Constant-value quasi-zero stiffness vibration isolation structure and method based on negative stiffness mechanism of three pairs of oblique rods

Abstract

The present invention discloses a constant-value quasi-zero stiffness vibration isolation structure and method based on the negative stiffness mechanism of three pairs of diagonal rods. The vibration isolation structure comprises a fixed plate, a bracket, a transverse guide rod, a diagonal rod, a diagonal rod hinge support, a support connection block, a vertical guide rod, a vertical spring, a hollow tube, a load plate and a transverse spring; brackets are symmetrically installed on both sides of the fixed plate, a vertical guide rod is installed in the middle of the fixed plate, a support connection block is installed on the upper part of the vertical guide rod, and a vertical guide rod linear bearing connected to the vertical guide rod is installed on the support connection block; a vertical spring is installed on the vertical guide rod between the bottom of the support connection block and the fixed plate; three transverse guide rods are equidistantly installed on each bracket, and a transverse spring is installed on each transverse guide rod; three pairs of diagonal rods are provided, one end of the diagonal rod is hinged to a U-shaped groove through an axle rod, and the other end is hinged to the diagonal rod hinge support; the load plate is connected and fixed to the support connection block through bolts passing through the hollow tube.

Description

Technical Field

[0001] The invention relates to the field of vibration control, and in particular to a constant-value quasi-zero stiffness vibration isolation structure and method based on a negative stiffness mechanism of three pairs of oblique rods. Background Art

[0002] The literature [1] studies a single pair of diagonal rod quasi-zero stiffness model with a third-order nonlinear stiffness factor. Under large excitation, the transmissibility bends to the right, reducing the vibration isolation frequency band. In addition, the parameter design method given in this literature is complex (including several inequalities), which is not convenient for design and application. The technical solution in the above literature cannot obtain the zero stiffness characteristic of a straight line near the static equilibrium point, cannot reduce the resonant frequency of the linear oscillator, and is affected by nonlinear factors. Under large excitation conditions, the vibration isolation frequency band will be reduced due to nonlinear bending to the right.

[0003] Reference [2] proposes a constant quasi-zero stiffness debugging method for an isolator based on a single pair of diagonal rods with negative stiffness mechanism. This application proposes another constant quasi-zero stiffness structure in the form of a different structure and a different debugging method, which is completely different from reference [2] in structure and debugging method. The horizontal spring of reference [2] requires a larger stiffness, while the horizontal spring of this patent application requires a smaller stiffness, which is more suitable for smaller size spaces in terms of structure. Although both are constant quasi-zero stiffness structures, there are some obvious differences in the use effects.

[0004] References:

[0005] [1]Thanh Danh Le,Kyoung Kwan Ahn,A vibration isolation system in lowfrequency excitation region using negative stiffness structure for vehicleseat,Journal of Sound and Vibration,2011,330,6311-6335.

[0006] [2] Zhao Feng, Cao Shuqian, Hou Yuanhang, Li Bo, Song Qian, A zero-stiffness vibration isolation structure and method composed of a single pair of diagonal rod negative stiffness mechanism [P], CN202111347500.9, 2022-03-01. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a constant-value quasi-zero stiffness vibration isolation structure and method based on a negative stiffness mechanism of three pairs of oblique rods.

[0008] The objective of the present invention is achieved through the following technical solutions:

[0009] A constant-value quasi-zero stiffness vibration isolation structure based on a three-pair diagonal rod negative stiffness mechanism, comprising a fixed plate, a bracket, a transverse guide rod, a diagonal rod, a diagonal rod hinge support, a support connection block, a vertical guide rod, a vertical spring, a hollow tube, a load plate and a transverse spring; brackets are symmetrically installed on both sides of the fixed plate, a vertical guide rod is installed in the middle of the fixed plate, a support connection block is installed on the upper part of the vertical guide rod, and a vertical guide rod linear bearing connected to the vertical guide rod is installed on the support connection block; a vertical spring is installed on the vertical guide rod between the bottom of the support connection block and the fixed plate;

[0010] The left and right ends of the support connection block are connected with oblique rod hinge supports, and the oblique rod hinge supports are of U-shaped structure; three linear bearings are installed on each of the brackets at equal intervals through fixings, and each linear bearing is equipped with a transverse guide rod, and each transverse guide rod is provided with a U-shaped groove at one end facing the vertical guide rod, and a spring clamp is provided on the transverse guide rod next to the U-shaped groove, and a transverse spring is installed on each transverse guide rod between the spring clamp and the fixing;

