A quasi-zero stiffness based vibration isolation platform optimization design method

Abstract

This invention discloses an optimized design method for a vibration isolation platform based on quasi-zero stiffness. The optimized design object is a prismatic vibration isolation platform, comprising a top plate, a bottom plate, a two-layer prismatic structure consisting of a rotating rod connected by bearings, a horizontal spring and a damper installed in the middle of the prismatic structure, and oblique springs installed within the prismatic structural units. The combination of the negative stiffness of the horizontal spring and the positive stiffness of the oblique spring forms the QZS effect. By comparing and analyzing parameters such as the combined stiffness of the horizontal and oblique springs, the rod length of the PIP, and the initial rotation angle, optimized parameters are selected to achieve the optimized design of the vibration isolation platform. This invention enables the prismatic vibration isolation platform to achieve a quasi-zero stiffness effect over a wider range and maintains stable performance under large vibration displacements. It helps to eliminate potential instabilities, bifurcation, and jumping phenomena under large vibration displacements, thereby improving the overall vibration isolation performance.

Description

Technical Field

[0001] This invention relates to the field of seismic damping platform technology, and in particular to an optimized design method for a damping platform based on quasi-zero stiffness. Background Technology

[0002] In engineering practice, structures inevitably endure adverse vibrations, making vibration suppression and structural protection crucial. Among various vibration control methods, passive isolation systems have been widely used due to their excellent structural performance and practicality. For linear isolation systems, to achieve low-frequency isolation across a wide frequency range, the natural frequency of the isolation system needs to be lowered. This leads to reduced stiffness and weakened load-bearing capacity, making it impossible to simultaneously achieve high load-bearing capacity and low natural frequency. However, by introducing a nonlinear stiffness, namely quasi-zero stiffness (QZS), the stiffness of the structure can approach zero when vibrating at its static equilibrium position, achieving low-frequency isolation without sacrificing the static load-bearing capacity. Therefore, the design and application of QZS have received considerable attention in recent years.

[0003] However, previous studies have shown that the QZS section of the QZS isolation system is limited, and instability, bifurcation, and jumping phenomena occur when the system generates large vibration displacements. Summary of the Invention

[0004] This invention provides an optimized design method for a vibration damping platform based on quasi-zero stiffness. By using inclined springs and horizontal springs to rationally combine positive and negative stiffness and optimize design parameters, the system can achieve a wider QZS (Quadrant Range of Stability) and remain stable under large vibration displacements, thereby improving the overall vibration isolation / seismic performance of the structure and effectively solving the technical problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] An optimization design method for a vibration damping platform based on quasi-zero stiffness includes the following steps:

[0007] Step 1: Construct a prismatic vibration isolation platform consisting of horizontal springs, inclined springs, rotating rods, and dampers;

[0008] Step 2: Construct a mathematical model of the prismatic vibration isolation platform and define optimization parameters, including the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the stiffness k of the horizontal spring. h The stiffness k1 of the inclined spring is determined within the following range: 0≤L≤L max k hmin ≤k h ≤k hmax k 1min ≤k1≤k 1max Solve the model;

[0009] Step 3: Select the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the horizontal spring stiffness k that meet the requirements. h Substituting the design variable value of the inclined spring stiffness k1 into formulas (1)-(3), we obtain the stiffness force curve of the prismatic vibration isolation platform under this set of parameters and the corresponding quasi-zero stiffness section width d1. Formulas (1)-(3) are expressed as follows:

[0010] F k =F h +F p (1)

[0011]

[0012]

[0013] In the formula, F h F is the stiffness force of the horizontal spring. p F is the stiffness force of the inclined spring. k y1 represents the combined nonlinear stiffness force of the prismatic vibration isolation platform, Δx represents the overall horizontal displacement of the prismatic vibration isolation platform, Δl represents the change in length of the inclined spring, and y1 represents the overall vertical displacement of the prismatic vibration isolation platform.

