Mechanoelectric coupling quasi-zero stiffness vibration isolation cell and vibration isolation device

Abstract

The application provides a force-electric coupling quasi-zero stiffness vibration isolation cell and vibration isolation device. The vibration isolation cell comprises: a connecting protrusion in the middle; N beam structures extending radially with the connecting protrusion as the center, the angle between each two of the N beam structures is 360° / N, and N is greater than or equal to 2; wherein at least one of the upper surface and the lower surface of the beam structure is fixed with a piezoelectric sheet, the actual thickness H p of the piezoelectric ceramic fiber satisfies a specific relationship with the actual thickness T' of the beam structure, and the relationship is related to the span height of the beam structure, the Young's modulus of the piezoelectric ceramic fiber, the electromechanical coupling coefficient of the piezoelectric ceramic fiber and the Young's modulus of the beam structure. The application can realize quasi-zero stiffness in the working area, greatly suppress the resonance peak and actively adjust the stiffness through external circuit design, and has important application prospects in vibration reduction and noise reduction of major equipment in the fields of aerospace and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, and particularly relates to a force-electric coupling quasi-zero stiffness vibration isolation cell and vibration isolation device. BACKGROUND

[0002] Vibration is ubiquitous in the field of aerospace. Vibration can cause friction and collision of components in instruments and equipment, not only the stability, accuracy and reliability of the structure will be affected, but also the fatigue damage of parts will be caused, which will affect the normal function and service life of the equipment and instruments. Especially in the use process of some precision instruments and equipment, any slight vibration will have a great impact on normal work. For example, the vibration generated in the use process of a reconnaissance satellite will reduce the accuracy of optical elements and thus affect the imaging effect; the vibration caused in the flight process of an airplane will also affect the work of sensitive instruments inside the airplane.

[0003] Vibration isolators are widely used in the field of vibration control due to their good feasibility and high reliability. At present, the main method to realize low-frequency vibration isolation of precision instruments is quasi-zero stiffness vibration isolation superstructure, which achieves low natural frequency to isolate low-frequency vibration through the characteristics of low stiffness and high load. Meanwhile, piezoelectric sheets are added to the beam structure of the vibration isolator to form a force-electric coupling vibration isolator, which can improve the performance of the vibration isolator and increase the controllability of vibration isolation.

[0004] However, in the process of implementing the present application, the applicant found that the force-electric coupling vibration isolator in the prior art still has a resonance peak, and has poor ability to cope with external load disturbance, and the vibration isolation effect is not ideal, and there is a need for further optimization. SUMMARY

[0005] (I) Technical problems to be solved

[0006] Therefore, the present application provides a force-electric coupling quasi-zero stiffness vibration isolation cell and vibration isolation device, in order to at least partially solve one of the above technical problems.

[0007] (II) Technical solutions

[0008] In a first aspect of the present application, a force-electric coupling quasi-zero stiffness vibration isolation cell is provided. The vibration isolation cell is characterized in that it comprises: a connecting protrusion in the middle; N beam structures extending radially with the connecting protrusion as the center, the angle between any two of the N beam structures is 360° / N, and N≥2; wherein at least one of the upper surface and the lower surface of the beam structure is fixed with a piezoelectric sheet, and the actual thickness H of the piezoelectric sheet satisfies: p ' and the actual thickness T of the beam structure satisfy:

[0009]

[0010] (Hp '=H p (T≤T'≤1.1T) or (T'=T; Hp≤H) p '≤1.2H p )

[0011] Among them, H p T is the theoretical thickness of the piezoelectric element; H is the theoretical thickness of the beam structure; E is the span of the beam structure; p k is the Young's modulus of the piezoelectric element. 31 denoted as ε, where ε is the electromechanical coupling coefficient of the piezoelectric element; E is the Young's modulus of the beam structure.

[0012] In some embodiments of the present invention, the actual thickness H of the piezoelectric sheet is... p The actual thickness T of the beam structure satisfies:

[0013]

[0014] (0.6≤a≤1.3;0.3≤b≤0.5;1.8≤c≤2.6)

[0015] The piezoelectric element has a Young's modulus between 25 GPa and 35 GPa; the beam structure is made of aluminum alloy; the span height H of the beam structure is between 2.1 mm and 3 mm; and T and H... p The unit is mm.

[0016] In some embodiments of the present invention, the thickness of the piezoelectric sheet is between 0.1 mm and 0.8 mm; the corresponding thickness of the beam structure is between 1.8 mm and 0.7 mm.

[0017] In some embodiments of the present invention, the piezoelectric sheet is disposed close to the connecting protrusion, and its length extending on the beam structure is between L / 5 and L / 3, wherein the length of the beam structure is L / 2.

[0018] In some embodiments of the present invention, the piezoelectric sheet extends L / 4 along the beam structure.

[0019] In some embodiments of the present invention, the two electrodes of the piezoelectric element are respectively connected to a resistive-inductive resonant circuit, wherein the resistive-inductive resonant circuit satisfies:

[0020]

[0021] Where L is the inductance parameter value, R is the resistance parameter value, f0 is the frequency corresponding to the resonance peak to be suppressed, in Hz, and kJ / L is the frequency of the resonance peak to be suppressed. 31 C is the electromechanical coupling coefficient of the piezoelectric element. p This is the intrinsic capacitance of the piezoelectric element.