[0011] Three oblique rods are symmetrically arranged on both sides of the vertical guide rod, one end of the oblique rod is hinged to the U-shaped groove through the shaft rod, and the other end is hinged to the oblique rod hinge support;

[0012] Connecting holes are respectively provided on both sides of the support connecting block, a hollow tube is provided on the connecting hole, a load plate is provided on the top of the hollow tube, and the load plate is connected and fixed to the connecting hole by bolts passing through the hollow tube.

[0013] Furthermore, a thick vertical through hole for the transverse guide rod to pass through is provided in the middle of the bracket, and two parallel thin vertical through holes are provided on both sides of the thick vertical through hole. The fixing piece adopts a connecting plate fixed with a fastening bolt and a linear bearing, and a through hole for the transverse guide rod to pass through is provided in the middle of the connecting plate, and bolt holes are provided on both sides of the connecting plate. The connecting plate is fixed to the bracket by fastening bolts passing through the bolt holes and the thin vertical through holes and connected to nuts.

[0014] Furthermore, three circular through holes are arranged at equal intervals on the bracket, the fixing member is a retaining spring, and the linear bearing and the bracket are fixed by the retaining spring.

[0015] The present invention also provides a method for debugging a constant-value quasi-zero stiffness vibration isolation structure based on the three pairs of diagonal rod negative stiffness mechanisms, comprising:

[0016] S1. According to the parameter conditions of the quasi-zero stiffness characteristic, determine the initial state of the lateral spring pre-compression δ 2 , the horizontal projection length a of the distance between the hinge points at both ends of the diagonal rod, and the length of the vertical spring, so that δ 2=a, the initial state refers to the state where the intersection of the three pairs of diagonal rods contacts the top of the free length vertical spring;

[0017] S2. Set the stiffness of the three pairs of transverse springs from top to bottom in the constant quasi-zero stiffness vibration isolation structure to be k 1 , k 3 and k 1 , the stiffness k of the vertical spring 2 , by determining the stiffness k of the transverse spring 1 and k 3 , determine the stiffness k of the vertical spring 2 , construct dimensionless parameters and Let the parameters α and α 1 satisfy

[0018] S3. After determining the above parameters, draw the force displacement curve fx, where f is the applied force, i.e. the force applied to the load plate, and x is the displacement from the initial position. At this time, the force displacement curve is an inclined straight line with a constant stiffness characteristic. Calculate the stiffness value K. Calculate the starting vibration isolation frequency based on the relationship between the vibration isolation mass m on the load plate. If the initial vibration isolation frequency does not meet the design requirements, steps S1 to S3 are repeated.

[0019] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0020] 1. The present invention proposes a constant quasi-zero stiffness vibration isolator constructed with three pairs of inclined rods and a horizontal spring negative stiffness mechanism. This structure is proposed for the first time in the research of constant quasi-zero stiffness.

[0021] 2. The present invention proposes a quasi-zero stiffness vibration isolation structure constructed with three pairs of diagonal rods and a negative stiffness mechanism, and performs parameter design to obtain force and stiffness expressions that are completely different from the prior art; at the static equilibrium point, the stiffness is set equal to zero and the second-order derivative of the stiffness is set equal to zero, and two zero stiffness parameter conditions are obtained. It is a new debugging method to adjust the constant quasi-zero stiffness on demand according to the parameter conditions, which is simple to debug and has excellent accuracy. During parameter design (theoretical and technical analysis), the so-called static equilibrium point position refers to the state in which the three pairs of diagonal rods are centrally symmetrical (or the state in which the middle pair of diagonal rods are horizontal). The three pairs of horizontal springs have the same free length.

[0022] 3. Through the constant quasi-zero stiffness debugging method of the present invention, a zero stiffness characteristic of a straight line near the static equilibrium point can be obtained, and a constant quasi-zero stiffness characteristic in a wider range can be obtained, which can reduce the resonant frequency of the linear oscillator without any nonlinear factors; compared with the traditional quasi-zero stiffness isolator with weak cubic nonlinear characteristics, under large excitation conditions, the vibration isolation frequency band will not be reduced due to nonlinear bending to the right.