[0014] Among them, △x and △l are determined by formulas (4)-(9):

[0015]

[0016]

[0017] Δx=2x1 (6)

[0018]

[0019]

[0020] Δl=l1-l0 (9)

[0021] In the formula, x1 represents the horizontal displacement of the half-prism vibration isolation platform, θ represents the initial rotation angle of the rotating rod, and Δh represents the change in platform height. Let l be the rotation angle of the rotating rod, L be the length of the rotating rod, l0 be the initial length of the inclined spring, and l1 be the length of motion of the inclined spring.

[0022] Step 4: Maintain the initial rotation angle θ of the rotating rod and the horizontal spring stiffness k as shown in Step 3. h With the spring stiffness parameter k1 unchanged, the length L of the rotating rod is changed, and step three is repeated to obtain the stiffness force curve of the prismatic vibration isolation platform under the changed length L of the rotating rod and the corresponding quasi-zero stiffness section width d1.

[0023] Step 5: Evaluate the stiffness force curve under the changed rotating rod length L in Step 4. If the quasi-zero stiffness section of the curve is optimized, proceed to the next step and obtain the optimized rotating rod length L. Otherwise, repeat Step 5. The evaluation criterion is the width of the quasi-zero stiffness section. A curve with a larger width indicates that the vibration isolation platform under this parameter set can achieve the quasi-zero stiffness (QZS) effect over a wider range, which helps to eliminate potential instabilities, bifurcation, and jumping phenomena in large vibration displacements and improves the overall vibration isolation performance.

[0024] Step Six: Control the design variable values ​​corresponding to the rotation rod length L and the initial rotation angle θ and horizontal spring stiffness k of the optimization parameters in Step Five. h By keeping the spring stiffness k1 constant and changing it, i.e. changing the combined stiffness of the prismatic vibration isolation platform, a set of data on the combined stiffness values ​​of the prismatic vibration isolation platform is obtained. These data are then substituted into formulas (1)-(3) to obtain the stiffness force curves of the prismatic vibration isolation platform under different combined stiffnesses.

[0025] Step 7: Evaluate the stiffness force curves of different combinations of stiffness under the optimized parameter of rotating rod length L in Step 6, select the optimal quasi-zero stiffness section, and obtain the corresponding optimized parameter of inclined spring stiffness k1. The evaluation criteria are the same as in Step 5.

[0026] Step 8: Based on the parameters obtained in Step 5 (rod length L) and Step 7 (skew spring stiffness k1), complete the optimized design of the prism-shaped vibration isolation platform under the given initial rotation angle θ of the rotating rod.

[0027] Step 9: Select the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the horizontal spring stiffness k that meet the requirements. h The design variable value of the inclined spring stiffness k1 controls the length L of the rotating rod and the horizontal spring stiffness k. h With the stiffness parameter k1 of the inclined spring unchanged, change the initial rotation angle θ of the rotating rod and repeat steps four to seven to complete the optimized design of the prism-shaped vibration isolation platform with a given rotating rod length L.

[0028] Further, in step one, the prismatic vibration isolation platform also includes a top plate, a bottom plate, and bearings. The top plate and the bottom plate are arranged parallel to each other and spaced apart. The rotating rods are arranged between the top plate and the bottom plate. There are four sets of rotating rods, which are symmetrically arranged at the four corners of the bottom plate. Each rotating rod is composed of an upper quadrilateral and a lower quadrilateral. The top of the upper quadrilateral is connected to the top plate through a bearing, and the bottom of the lower quadrilateral is connected to the bottom plate through a bearing. The upper quadrilateral and the lower quadrilateral are hinged together. The oblique springs are respectively installed on one diagonal of the upper quadrilateral and the lower quadrilateral. The two oblique springs share an inner hinge point. A longitudinal rod is connected between the inner sides of the two sets of rotating rods. The horizontal spring and the damper are connected between the two sets of longitudinal rods. The horizontal spring and the damper are arranged parallel to each other.

[0029] The beneficial effects of this invention are as follows: By optimizing the stiffness ratio of the horizontal spring and the inclined spring, the length of the rotating rod, and the initial rotation angle parameters of the rotating rod installed inside the prismatic vibration isolation platform, the prismatic vibration isolation platform can achieve a quasi-zero stiffness effect over a wider range and maintain stable performance under large vibration displacements. This helps to eliminate potential instabilities, bifurcation, and jumping phenomena in large vibration displacements and improves the overall vibration isolation performance. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of 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, wherein:

[0031] Figure 1 This is a schematic diagram of the prismatic vibration isolation platform of the present invention.