[0022] In some embodiments of the present application, the first electrode end of the piezoelectric sheet is grounded, and the second electrode end is electrically connected to a negative capacitance circuit; the impedance of the negative capacitance circuit is: wherein, α is the negative capacitance ratio of the negative capacitance circuit, C p is the intrinsic capacitance value of the piezoelectric sheet; the negative capacitance circuit comprises: a power amplifier, the positive input end of which is electrically connected to the second electrode end of the piezoelectric sheet, and the positive input end and the output end of which are electrically connected through a capacitor C; a slide rheostat, the first terminal post of which is grounded, the second terminal post of which is electrically connected to the output line of the power amplifier, and the moving slide of which is electrically connected to the negative input end of the power amplifier.

[0023] In some embodiments of the present application, N=2, the base beam is composed of two beam structures, and piezoelectric sheets are fixed on the upper and lower surfaces of the two beam structures; the vibration isolation unit further comprises: a U-shaped base having two upward protruding connecting ends, the inner sides of the two connecting ends being connected to the sides of the two beam structures away from the connecting protrusions, respectively; wherein, S≥5T; D≥T, S is the length of the two connecting ends in the extension direction of the beam structure, and D is the width of the connecting protrusion protruding on the cosine curve beam.

[0024] In the second aspect of the present application, a force-electric coupling quasi-zero stiffness vibration isolation device is provided, comprising: an upper connecting plate, a lower connecting plate, and a vibration isolation main structure connected between the upper connecting plate and the lower connecting plate; the vibration isolation main structure comprises: a periodic array of J×K groups of supercells; each group of supercells comprises: two vibration isolation units as above sharing the same connecting protrusion, J≥1, K≥1.

[0025] In some embodiments of the present application, the piezoelectric sheet is a piezoelectric ceramic fiber.

[0026] In some embodiments of the present application, the base beam is a cosine curve beam.

[0027] In some embodiments of the present application, the vibration isolation main structure is made of an aluminum alloy material.

[0028] In some embodiments of the present application, the vibration isolation main structure, the upper connecting plate and the lower connecting plate are integrally manufactured by additive manufacturing technology.

[0029] In some embodiments of the present application, in the vibration isolation unit, the connection form of the beam structure and the connecting protrusion is a fillet or a chamfer.

[0030] In some embodiments of the present application, the piezoelectric sheet is bonded and fixed to the connecting beam.

[0031] (Three) beneficial effects

[0032] From the above technical solutions, the present application has at least one of the following beneficial effects relative to the prior art:

[0033] (1) The thicknesses of the beam structure and the piezoelectric sheet are determined by the Young's modulus of the beam structure and the Young's modulus of the piezoelectric sheet, the quasi-zero stiffness can be realized in the working area, and the application prospect is important in the field of vibration and noise reduction of major equipment in aerospace and other fields.

[0034] (2) On the basis of the accurate Young's modulus-beam structure / piezoelectric sheet thickness relationship formula, further empirical formula under the approximate conditions of using aluminum alloy material for the beam structure and commercial piezoelectric sheet is proposed, which is beneficial to quickly determine the thickness of each part and improve the universality of the technical scheme application.

[0035] (3) Through the analysis of the first order modal shape of the beam structure, the optimal length and optimal position of the piezoelectric sheet are obtained when the maximum corresponding modal electromechanical coupling coefficient on both sides of the convex is obtained, and the optimal control effect of the beam structure can be realized, and the piezoelectric sheet force-electric coupling effect is fully utilized.

[0036] (4) The piezoelectric sheet of the vibration isolation unit cell is connected with an external resistance inductance resonance circuit, which greatly reduces the resonance peak and widens the effective vibration isolation interval.

[0037] (5) The vibration isolation unit cell is connected with an external negative capacitance circuit, which can improve the adaptability of the superstructure, realize the active control of the stiffness of the beam structure, and enhance the safety factor and working performance of the precision instrument equipment in the complex and changeable working environment.

[0038] (6) The force-electric coupling quasi-zero stiffness vibration isolation device of the embodiment has the advantages of simple structure, convenient installation, wide vibration isolation frequency band, small resonance influence and strong anti-interference ability, and has good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 It is a perspective view of the force-electric coupling quasi-zero stiffness vibration isolation unit of the embodiment of the application.

[0040] Figure 2A And Figure 2B It is a schematic view of other types of beams suitable for the technical scheme of the application.

[0041] Figure 3 It is Figure 1 It is a schematic view of one of the two beam structures constituting the cosine curve beam in the force-electric coupling quasi-zero stiffness vibration isolation unit shown in the figure.

[0042] Figure 4 It is applied to Figure 1 Two typical examples of the shunt circuit in the force-electric coupling quasi-zero stiffness vibration isolation unit shown in the figure.

[0043] Figure 5 It is a schematic view of the force-electric coupling quasi-zero stiffness vibration isolation supercell of the embodiment of the application.

[0044] Figure 6A perspective view of the force-electric coupling quasi-zero stiffness vibration isolation device according to an embodiment of the present application.

[0045] Figure 7 A front view of the force-electric coupling quasi-zero stiffness vibration isolation device according to an embodiment of the present application. Figure 6

[0046] Figure 8a A nonlinear force-displacement relationship diagram of the first example of the force-electric coupling quasi-zero stiffness vibration isolation device according to the present application.

[0047] Figure 8b A resonance frequency-amplitude curve of the first example of the force-electric coupling quasi-zero stiffness vibration isolation device according to the present application.