[0023] 4. The present invention solves the problem of cubic nonlinearity of traditional quasi-zero stiffness vibration isolators and can be used for low-frequency vibration isolation problems under large excitation amplitude and variable load conditions. The present invention is a constant-value quasi-zero stiffness vibration isolation structure, which has infinite static equilibrium positions in terms of specific application effects.

[0024] 5. The present invention can be applied to engineering applications of low-frequency vibration isolation, and solves the contradictory problem that the traditional linear stiffness vibration isolation system requires small dynamic stiffness but produces large static deformation during low-frequency vibration isolation. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a structural schematic diagram of the constant-value quasi-zero stiffness vibration isolation structure of the present invention.

[0026] Figure 2a and Figure 2b They are respectively a front view and a left view of one embodiment of the bracket.

[0027] Figure 3a and Figure 3b They are respectively a front view and a left view of another embodiment of the bracket.

[0028] Figure 4 It is the front view of the diagonal rod.

[0029] Figure 5a and Figure 5b They are the front view and top view of the diagonal rod hinge support respectively.

[0030] Figure 6a and Figure 6b They are the front view and top view of the transverse guide rod respectively.

[0031] Figure 7a and Figure 7b They are the front view and top view of the support connection block respectively.

[0032] Figure 8a and Figure 8b They are respectively simplified mechanical schematic diagrams of the constant-value quasi-zero stiffness vibration isolation structure of the present invention.

[0033] Figure 9a and Figure 9b They are schematic diagrams of stiffness-displacement curve and force-displacement curve respectively.

[0034] Figure markings: 1-fixed plate, 2-bracket, 3-lateral guide rod linear bearing, 4-lateral guide rod, 5-spring clamp, 6-radial bearing, 7-diagonal rod, 8-diagonal rod hinge support, 9-support connecting block, 10-vertical guide rod, 11-vertical spring, 12-hollow tube, 13-load plate, 14-vertical guide rod linear bearing, 15-lateral spring, 16-thick vertical through hole, 17-thin vertical through hole. DETAILED DESCRIPTION

[0035] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0036] like Figure 1 As shown, this embodiment provides a constant quasi-zero stiffness vibration isolation structure based on three pairs of diagonal rod negative stiffness mechanism, including a fixing plate 1, a bracket 2, a transverse guide rod 4, a diagonal rod 7, a diagonal rod hinge support 8, a support connection block 9, a vertical guide rod 10, a vertical spring 11, a hollow tube 12, a load plate 13 and a transverse spring 15;

[0037] The brackets 2 are symmetrically mounted on both sides of the fixed plate 1, and the bottom of the brackets 2 is fixedly connected to the fixed plate 1 by standard bolts. A vertical guide rod 10 is mounted in the middle of the fixed plate 1, and a support connection block 9 is mounted on the upper part of the vertical guide rod 10, and a vertical guide rod linear bearing 14 connected to the vertical guide rod 10 is mounted on the support connection block 9; a vertical spring 11 is mounted on the vertical guide rod 10 between the bottom of the support connection block 9 and the fixed plate 1;

[0038] The left and right ends of the support connection block 9 are connected with the oblique rod hinge support 8, and the oblique rod hinge support 9 is a U-shaped structure; three linear bearings are installed on each bracket 2 at equal intervals through a fixing piece, and each linear bearing is equipped with a transverse guide rod 4, and each transverse guide rod 4 is provided with a U-shaped groove at one end facing the vertical guide rod 10, and a spring clamp 5 is provided on the transverse guide rod next to the U-shaped groove, and a transverse spring 15 is installed on each transverse guide rod 4 between the spring clamp 5 and the fixing piece;

[0039] Three oblique rods 7 are symmetrically arranged on both sides of the vertical guide rod 10. The structure of the oblique rod 7 is shown in FIG. Figure 4 The two ends of each diagonal rod 7 are respectively hinged to the diagonal rod hinge support 8 and the U-shaped groove on the transverse guide rod 4 through the radial bearing 6 and the pin. Figure 4 ) has a round hole at the end, which matches the outer ring of the radial bearing (the radial bearing is relatively small, with an outer diameter of 5mm, an inner diameter of 2mm, and a thickness of about mm. Most sales platforms call it miniature bearings). Insert one end of the inclined rod 7 with the radial bearing into the transverse guide rod 4 ( Figure 6b Then insert the pin into Figure 6a The small hole on the right side also passes the endoporus of the radial bearing. At this moment, the diagonal rod 7 and the transverse guide rod 4 were hinged together by the radial bearing.