[0032] Figure 2 This is a mathematical model diagram of the prismatic vibration isolation platform of the present invention.

[0033] Figure 3 This is a schematic diagram showing the deformation of a single unit in the prismatic vibration isolation platform of the present invention.

[0034] Figure 4 This is a schematic diagram of the adjustable quasi-zero stiffness principle of the prismatic vibration isolation platform of the present invention.

[0035] Figure 5 This is the combined stiffness force curve when L = 0.15 according to the present invention.

[0036] Figure 6 This is the combined stiffness force curve when L = 0.20 according to the present invention.

[0037] Figure 7 For the present invention Combined stiffness force curve at time.

[0038] Figure 8 For the present invention Combined stiffness force curve at time.

[0039] Figure 9 This is the optimized stiffness force curve of the present invention.

[0040] Figure 10 This is a diagram showing the vibration isolation performance of the quasi-zero stiffness effect of the present invention.

[0041] Attached reference numerals: 1. Horizontal spring; 2. Inclined spring; 3. Damper; 4. Rotating rod; 5. Bearing; 6. Top plate; 7. Bottom plate; 8. Vertical rod. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0043] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0044] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0045] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0046] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0047] This invention provides an optimized design method for a vibration isolation platform based on quasi-zero stiffness. For the proposed prismatic vibration isolation platform (PIP), the first stage optimizes the selection of the rotating rod length or initial angle parameters. The second stage optimizes the stiffness ratio of the horizontal and inclined springs installed inside the prismatic vibration isolation platform, adjusting the combined stiffness of the structure. This allows the PIP to achieve a quasi-zero stiffness (QZS) effect over a wider range. Furthermore, according to the optimized stiffness-force curve, the structure maintains stable performance even under large vibration displacements, helping to eliminate potential instabilities, bifurcation, and jumping phenomena during large vibration displacements, thereby improving overall vibration isolation performance.

[0048] The combination of the negative stiffness of the horizontal spring and the positive stiffness of the inclined spring constitutes the QZS effect. When the PIP is compressed and undergoes significant deformation, the horizontal spring generates negative stiffness. By adding a certain amount of positive stiffness to the structure, the combined stiffness of the structure can be controlled. For example... Figure 4 As shown, the inclined spring always contributes to the positive stiffness of the structure, but the increase in compressive displacement leads to an increase in the negative stiffness of the horizontal spring. The structure exhibits positive stiffness in the initial loading stage, but as the displacement further increases, negative stiffness appears, leading to structural failure. To improve vibration isolation performance, the QZS range needs to be expanded. By combining these two types of springs, the overall force and compressive displacement response of a platform with a significant upward branch in the equilibrium path can be described.

[0049] like Figure 1 As shown, the prismatic vibration isolation platform includes a horizontal spring 1, a diagonal spring 2, a damper 3, a rotating rod 4, a bearing 5, a top plate 6, and a bottom plate 7. The top plate 6 and the bottom plate 7 are arranged parallel to each other and spaced apart. The rotating rod 4 is located between the top plate 6 and the bottom plate. There are four sets of rotating rods 4, which are symmetrically arranged at the four corners of the bottom plate 7. The rotating rod 4 is composed of an upper quadrilateral and a lower quadrilateral. The top of the upper quadrilateral is connected to the top plate 6 through the bearing 5, and the bottom of the lower quadrilateral is connected to the bottom plate 7 through the bearing 5. The upper quadrilateral and the lower quadrilateral are hinged together. The diagonal spring 2 is installed on one diagonal of the upper quadrilateral and the lower quadrilateral respectively. The two diagonal springs 2 share an inner hinge point. A longitudinal rod 8 is connected between the inner sides of the two sets of rotating rods 4. The horizontal spring 1 and the damper 3 are connected between the two sets of longitudinal rods 8. The horizontal spring 1 and the damper 3 are arranged parallel to each other.