[0048] Figure 9a A frequency-amplitude curve of the second example of the force-electric coupling quasi-zero stiffness vibration isolation device according to the present application when the load is 22.6 kg.

[0049] Figure 9b A frequency-amplitude curve of the second example of the force-electric coupling quasi-zero stiffness vibration isolation device according to the present application when the load mass is changed to 24.1 kg.

[0050] Figure 9c A frequency-amplitude curve of the second example of the force-electric coupling quasi-zero stiffness vibration isolation device according to the present application when the load mass is changed to 24.1 kg and a negative capacitance circuit is added. DETAILED DESCRIPTION

[0051] The inventive concept of the present application is to realize the optimal control effect of the beam structure by analyzing the modal vibration mode and optimizing the parameters of the beam structure / piezoelectric sheet thickness, the piezoelectric sheet length, the fixed position, the resonance circuit, the negative capacitance circuit, etc. in the force-electric coupling vibration isolation unit, and fully exert the force-electric coupling effect of the piezoelectric sheet.

[0052] The present application first provides a force-electric coupling quasi-zero stiffness vibration isolation unit, and further provides a vibration isolation device using the vibration isolation unit. Those skilled in the art should understand that the vibration isolation unit in the present application can be used alone and can solve the corresponding technical problems and produce the corresponding beneficial effects.

[0053] To make the objects, technical solutions and advantages of the present application clearer, further detailed description will be made below with reference to the specific embodiments and the accompanying drawings.

[0054] I. Force-electric coupling quasi-zero stiffness vibration isolation unit

[0055] In an exemplary embodiment of the present application, a force-electric coupling quasi-zero stiffness vibration isolation unit is provided. Figure 1 A perspective view of the force-electric coupling quasi-zero stiffness vibration isolation unit according to an embodiment of the present application. ​

[0056] As Figure 1 shown, the force-electric coupling quasi-zero stiffness vibration isolation unit of the embodiment comprises:

[0057] a U-shaped base 211 having two connecting ends protruding upward;

[0058] a base beam 212 formed by extending inwardly from the two connecting ends of the U-shaped base;

[0059] a connecting protrusion 213 arranged at the middle position of the cosine curve beam and protruding away from the U-shaped base;

[0060] four pieces of piezoelectric ceramic fibers 3 arranged above and below the cosine curve beam at the left and right sides of the connecting protrusion;

[0061] four sets of shunt circuits respectively connected to the two electrodes of the corresponding piezoelectric ceramic fibers to control the piezoelectric ceramic fibers;

[0062] In which, the thickness of the piezoelectric ceramic fibers and the thickness of the cosine curve beam satisfy a specific relationship to achieve the best vibration reduction effect, which will be described in detail below.

[0063] The following describes each part of the force-electric coupling quasi-zero stiffness vibration isolation unit of the embodiment in detail.

[0064] In the embodiment, the base beam 212 can be regarded as two beam structures (212a, 212b) separated by 180° from each other, and the U-shaped base corresponds to the two beam structures. However, the focus of the present application is to optimize the beam structure / piezoelectric ceramic fiber thickness, piezoelectric ceramic fiber length, and fixing position, resonant circuit, negative capacitance circuit, etc. parameters, and is not limited to Figure 1 the vibration isolation unit shown, which is also applicable to other types of vibration isolation units, for example: ① a vibration isolation unit comprising three beam structures, as shown in Figure 2A ; ② a vibration isolation unit comprising four beam structures, etc.

[0065] By extension, the technical solution of the present application is applicable to a force-electric coupling quasi-zero stiffness vibration isolation unit comprising N beam structures, which extend radially around the connecting protrusion with an angle of 360° / N between each other, and N≥2.

[0066] In the embodiment, the base beam 212 is a cosine curve beam composed of two beam structures. The connecting protrusion 213 is in the shape of a rectangular column to adapt to the cosine curve beam. However, in other embodiments of the present application, the shape of the connecting protrusion is determined depending on the number and structure of the beam structures, for example, Figure 2A the vibration isolation unit shown in Figure 2BIn the shown vibration isolation unit, the connecting protrusion is in the shape of a square column. The connection between the cosine curve beam 212 and the connecting protrusion 213 is in the form of a rounded or chamfered corner.

[0067] The piezoelectric ceramic fiber used in the present application is an advanced thin sheet type actuator and sensor with high flexibility and high reliability. It is composed of a rectangular piezoelectric ceramic rod wrapped by an adhesive, an electrode and a polyimide film layer. The positive and negative electrodes are alternately bonded to the film wrapping the piezoelectric ceramic rod, which can apply a cross voltage to the piezoelectric ceramic rod or output a voltage from the piezoelectric ceramic rod. After packaging, the piezoelectric ceramic fiber has high sealing property, strong piezoelectric property, and good toughness.

[0068] It should be particularly pointed out that the piezoelectric ceramic fiber is only a preferred implementation manner of the present application. In other embodiments of the present application, other types of piezoelectric sheets can also be used as long as their thickness and / or position meet the specific relationship proposed in the present application, and the present application can be implemented, which is also within the protection scope of the present application.

[0069] In the present embodiment, piezoelectric ceramic fibers are arranged on both upper and lower sides of the two beam structures 212a and 212b, which can maximize the vibration reduction effect. However, in fact, as long as at least one piezoelectric ceramic fiber is arranged, the vibration reduction effect can be achieved. Therefore, the present application does not limit the number of piezoelectric ceramic fibers in the vibration isolation unit.