[0040] Connecting holes are respectively provided on both sides of the support connecting block 9, on which a hollow tube 12 is provided, and a load plate 13 is provided on the top of the hollow tube 12. The load plate 13 is fixedly connected to the connecting hole by bolts passing through the hollow tube 12.

[0041] For details, see Figure 2a and Figure 2b In this embodiment, three circular through holes are arranged at equal intervals on the bracket 2, and the fixing part adopts a retaining spring. The linear bearing 3 of the standard part has a retaining spring groove. The transverse guide rod linear bearing 3 is connected to the bracket 2 through the standard retaining spring to constrain the lateral displacement of the transverse guide rod linear bearing 3.

[0042] In the specific implementation process, the bracket 2 can also be used. Figure 3a and Figure 3b In the structure shown in the embodiment, a thick vertical through hole 16 for the transverse guide rod 4 to pass through is provided in the middle of the bracket, and two parallel thin vertical through holes 17 are provided on both sides of the thick vertical through hole 16. The fixing parts are fastening bolts and connecting plates. A linear bearing for connecting the transverse guide rod is installed in the middle of the connecting plate. Bolt holes are provided on both sides of the connecting plate. The connecting plate is fixed to the bracket 2 by fastening bolts passing through the bolt holes and the thin vertical through holes 17 and connected with nuts.

[0043] See Figure 5a and 5b In this embodiment, the diagonal rod hinge support 8 is a U-shaped structure, consisting of a bottom plate and two side plates. The bottom plate is provided with bolt holes for connecting with the support connecting block 9, and three axial holes are symmetrically provided on the two side plates for hinge connection with the diagonal rod.

[0044] See Figure 6a and 6b A U-shaped groove is provided at one end of the transverse guide rod, and axial holes for hinged connection of the oblique rod are symmetrically opened on the side plates on both sides of the U-shaped groove, and a groove for installing the spring clamping plate 5 is provided on the transverse guide rod beside the U-shaped groove.

[0045] See Figure 7a and 7b Bolt holes for connecting the hinge support 8 are provided at both ends of the support connecting block, a bearing hole is provided in the middle, and connecting holes for fixing the load plate are provided on both sides.

[0046] In this embodiment, the diagonal rod hinge support 8 is connected to the support connection block 9 by a stud, and the support connection block 9, the hollow tube 12, the load plate 13, and the vertical guide rod linear bearing 14 are fastened together by standard long bolts. The vibration isolation mass force exerted on the load plate 13 can be transmitted to the three pairs of diagonal rods 7. The transverse guide rod 4 can move horizontally with low friction after being constrained by the transverse guide rod linear bearing 3. The transverse spring 15 is axially constrained by the spring clamp 5 and the transverse guide rod linear bearing 3. The elastic force of the transverse spring can be transmitted to the load plate 13 through the diagonal rod 7 to obtain vertical force support force, especially to obtain negative stiffness characteristics in the vertical direction. The vertical spring 11 is constrained by the vertical guide rod 10, and the vertical displacement is limited by the vertical guide rod linear bearing 14 and the fixed plate 1, so that the load plate 13 obtains load-bearing capacity.

[0047] The constant quasi-zero stiffness vibration isolation structure constructed by three pairs of diagonal rod negative stiffness mechanisms, the mechanical schematic diagram in the initial state, see Figure 8a and Figure 8b . k 2 is the vertical spring stiffness, f h is the inward elastic force generated by the transverse spring (or horizontal tension spring), f h_u The stiffness is k 1 The elastic force generated by the upper lateral spring under the initial state pre-compression amount δ, f h_m The stiffness is k 3 The initial precompression of the lateral spring is δ 1 The elastic force generated under the condition, f h_l The stiffness is k 1 The lower pair of transverse springs is pre-compressed in the initial state δ 2 The elastic force generated under the condition, h is the vertical distance from the initial state to the static equilibrium position, the initial state is the state where the intersection of the three pairs of diagonal rods is in contact with the upper end of the vertical spring in the free state, x is the displacement from the initial position, and y is the displacement from the static equilibrium position. a is the horizontal projection length of the distance between the hinge points at both ends of the diagonal rod in the initial state; the ratio of the upper and lower lateral spring stiffness to the vertical spring stiffness α; the ratio of the middle lateral spring stiffness to the vertical spring stiffness α 1 ;δ refers to the pre-compression length of the upper lateral spring in the initial state;δ 1 Refers to the pre-compression length of the lateral spring in the initial state; δ 2 Refers to the pre-compression length of the lower pair of transverse springs in the initial state. The vertical distance from the horizontal position of the upper pair of diagonal springs to the horizontal position of the lower pair of diagonal springs is 2d, and the middle position of 2d is the static equilibrium position.