[0050] The method includes the following steps:

[0051] Step 1: Construct a prismatic vibration isolation platform consisting of horizontal springs, inclined springs, rotating rods, and dampers;

[0052] See details Figure 1As shown, horizontal spring 1 is installed in the middle of the prism structure, generating adjustable negative stiffness during large deformations; oblique spring 2 is installed inside the prism structure unit, generating adjustable positive stiffness. By combining negative and positive stiffness, PIP can achieve adjustable nonlinear quasi-zero stiffness (QZS) characteristics; horizontal damper 3 is arranged parallel to horizontal spring 1, generating nonlinear displacement-related damping, which is also beneficial for vibration isolation; rotating rod 4 connects top plate 6 and bottom plate 7 through bearing 5; excitation is transmitted from bottom plate 7, and the mass (protected target) is placed on top plate 6.

[0053] Step 2: Construct a mathematical model of the prismatic vibration isolation platform and define optimization parameters, including the horizontal spring stiffness k. h The parameters, including the stiffness k1 of the inclined spring, the length L of the rotating rod, and the initial rotation angle θ of the rotating rod, are determined to have a range of 0 ≤ L ≤ L. max , k hmin ≤k h ≤k hmax k 1min ≤k1≤k 1max Solving the model specifically includes:

[0054] The mathematical model of PIP is as follows: Figure 2 As shown, a single prism element 9 of PIP is selected for calculation, and the relevant parameter information is as follows. Figure 3 As shown in the figure, M represents the upper mass, c represents the damper, ho is the initial height of the platform, hc is the height of the platform during vibration, and Δh is the change in platform height.

[0055] Optimize the horizontal spring stiffness k h The stiffness of the inclined spring k1, the length of the rotating rod L, and the initial rotation angle θ of the rotating rod;

[0056] It should be noted that the optimization goal is to widen the bandwidth d1 of the quasi-zero stiffness section.

[0057] Define the parameter range: 0 ≤ L ≤ L max , k hmin ≤k h ≤k hmax k 1min ≤k1≤k 1max .

[0058] Step 3: Select the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the horizontal spring stiffness k that meet the requirements. h Substituting the design variable value of the inclined spring stiffness k1 into formulas (1)-(3), we obtain the stiffness force curve of the structure under this set of parameters and the width d1 of the quasi-zero stiffness section on this stiffness force curve. Formulas (1)-(3) are expressed as follows:

[0059] F k =F h +F p (1)

[0060]

[0061]

[0062] In the formula, F h F is the stiffness force of the horizontal spring. p F is the stiffness force of the inclined spring. k y1 represents the combined nonlinear stiffness force of the structure, Δx represents the overall horizontal displacement of the structure, Δl represents the change in length of the inclined spring, and y1 represents the overall vertical displacement of the structure.

[0063] Among them, △x and △l are determined by formulas (4)-(9):

[0064]

[0065]

[0066] Δx=2x1 (6)

[0067]

[0068]

[0069] Δl=l1-l0 (9)

[0070] In the formula, x1 represents the horizontal displacement of the half-prism structure, θ is the initial angle of the rotating rod, and Δh represents the change in platform height. L is the rotation angle of the rotating rod, L is the length of the rotating rod, l1 is the movement length of the inclined spring, and l0 is the initial length of the inclined spring; among them, the half-prism structure refers to two longitudinal rotating rods.

[0071] Step 4: Control the initial rotation angle θ of the rotating rod and the stiffness k of the horizontal spring in Step 3. h With the spring stiffness parameter k1 unchanged, change the length L of the rotating rod and repeat step three to obtain the stiffness force curve and the corresponding quasi-zero stiffness section width d1 under the changed length L of the rotating rod.

[0072] Step 5: Evaluate the stiffness force curve under the change of the rotating rod length L in Step 4. If the quasi-zero stiffness section of the curve is optimized, proceed to the next step and obtain the optimized rotating rod length L. Otherwise, repeat Step 5.

[0073] Step Six: Control the design variable values ​​corresponding to the rotation rod length L and the initial rotation angle θ and horizontal spring stiffness k of the optimization parameters in Step Five. hBy keeping the spring stiffness constant and changing the spring stiffness k1, i.e. changing the combined stiffness of the structure, a set of data on the combined stiffness values ​​of the structure is obtained. These data are then substituted into formulas (1)-(3) to obtain the structure under different combined stiffnesses (i.e., different k values). h Stiffness force curves under the ratio of k1 to k2.