[0070] In the present embodiment, the piezoelectric ceramic fiber 3 is attached to one end of the beam structure near the connecting protrusion, and the cosine curve beam is connected to the U-shaped base. The piezoelectric ceramic fiber is fixed to the beam structure by pasting. However, in other embodiments of the present application, the piezoelectric ceramic fiber can also be fixed to the beam structure by other means, such as screwing, which can also achieve the present application, and the present application does not limit this.

[0071] Figure 3 For Figure 1 The schematic diagram of one of the two beam structures constituting the cosine curve beam in the shown force-electric coupling quasi-zero stiffness vibration isolation unit. As shown in Figure 1 and Figure 3 In the present embodiment, the width of the vibration isolation unit curve beam is B, the cross height of the curve beam is H, the thickness of the curve beam is T, the length of the curve beam is L, the length of a single beam structure is L / 2, and the transverse length of the piezoelectric fiber is L p , the thickness is H p , S is the length of the connecting end along the extension direction of the beam structure, and D is the width of the connecting protrusion protruding on the cosine curve beam.

[0072] In order to make the U-shaped base have a better constraint effect, the length of the outer wall at both ends of the vibration isolation unit is S≥5T; in order to make the connecting part not easy to be damaged, the length of the middle protrusion is D≥T.

[0073] 1. Optimization of piezoelectric ceramic fiber length and position

[0074] The control effect of the piezoelectric material is determined by the modal electromechanical coupling coefficient, as shown in equation 1. The modal electromechanical coupling coefficient is proportional to the difference between the derivatives of the piezoelectric ceramic fiber at both ends under the corresponding modal shape. In the present application, only the first-order modal is considered.

[0075]

[0076] where x i represents the position coordinate of one end of the piezoelectric ceramic fiber close to the edge of the beam, x i+1 represents the position coordinate of the other end of the piezoelectric ceramic fiber, D1(x i , x i+1 ) represents the modal electromechanical coupling coefficient, represents the difference between the derivatives of the modal shape function at x i+1 and x i .

[0077] In the present application, the first-order modal shape of the curved beam can be represented as:

[0078]

[0079] where,

[0080] Therefore, when the corresponding modal electromechanical coupling coefficients on both sides of the protrusion are maximum, the length of the piezoelectric ceramic fiber should be L / 4, and it should be attached to the position closest to the protrusion.

[0081] In the present embodiment, the length of the piezoelectric ceramic fiber is L / 4, and it is attached to the position closest to the connecting protrusion, which can achieve the optimal effect. However, in other embodiments of the present application, the length of the piezoelectric ceramic fiber extending on the beam structure is between L / 5 and L / 3, which can still achieve a certain vibration reduction effect.

[0082] 2. Optimization of piezoelectric ceramic fiber and beam structure thickness

[0083] According to the different degrees of compression of the cosine curve beam and the different forms of the external circuit of the piezoelectric material, the unit cell will exhibit different mechanical properties. For a cosine curve beam with piezoelectric material attached, in order to achieve quasi-zero stiffness in the working area, the energy method can be used to solve the force-displacement relationship first. The work done by the force is equal to the bending energy and compression energy of the cosine curve beam. After obtaining the stiffness expression, optimization analysis is performed.

[0084] In the present embodiment, the base beam is a cosine curve beam, and the preformed shape of the cosine curve beam is:

[0085]

[0086] The shape of the beam after deformation can be expressed by modal superposition method, and the contribution of the first order mode is much larger than that of the high order modes, so the shape of the beam after deformation is:

[0087]

[0088] The displacement of the base beam at the midpoint can be expressed as:

[0089]

[0090] The bending energy of the curved beam with piezoelectric film can be calculated into three sections, the first section is only the base beam structure, the second section is the laminated structure of piezoelectric ceramic fiber material and base, and the third section is also only the base structure, so the bending energy of the whole beam can be expressed as:

[0091]

[0092] wherein, is the bending stiffness of the base beam,

[0093] is the equivalent bending stiffness of the piezoelectric ceramic fiber beam.

[0094] The compression amount of the piezoelectric ceramic fiber can be expressed as:

[0095]

[0096] The compression amount of the base beam can be expressed as:

[0097]

[0098] The equivalent axial force of the piezoelectric ceramic fiber and the base beam can be written by Hooke's law:

[0099]

[0100] Therefore, the compression energy of them can be expressed as:

[0101]

[0102] The potential energy generated by the pressure is:

[0103]

[0104] The total energy of the system is:

[0105] u tot =u b +u s +u f (12)

[0106] The force-displacement relationship can be obtained from the principle of minimum potential energy.

[0107]

[0108] To achieve near-zero stiffness in the working region, i.e., when the first derivative of the force-displacement curve is close to zero, the parameters of the beam and the piezoelectric ceramic fiber must satisfy the following relationship:

[0109]

[0110] Where, k 31 E is the electromechanical coupling coefficient of the piezoelectric ceramic fiber, and E is the Young's modulus of the matrix beam material. p This represents the Young's modulus of the piezoelectric ceramic fiber under short-circuit conditions.

[0111] Those skilled in the art should understand that, as shown in equation (14) above, which is the theoretically optimal solution calculated in theory, a mechanically coupled curved beam with stiffness closest to zero can be designed. However, in practical applications, the optimal solution can be set near the actual solution. The following explains two scenarios:

[0112] (1) With a fixed piezoelectric ceramic fiber thickness, determine the optimal thickness of the beam structure:

[0113] piezoelectric ceramic fiber H p '=H p Substituting into equation (14), the theoretical thickness T of the beam structure is obtained. The actual thickness T' of the beam structure can be taken within the following range: T≤T'≤1.1T.