[0048] First, the expression of the applied force f is obtained. In order to analyze the characteristics of a wider range of structural parameters, the applied force f and its expression are dimensionless rigidified, see formula (1), and the dimensionless applied force can be obtained. expression, find expression right The first-order derivative of can be obtained as dimensionless stiffness See formula (2); formula (3) is a parameter expression; at the static equilibrium position, for the dimensionless stiffness By taking the second-order derivative and setting the stiffness equal to zero, we can obtain the parameter conditions of the zero stiffness characteristic, see formula (4). Taking the static equilibrium position as the zero point displacement, the static equilibrium point is Figure 8a At the middle position of 2d (the middle rod is in a horizontal state), the quasi-zero stiffness characteristics near the static equilibrium point are as follows: Figure 8bAs shown, it has the characteristics of constant quasi-zero stiffness (the dynamic stiffness of the vertical spring can be reduced to a constant quasi-zero stiffness state through the negative stiffness mechanism of the double pairs of diagonal rods, while maintaining a relatively high static stiffness to withstand the load), especially the constant quasi-zero stiffness can be adjusted as needed.

[0049] The diagonal rod and the transverse spring generate vertical negative stiffness, which is called the double diagonal rod negative stiffness mechanism. It is connected in parallel with the positive stiffness of the vertical spring. Near the static equilibrium point (the static equilibrium point is the position where the upper and lower diagonal rods are symmetrical), according to the debugging method of formula (5), a constant quasi-zero stiffness characteristic can be obtained vertically.

[0050]

[0051]

[0052] Among them, P 1 To P 9 is an intermediate variable. The dimensionless applied force, Dimensionless x displacement, α, α 1 Dimensionless stiffness, The tilt angle of the inclined rod, γ is the dimensionless initial position, Dimensionless compression in the initial state.

[0053]

[0054]

[0055] Constant quasi-zero stiffness ( Figure 8b The debugging method shown in the figure makes the ratio α of the selected lateral spring stiffness to the vertical spring stiffness satisfy And the pre-compression length δ of the transverse spring is equal to the horizontal length a between the two hinge points of the lower pair of diagonal rods of the diagonal rod in the initial state. If the above two conditions are met, the constant value quasi-zero stiffness characteristic can be obtained.

[0056] This embodiment is a structure and debugging method for realizing a constant quasi-zero stiffness mechanical property, which belongs to the research scope of quasi-zero stiffness vibration isolation and is applied to low-frequency vibration isolation engineering problems below a dozen Hz, such as low-frequency excitation and response caused by waves on ships, low-frequency excitation caused by vehicles on human bodies, and low-frequency excitation and response caused by spacecraft adjustments. The present invention is applied to engineering applications of low-frequency vibration isolation to solve the contradictory problem that traditional linear stiffness vibration isolation systems require small dynamic stiffness but produce large static deformation during low-frequency vibration isolation.

[0057] The specific debugging methods are as follows:

[0058] The first step is to make a three-pair oblique rod negative stiffness mechanism to construct a constant value quasi-zero stiffness vibration isolation structure according to the structural description of this application;

[0059] The second step is to determine the pre-compression amount δ of the transverse spring, the horizontal projection length a of the diagonal rod, and the length of the vertical spring in the initial state according to formula (5), so that δ = a in the initial state;

[0060] The third step is to determine the stiffness k of the transverse spring according to formula (5): 1 and k 3 , determine the stiffness k of the vertical spring 2 , construct dimensionless parameters and Let the parameters α and α 1 satisfy

[0061] Step 4: After determining the above parameters, draw the force displacement curve fx, see Figure 9b ,in Figure 9a The force displacement curve is a straight line that slopes upward and has a constant stiffness characteristic. The stiffness value K is calculated. According to the relationship between the vibration isolation mass m, the starting vibration isolation frequency is calculated. If the initial vibration isolation frequency does not meet the design requirements, repeat steps 2 to 4.

