direction of the second electromagnetic coils 6 is perpendicular to the axial direction of the inertial channel 7 to ensure that the direction of the generated second magnetic field is perpendicular to the flow direction of the magnetorheological fluid 2 in the inertial channel 7. By controlling the second electromagnetic field covering the inertial channel 7 with each second electromagnetic coil 6, the controllability of the distribution of the second magnetic field can be improved. Preferably, by changing the current provided by each second power source to the corresponding second electromagnetic coil, the magnitude of the second magnetic field in different sections of the inertial channel 7 is different, thereby improving the adjustability of the damping.

[0038] In one specific embodiment, an aluminum block structure 8 separates two adjacent second electromagnetic coils 6, so as to separate the different coils using the aluminum block structure 8.

[0039] In one specific embodiment, the buffer structure 10 can be a buffer spring or a buffer damper, etc. More preferably, the buffer structure 10 is part of the inner cavity of the buffer section, which is a completely airtight space and is filled with air that can be compressed by the sliding of the partition. The partition separates the buffer structure 10 from the magnetorheological fluid 2. When the device is working, the magnetorheological fluid 2 in the device will flow up and down along the inertial channel 7. The purpose of setting the buffer structure 10 is to provide space for the flowing magnetorheological fluid 2. That is, when the magnetorheological fluid 2 flows in the direction away from the first cavity structure 1, the partition 9 moves synchronously, so that the magnetorheological fluid 2 can flow smoothly in the direction away from the first cavity structure 1. The air inside the buffer structure 10 is compressed by the partition 9, generating a force towards the partition 9 and acting on the partition 9. In this process, the air in the buffer structure 10 can be equivalent to a spring. When the magnetorheological fluid 2 flows in the direction closer to the first cavity structure 1, the partition 9 moves synchronously, and the air in the buffer structure 10 recovers its deformation.

[0040] Furthermore, a control method is also provided, in which the liquid-elastic active vibration isolation device applies the following control equation:

[0041]

[0042] Where M is the mass of the lower liquid wall, m is the mass of the magnetorheological fluid 2 in the inertial channel 7, R1 is the ratio of the cross-sectional area of ​​the upper liquid cavity to the cross-sectional area of ​​the inertial channel 7, R2 is the ratio of the cross-sectional area of ​​the lower liquid cavity to the cross-sectional area of ​​the inertial channel 7, x1 is the vertical downward displacement of the upper liquid wall, x2 is the vertical downward displacement of the lower liquid wall, c is the viscous damping of the magnetorheological fluid 2, K1 is the stiffness of the magnetorheological elastomer 3, and K2 is the equivalent stiffness of the lower buffer cavity.

[0043] Furthermore, the displacement transfer rate of the liquid-elastic active vibration isolation device is:

[0044]

[0045] Where ω is the angular frequency and i is the imaginary number.

[0046] Figure 2 The transmissivity curves of the liquid-elastic active vibration isolation device are shown when the stiffness of the magnetorheological elastic body 3 is changed. The horizontal axis represents angular frequency, and the vertical axis represents the logarithmic displacement transmissivity. The four different colored curves correspond to different stiffnesses K1 of the magnetorheological elastic body 3, namely 10, 15, 20, and 25. Figure 2 It can be observed that as the stiffness of the magnetorheological elastomer 3 increases, both the resonant frequency and the anti-resonant frequency of the liquid-elastic active vibration isolation device shift to higher frequencies. Furthermore, as the stiffness of the magnetorheological elastomer 3 increases, the extreme values ​​of displacement transmissivity at both the resonant frequency and the anti-resonant frequency also increase.

[0047] Figure 3The transmissivity curve of the hydrodynamic active vibration isolation device is shown when the magnetorheological fluid damping is changed. The x and y axes of the curve are set as follows: Figure 2 The five curves correspond to different damping values ​​c for the magnetorheological fluid 2, namely 0.001, 0.003, 0.005, 0.007, and 0.009. (The last sentence appears to be incomplete and possibly refers to a different process.) Figure 3 It can be observed that as the damping of magnetorheological fluid 2 increases, the resonant frequency shifts slightly lower, while the anti-resonant frequency shifts slightly higher, and the extreme values ​​of displacement transmissibility at both the resonant and anti-resonant frequencies decrease.