[0114] (2) Determine the thickness of the fixed beam structure and the thickness of the fixed ceramic fibers:

[0115] Substituting the thickness T' = T of the beam structure into (14), the theoretical thickness H of the piezoelectric ceramic fiber is obtained. p The actual thickness H of the piezoelectric ceramic fiber p 'Values ​​can be taken from the following range: H' p ≤H p '≤1.2H p .

[0116] In this embodiment, the thickness of the beam structure and the piezoelectric ceramic fiber are determined by the Young's modulus of the beam structure and the Young's modulus of the piezoelectric ceramic fiber under short-circuit conditions. This enables the achievement of quasi-zero stiffness in the working region and proposes a design method for a force-electric coupling quasi-zero stiffness unit cell. This method has significant application prospects in vibration reduction and noise reduction of major equipment in aerospace, transportation and other fields.

[0117] Further, on the basis of the above-mentioned formula (14), the present application also proposes a more practical empirical formula, when H is between 2.1 mm and 3 mm, the material of the beam is aluminum alloy, and the piezoelectric material is piezoelectric ceramic fiber, and the Young's modulus is between 25 GPa and 35 GPa. After using numerical software to fit, T and H p In the numerical sense, the following is satisfied:

[0118]

[0119] wherein 0.6≤a≤1.3, 0.3≤b≤0.5, 1.8≤c≤2.6, T and H p The units of T and H are mm.

[0120] According to formula (15), when the thickness of the piezoelectric ceramic fiber is 0.1-0.8 mm, the thickness of the corresponding base beam should be between 1.8-0.7 mm. In practice, it is relatively difficult to achieve a true zero stiffness, and here the stiffness can be designed as an extremely small value close to zero, and the extremely small value is specified as 5% of the initial stiffness, so the thickness that can be used in practice is 0-0.1 mm fluctuating upward from the theoretical value.

[0121] Specifically, the piezoelectric ceramic fiber used in this embodiment has a thickness of 0.3 mm, and the thickness of the aluminum cosine curve beam in the vibration isolation unit is 1.6-1.7 mm. The unit will have a stress characteristic that the equivalent stiffness first decreases and then increases with lateral compression, and the minimum equivalent stiffness can be close to zero.

[0122] On the basis of the precise Young's modulus-beam structure / piezoelectric ceramic fiber thickness relationship formula, the present application further proposes an empirical formula under the approximate conditions of using aluminum alloy material for the beam structure and using commercial piezoelectric ceramic fiber, which is beneficial to quickly determine the thickness of each part and improve the universality of the technical scheme.

[0123] 3, shunt circuit 1: LR resonant circuit

[0124] As shown in Figure 1 , two electrodes are connected to the shunt circuit from the piezoelectric ceramic fiber of the beam structure. Figure 4 For application in Figure 1 two typical examples of the shunt circuit in the force-electric coupling quasi-zero stiffness vibration isolation unit.

[0125] In an embodiment of the present application, the shunt circuit is an LR resonant circuit, as shown in Figure 4 (a) of the figure.

[0126] In this embodiment, the LR resonant circuit includes a resistor R and an inductor L connected in series. The two ends of the LR resonant circuit are electrically connected to the two electrodes of the piezoelectric ceramic fiber.

[0127] When the embodiment is used to suppress a certain resonance peak, the circuit parameters set in the resonant circuit need to meet:

[0128]

[0129] wherein L is an inductance parameter value, R is a resistance parameter value, f0 is a frequency corresponding to the resonance peak to be suppressed, in Hz, k 31 is a mechanical-electrical coupling coefficient, C p is an intrinsic capacitance of the piezoelectric ceramic fiber.

[0130] In the present embodiment, the piezoelectric ceramic fiber of the vibration isolation unit cell is connected to an external resistance-inductance resonant circuit, which greatly reduces the resonance peak value and widens the effective vibration isolation interval.

[0131] 4. Shunt circuit 2: negative capacitance circuit

[0132] In another embodiment of the present application, the shunt circuit is a negative capacitance circuit, as shown in FIG. (b) of Figure 4 .

[0133] In the present embodiment, the first electrode end of the piezoelectric ceramic fiber is grounded, and the second electrode end is electrically connected to the negative capacitance circuit.

[0134] The impedance of the negative capacitance circuit is: wherein a is the negative capacitance ratio of the negative capacitance circuit, C p is the intrinsic capacitance value of the piezoelectric ceramic fiber.

[0135] The negative capacitance circuit comprises: a power amplifier, the positive input end of which is electrically connected to the second electrode end of the piezoelectric ceramic fiber, and the positive input end and the output end thereof are electrically connected through a capacitor C; a slide rheostat, the first terminal of which is grounded, and the second terminal thereof is electrically connected to the output line of the power amplifier, and the moving slide thereof is electrically connected to the negative input end of the power amplifier.

[0136] In the present embodiment, the vibration isolation unit cell is connected to an external negative capacitance circuit, which can improve the adaptability of the superstructure, realize active control of the stiffness of the beam structure, and enhance the safety factor and working performance of the precision instrument equipment in complex and variable working environments.