[0062] The present invention finally experiments with a vibration isolator with constant quasi-zero stiffness characteristics, which solves the problem of cubic nonlinearity of traditional quasi-zero stiffness vibration isolators and can be used for low-frequency vibration isolation problems under large excitation amplitude and variable load conditions. Traditional cubic nonlinear stiffness vibration isolators have only one static equilibrium position, while the present invention is a constant quasi-zero stiffness vibration isolator with infinite static equilibrium positions.

[0063] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, a person of ordinary skill in the art can also make many forms of specific changes under the guidance of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A method for debugging a constant-value quasi-zero stiffness vibration isolation structure based on a negative stiffness mechanism of three pairs of diagonal rods, the vibration isolation structure comprising a fixed plate, a bracket, a transverse guide rod, a diagonal rod, a diagonal rod hinge support, a support connection block, a vertical guide rod, a vertical spring, a hollow tube, a load plate and a transverse spring; brackets are symmetrically installed on both sides of the fixed plate, a vertical guide rod is installed in the middle of the fixed plate, a support connection block is installed on the upper part of the vertical guide rod, a vertical guide rod linear bearing connected to the vertical guide rod is installed on the support connection block; a vertical spring is installed on the vertical guide rod between the bottom of the support connection block and the fixed plate; the left and right ends of the support connection block are connected to the diagonal rod hinge support, and the diagonal rod hinge support is U-shaped Structure; three linear bearings are installed at equal intervals on each of the brackets through fixings, each linear bearing is equipped with a transverse guide rod, each transverse guide rod is provided with a U-shaped groove at one end facing the vertical guide rod, a spring clamp is provided on the transverse guide rod next to the U-shaped groove, and a transverse spring is installed on each transverse guide rod between the spring clamp and the fixing; three oblique rods are symmetrically arranged on both sides of the vertical guide rod, one end of the oblique rod is hinged to the U-shaped groove through an axle rod, and the other end is hinged to the oblique rod hinge support; connecting holes are provided on both sides of the support connecting block, a hollow tube is provided on the connecting hole, a load plate is provided on the top of the hollow tube, and the load plate is connected and fixed to the connecting hole by bolts passing through the hollow tube; A thick vertical through hole for the transverse guide rod to pass through is provided in the middle of the bracket, and two parallel thin vertical through holes are provided on both sides of the thick vertical through hole. The fixing member adopts a connecting plate fixed with a fastening bolt and a linear bearing, and a through hole for the transverse guide rod to pass through is provided in the middle of the connecting plate, and bolt holes are provided on both sides of the connecting plate. The connecting plate is fixed to the bracket by fastening bolts passing through the bolt holes and the thin vertical through holes and connected with nuts; The bracket is provided with three circular through holes at equal intervals, the fixing member is a retaining spring, and the linear bearing and the bracket are fixed by the retaining spring; the characteristic is that: include: S1. According to the parameter conditions of the quasi-zero stiffness characteristic, determine the pre-compression amount δ2 of the upper and lower transverse springs in the initial state, the horizontal projection length a of the distance between the hinge points at both ends of the diagonal rod, and the length of the vertical spring, so that δ2=a in the initial state. The initial state refers to the state where the intersection of the three pairs of diagonal rods contacts the top of the vertical spring of free length; S2. Set the stiffness of the three pairs of lateral springs from top to bottom in the constant quasi-zero stiffness vibration isolation structure to be k1, k3 and k1 respectively, and the stiffness of the vertical spring to be k2. By determining the stiffness k1 and k3 of the lateral springs, the stiffness k2 of the vertical spring is determined, and the dimensionless parameter is constructed. and Make the parameters α and α1 satisfy S3. After determining the above parameters, draw the force displacement curve fx, where f is the applied force, i.e. the force applied to the load plate, and x is the displacement from the initial position. At this time, the force displacement curve is an inclined straight line with a constant stiffness characteristic. Calculate the stiffness value K. Calculate the starting vibration isolation frequency based on the relationship between the vibration isolation mass m on the load plate. If the initial vibration isolation frequency does not meet the design requirements, steps S1 to S3 are repeated.

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