[0048] Any adaptive changes made according to actual needs are within the scope of protection of this invention.

[0049] It should be noted that, for those skilled in the art, it is obvious that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0050] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A liquid-elastic active vibration isolation device, characterized in that, It includes a first cavity structure, a second cavity structure, and a magnetorheological fluid filled in the cavities of the first cavity structure and the second cavity structure; The first cavity structure has mounting holes; The second cavity structure includes a communicating channel and a buffer section. The channel is inserted into the mounting hole and communicates with the first cavity structure. At least one magnetorheological elastomer capable of adjustable stiffness under a magnetic field is sleeved between the outer peripheral wall of the channel and the inner peripheral wall of the mounting hole. The magnetorheological elastomer has a ring-shaped structure and is equipped with a first magnetic field for changing its stiffness. The buffer section is located outside the first cavity structure, and a partition for isolating the inner cavity of the buffer section is slidably and sealed inside it. The portion of the inner cavity of the buffer section located on one side of the partition is connected to the channel. The portion of the inner cavity of the buffer section located on the other side of the partition is provided with a buffer structure connected to the partition. The buffering direction of the buffer structure is the same as the sliding direction of the partition. The magnetorheological fluid is equipped with a second magnetic field for changing its viscous damping, and the magnetic field direction of the second magnetic field is perpendicular to the flow direction of the magnetorheological fluid.

2. The liquid-elastic active vibration isolation device according to claim 1, characterized in that, Two magnetorheological elastomers are sleeved between the outer peripheral wall of the channel and the inner peripheral wall of the mounting hole, and the two magnetorheological elastomers are spaced apart along the insertion direction of the channel.

3. The liquid-elastic active vibration isolation device according to claim 2, characterized in that, A first electromagnetic coil that provides the first magnetic field is provided between the inner peripheral wall of the mounting hole and the outer peripheral wall of the channel portion. The first electromagnetic coil is electrically connected to a first power source that energizes it.

4. The liquid-elastic active vibration isolation device according to claim 3, characterized in that, The first electromagnetic coil is located between the two magnetorheological elastomers.

5. The liquid-elastic active vibration isolation device according to any one of claims 1 to 4, characterized in that, An inertial channel is provided inside the channel section, connecting the first cavity structure and the buffer section, and the second magnetic field covers the inertial channel.

6. The liquid-elastic active vibration isolation device according to claim 5, characterized in that, The flow cross-sections of the inner cavities of the first cavity structure and the buffer section are both larger than the flow cross-section of the inertial channel.

7. The liquid-elastic active vibration isolation device according to claim 5, characterized in that, The channel section contains a plurality of second electromagnetic coils that provide the second magnetic field. Each second electromagnetic coil is electrically connected to a second power source that energizes it. The second electromagnetic coils are spaced apart along the axial direction of the inertial channel, and the axial direction of the second electromagnetic coils is perpendicular to the axial direction of the inertial channel.

8. The liquid-elastic active vibration isolation device according to claim 7, characterized in that, An aluminum block structure separates the two adjacent second electromagnetic coils.

9. The liquid-elastic active vibration isolation device according to claim 5, characterized in that, The buffer structure is a part of the inner cavity of the buffer section, and its interior is filled with air that can be compressed by the sliding of the partition.

10. A control method applied to the liquid-elastic active vibration isolation device as described in any one of claims 1 to 9, characterized in that, Apply the following governing equations: Where M is the mass of the lower liquid wall, m is the mass of the magnetorheological fluid in the inertial channel, R1 is the ratio of the cross-sectional area of ​​the upper liquid cavity to the cross-sectional area of ​​the inertial channel, R2 is the ratio of the cross-sectional area of ​​the lower liquid cavity to the cross-sectional area of ​​the inertial channel, x1 is the vertical downward displacement of the upper liquid wall, x2 is the vertical downward displacement of the lower liquid wall, c is the viscous damping of the magnetorheological fluid, K1 is the stiffness of the magnetorheological elastomer, and K2 is the equivalent stiffness of the lower buffer cavity.

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