[0137] II. Force-electric coupling quasi-zero stiffness vibration isolation supercell

[0138] Based on the above vibration isolation unit cell, the present application further provides a vibration isolation supercell.

[0139] Figure 5 is a schematic diagram of the vibration isolation supercell of the present application. Please refer to Figure 1 and Figure 5, the force-electric coupling quasi-zero stiffness vibration isolation supercell comprises two vibration isolation cells as described in the above embodiment sharing the same connecting protrusion. The two vibration isolation cells are identical in shape and size and opposite in top.

[0140] In other words, the vibration isolation supercell composed of two symmetrical vibration isolation cells is formed by rotating 180° around the midpoint of the connecting protrusion end of the vibration isolation cell.

[0141] The vibration isolation supercell of the embodiment can be used as a repeated unit to construct the main structure of the vibration isolation device.

[0142] III. Force-electric coupling quasi-stiffness vibration isolation device

[0143] Based on the vibration isolation cell and the vibration isolation supercell as described above, in an exemplary embodiment of the present application, a force-electric coupling quasi-zero stiffness vibration isolation device is provided.

[0144] Figure 6 It is a perspective view of the force-electric coupling quasi-zero stiffness vibration isolation device of the embodiment of the present application. Figure 7 It is a perspective view of the force-electric coupling quasi-zero stiffness vibration isolation device of the embodiment of the present application. Figure 6 It is a front view of the force-electric coupling quasi-zero stiffness vibration isolation device as shown in Figure 6 and Figure 7 The force-electric coupling vibration isolation device of the embodiment comprises an upper connecting plate 1, a lower connecting plate 4, and a vibration isolation main structure 2 connected between the upper connecting plate and the lower connecting plate.

[0145] The vibration isolation main structure 2 comprises a periodic array of JxK groups of supercells, J≥1, K≥1. Each group of supercells comprises two vibration isolation cells as described above sharing the same connecting protrusion. In each vibration isolation cell, the part of the cosine curve beam close to the top protrusion is covered with piezoelectric ceramic fiber 3.

[0146] The material of the vibration isolation main structure 2 is selected from materials that have good combination effect with the piezoelectric ceramic fiber 3 and similar modulus, such as aluminum alloy material. The superstructure is prepared by additive manufacturing technology, the upper connecting plate 1 is integrally manufactured with the lower connecting plate 4 and the curve beam, and finally the piezoelectric ceramic fiber 3 is pasted.

[0147] In the following, the force-electric coupling quasi-zero stiffness vibration isolation device shown in Figure 6 will be studied. The main material is aluminum alloy, and four pieces of piezoelectric ceramic fiber are pasted on the upper and lower surfaces of the two ends of the curve beam to form a force-electric coupling quasi-zero stiffness vibration isolation cell. The functions of the two specific embodiments will be described below.

[0148] 1. First example of vibration isolation device

[0149] Please refer to Figure 1The geometric parameters of the vibration isolation cell in this example are as follows: the length of the curved beam L = 100 mm, the curved beam span height H = 2.1 mm, the thickness T = 1.6 mm, the width B = 14 mm, the length of the piezoelectric ceramic fiber L = 25 mm, the thickness H = 0.3 mm, the modulus of the base beam E = 70 GPa, the modulus of the piezoelectric ceramic fiber E = 32.58 GPa, and the electromechanical coupling coefficient k = 0.335. In order to ensure sufficient restraint force, the total width of the protrusions connecting two adjacent supercells S = 10 mm, and the width of the protrusions connecting two symmetric cells in the supercell D = 3 mm. p p p 31

[0150] In this example, an LR resonant circuit is used as the shunt circuit of the piezoelectric ceramic fiber. Please refer to FIG. 1(a) for the impedance, which can be represented as Z = R + iωL, where R is the resistance value, L is the inductance value, i is the imaginary unit, and ω is the frequency. Figure 4

[0151] The quasi-zero stiffness superstructure with external circuit is simulated in the finite element software COMSOL. In the finite element, the contact end of the piezoelectric ceramic fiber and the curved beam is grounded, and a point charge constraint condition is applied on the other surface where V is the voltage on the surface of the piezoelectric ceramic fiber.

[0152] The nonlinear force-displacement relationship of the force-electric coupling quasi-zero stiffness vibration isolation device in this example is shown in FIG. 2. It has a small dynamic stiffness at 2.1 mm. In the case where the piezoelectric ceramic fiber is not powered or not connected to the circuit, the mounting surface load on the vibration isolation cell is 18.7 kg, and a 0.01 mm displacement harmonic excitation is applied on the lower connecting surface. The response in the frequency range of 0-10 Hz is calculated using the finite element software COMSOL, and the amplitude curve is plotted as shown in FIG. 3. The resonance frequency of the cell is 2.5 Hz, and the resonance peak value is 90 dB. Figure 8a Figure 8b The LR resonant circuit is connected to the ends of the piezoelectric ceramic fiber, and the resistance and inductance parameters of the circuit are adjusted using the results calculated in equation (16). Similarly, a 0.01 mm displacement harmonic excitation is applied on the lower mounting surface of the cell. The response in the frequency range of 0-10 Hz is calculated using the finite element software COMSOL, and the amplitude curve is plotted. The maximum resonance peak value of the cell is about 30 dB. Through the finite element simulation experiment, we can see that after connecting the circuit, the amplitude response at the resonance frequency of 2.5 Hz is reduced by about 60 dB, as shown in FIG. 4.

[0153] The LR resonant circuit is connected to the ends of the piezoelectric ceramic fiber, and the resistance and inductance parameters of the circuit are adjusted using the results calculated in equation (16). Similarly, a 0.01 mm displacement harmonic excitation is applied on the lower mounting surface of the cell. The response in the frequency range of 0-10 Hz is calculated using the finite element software COMSOL, and the amplitude curve is plotted. The maximum resonance peak value of the cell is about 30 dB. Through the finite element simulation experiment, we can see that after connecting the circuit, the amplitude response at the resonance frequency of 2.5 Hz is reduced by about 60 dB, as shown in FIG. 4. Figure 8b ​​​​​​The principle of cutting the resonance peak is to generate greater damping at the resonance frequency, thereby reducing the resonance peak value and not having a greater impact on other positions; it can also be understood that when the curved beam vibrates, it drives the piezoelectric ceramic fiber to displace, and the circuit can absorb the vibration energy and dissipate it.

[0154] 2. Second example of vibration isolation device

[0155] Please refer to Figure 1 In this example, the geometric parameters of the unit cell are: curved beam length L = 100 mm, span height H = 2.1 mm, thickness T = 1.7 mm, width B = 14 mm, piezoelectric ceramic fiber length L p = 25 mm, thickness H p = 0.3 mm, beam modulus E = 70 GPa, piezoelectric ceramic fiber short circuit Young's modulus E p = 32.58 GPa, electromechanical coupling coefficient k 31 = 0.335.

[0156] This example increases the equivalent elastic modulus of the piezoelectric ceramic fiber through negative capacitance control, thereby adjusting the stiffness of the entire structure. The negative capacitance circuit is a widely used circuit form in the field of active control, and in this patent, only one implementation form is given, as shown in Figure 4 (b) of the figure. By adjusting the ratio of R1 and R2 through the position of the sliding piece of the sliding resistor, the size of the negative capacitance connected to the circuit is adjusted, and the function of adjusting the equivalent modulus of the piezoelectric ceramic fiber is realized, thereby realizing the active control of the equivalent stiffness of the supercell. The impedance of the negative capacitance circuit can be described as where α is the negative capacitance ratio, C p is the intrinsic capacitance value of the piezoelectric ceramic fiber.

[0157] Figure 9a is the frequency-amplitude curve of the second example of the force-electric coupling quasi-zero stiffness vibration isolation device of the present application when the load is 22.6 kg. As shown in Figure 9a , the resonance frequency is 4 Hz. Figure 9b is the frequency-amplitude curve of the force-electric coupling quasi-zero stiffness vibration isolation device of the present application when the load mass changes to 24.1 kg. As shown in Figure 9b , the resonance frequency changes to 6.5 Hz.

[0158] When the load mass is 24.1 kg, after the negative capacitance circuit with a negative capacitance ratio of -0.7 is connected and controlled, the resonance frequency becomes 4.8 Hz. Figure 9c is the frequency-amplitude curve after the negative capacitance circuit is connected in the second example of the force-electric coupling quasi-zero stiffness vibration isolation device of the present application. By comparing Figure 9b and 9cWhen the negative capacitance circuit is added, the stiffness of the force-electric coupling unit cell is reduced.

[0159] Thus far, the various embodiments of the present application are introduced.

[0160] In summary, through the analysis of the modal shape, the thickness of the beam structure / piezoelectric ceramic fiber, the length of the piezoelectric ceramic fiber, and the fixed position, resonant circuit, negative capacitance circuit and other parameters in the force-electric coupling vibration isolation unit cell are optimized, the optimal control effect of the beam structure is realized, the force-electric coupling effect of the piezoelectric ceramic fiber is fully utilized, and the present application has good popularization and application prospect.

[0161] It should be noted that for some implementations, if they are not the key content of the present application and are well known to those skilled in the art, they are not described in detail in the drawings or the text of the specification, at this time, they can be understood by referring to the related prior art. The above part has described the embodiments of the present application as much as possible in combination with the drawings. Based on the above description, those skilled in the art should have a clear understanding of the present application.

[0162] It should also be noted that the directional language mentioned in the embodiments, such as "up", "down", "front", "back", "left", "right", "inside", "outside", etc., is only the direction of the drawings, and is not used to limit the protection scope of the present application. Throughout the drawings, the same elements are represented by the same or similar reference numerals. Moreover, the shapes and sizes of the components in the drawings do not reflect the true size and ratio, but only illustrate the content of the embodiments of the present application. In addition, in the claims, any reference symbol located between parentheses should not be construed as a limitation on the claims.

[0163] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "connected", "connected" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected, it can be directly connected, or indirectly connected through an intermediate medium, it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0164] Unless expressly stated to the contrary, numeric parameters in the specification and claims of this application can be approximations. Accordingly, unless indicated otherwise, the numerical parameters set forth in the specification and claims are approximations. It is intended that the description and examples set forth herein are non-limiting.

[0165] It is understood that the examples provided above are for illustrative purposes only and that the present application can be embodied in many different forms without departing from the spirit or scope of the present application. In addition, the various elements and methods described above are not limited to the specific embodiments set forth but can be readily implemented with simple modifications or substitutions.

[0166] Similarly, it is to be understood that the use of certain terms or expressions in the description above are for illustrative purposes only and that the present application is not limited to the embodiments set forth in the description or the examples. Moreover, the various elements and methods described above are not limited to the specific embodiments set forth but can be readily implemented with simple modifications or substitutions.

[0167] The above detailed description of various embodiments of the application has been presented for the purposes of illustration and description. It is understood that the description is not intended to limit the application to the specific embodiments disclosed, but it is intended to cover all modifications and equivalents falling within the scope of the application.

Claims

1. A vibration isolation unit cell with quasi-zero stiffness achieved through electromechanical coupling, characterized in that, include: The connecting protrusion in the middle; With the connecting protrusion as the center, there are N beam structures extending radially, and the angle between each pair of these N beam structures is 360° / N, where N≥2; A piezoelectric sheet is fixed on at least one of the upper and lower surfaces of the beam structure, wherein the actual thickness H of the piezoelectric sheet is... p The actual thickness T of the beam structure satisfies: (H p ' = H p ; T ≤ T' ≤ 1.1T) or (T' = T; H p ≤ H p ' ≤ 1.2H p ) Among them, H p T is the theoretical thickness of the piezoelectric element; H is the theoretical thickness of the beam structure; E is the span of the beam structure; p k is the Young's modulus of the piezoelectric element. 31 denoted as , where is the electromechanical coupling coefficient of the piezoelectric element; E is the Young's modulus of the beam structure. The piezoelectric sheet is positioned close to the connecting protrusion, and its length extending along the beam structure is between L / 5 and L / 3, wherein the length of the beam structure is L / 2.

2. The vibration isolation unit cell according to claim 1, characterized in that, The actual thickness H of the piezoelectric element p The actual thickness T of the beam structure satisfies: (0.6≤a≤1.3;0.3≤b≤0.5;1.8≤c≤2.6) The piezoelectric element has a Young's modulus between 25 GPa and 35 GPa; the beam structure is made of aluminum alloy; the span height H of the beam structure is between 2.1 mm and 3 mm; and T and H... p The unit is mm.

3. The vibration isolation unit cell according to claim 1, characterized in that, The thickness of the piezoelectric sheet is between 0.1 mm and 0.8 mm; The thickness of the beam structure is between 1.8 mm and 0.7 mm.

4. The vibration isolation unit cell according to claim 1, characterized in that, The piezoelectric sheet extends L / 4 of the beam structure.

5. The vibration isolation unit cell according to claim 1, characterized in that, The two electrodes of the piezoelectric element are respectively connected to a resistor-inductor resonant circuit, which satisfies the following: Where L is the inductance parameter value, R is the resistance parameter value, f0 is the frequency corresponding to the resonance peak to be suppressed, in Hz, and kJ / L is the frequency of the resonance peak to be suppressed. 31 C is the electromechanical coupling coefficient of the piezoelectric element. p This is the intrinsic capacitance of the piezoelectric element.

6. The vibration isolation unit cell according to claim 1, characterized in that, The first electrode of the piezoelectric element is grounded, and the second electrode is electrically connected to the negative capacitor circuit. The impedance of the negative capacitor circuit is: Where α is the negative capacitance ratio of the negative capacitor circuit, and C p ω represents the intrinsic capacitance of the piezoelectric element, where i is the imaginary unit and ω is the frequency. The negative capacitor circuit includes: a power amplifier, whose positive input terminal is electrically connected to the second electrode of the piezoelectric element, and whose positive input terminal and output terminal are electrically connected through a capacitor C; a sliding rheostat, whose first terminal is grounded, whose second terminal is electrically connected to the output line of the power amplifier, and whose movable slider is electrically connected to the negative input terminal of the power amplifier.

7. The vibration isolation unit cell according to claim 1, characterized in that, N=2, the base beam is composed of two beams, and piezoelectric sheets are fixed on the upper and lower surfaces of the two beams; The vibration isolation unit cell also includes: a U-shaped base with two upwardly protruding connecting ends, the inner sides of which are respectively connected to the side of two beam structures away from the connecting protrusions; Where S≥5T; D≥T, S is the length of the two connecting ends along the extension direction of the beam structure, and D is the width of the connecting protrusion on the base beam.

8. A vibration isolation device with quasi-zero stiffness achieved through electromechanical coupling, characterized in that, include: An upper connecting plate, a lower connecting plate, and a vibration isolation main structure connecting the upper connecting plate and the lower connecting plate; The vibration isolation main structure includes: J×K groups of supercells arranged in a periodic array; each group of supercells includes: two vibration isolation unit cells sharing the same connecting protrusion as described in any one of claims 1 to 7, where J≥1 and K≥1.

9. The vibration isolation device according to claim 8, characterized in that, The piezoelectric element is a piezoelectric ceramic fiber; and / or The vibration isolation main structure is made of aluminum alloy material; and / or The vibration isolation main structure is integrally manufactured with the upper connecting plate and the lower connecting plate using additive manufacturing technology; and / or In the vibration isolation unit cell, the connection between the beam structure and the connecting protrusion is a rounded corner or chamfer; and / or The piezoelectric sheet is bonded and fixed to the beam structure.

10. A vibration isolation device with quasi-zero stiffness achieved through electromechanical coupling, characterized in that, include: An upper connecting plate, a lower connecting plate, and a vibration isolation main structure connecting the upper connecting plate and the lower connecting plate; The vibration isolation main structure includes: J×K groups of supercells arranged in a periodic array; each group of supercells includes: two vibration isolation unit cells as described in claim 7 that share the same connecting protrusion, where J≥1 and K≥1; The base beam is a cosine curve beam.

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