[0074] Step 7: Evaluate the stiffness-force curves of different stiffness combinations under the optimized parameter of the rotating rod length L from Step 6, select the optimal quasi-zero stiffness segment, and obtain the corresponding optimized parameter, the inclined spring stiffness k1. (Refer to...) Figure 5 , Figure 6 The optimization parameter k1 is 4500 for L=0.15 and L=0.20.

[0075] Step 8: Based on the parameters obtained in Step 5 (rod length L) and Step 7 (skew spring stiffness k1), optimize the spring combination stiffness, thus completing the optimized design of the prism-shaped vibration isolation platform under a given initial rotation angle θ of the rotating rod.

[0076] Step 9: Select a horizontal spring stiffness k that meets the requirements. h The design variables, including the stiffness k1 of the inclined spring, the length L of the rotating rod, and the initial rotation angle θ of the rotating rod, control the stiffness k of the horizontal spring. h With the spring stiffness k1 and the rotating rod length L remaining constant, change the initial rotation angle θ of the rotating rod and repeat steps four through seven to complete the optimized design of the prismatic vibration isolation platform with a given rotating rod length L. (See...) Figure 7 , Figure 8 Parameter L = 0.20, k h =20000, θ are respectively and When k1 changes from 0, the corresponding stiffness force curves are optimized with parameters k1 of 4500 and 14000.

[0077] Figure 9 Optimized static force curves to expand the QZS range. Based on the static force curves, the operating position of the PIP can be optimized to achieve good vibration isolation performance. Four points on the curve are labeled A, B, C, and D, where C and D are within the QZS range. To illustrate the dynamic characteristics of the QZS effect, Figure 10 The displacement transmissibility at four operating positions (A, B, C, and D) is shown, and the vibration isolation performance at these four points is compared: as the operating position changes from A to D, the peak displacement transmissibility gradually shifts to the left as the excitation frequency decreases, indicating a comprehensive improvement in the structure's vibration isolation performance. Points C and D are located at... Figure 9Within the QZS range shown, the vibration isolation performance at points A and B is improved compared to that at points B, and the PIP exhibits the best vibration isolation performance at its operating position D, characterized by the lowest resonant frequency (widest isolation frequency range) and the lowest resonant peak value. This phenomenon demonstrates the necessity of expanding the QZS range, as the QZS effect can provide excellent vibration isolation performance for the structure. Without the inclined spring and optimized stiffness, the QZS of the PIP is very limited (point D is nonexistent), and due to the negative stiffness effect (instability problem), the platform will collapse under large vibrations, compromising the stability of the structure. Therefore, QZS-based optimization design is essential to improve structural stability while achieving good vibration isolation performance.

[0078] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. Other modifications can be easily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A vibration damping platform optimization design method based on quasi-zero stiffness, characterized in that: Includes the following steps: Step 1: Construct a prismatic vibration isolation platform consisting of horizontal springs, inclined springs, rotating rods, and dampers; Step 2: Construct a mathematical model of the prismatic vibration isolation platform and define optimization parameters, including the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the stiffness k of the horizontal spring. h The stiffness k1 of the inclined spring is determined within the following range: 0≤L≤L max k hmin ≤k h ≤k hmax k 1min ≤k1≤k 1max Solve the model; Step 3: Select the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the horizontal spring stiffness k that meet the requirements. h Substituting the design variable value of the inclined spring stiffness k1 into formulas (1)-(3), we obtain the stiffness force curve of the prismatic vibration isolation platform under this set of parameters and the corresponding quasi-zero stiffness section width d1. Formulas (1)-(3) are expressed as follows: F k =F h +F p (1) In the formula, F h F is the stiffness force of the horizontal spring. p F is the stiffness force of the inclined spring. k y1 represents the combined nonlinear stiffness force of the prismatic vibration isolation platform, Δx represents the overall horizontal displacement of the prismatic vibration isolation platform, Δl represents the change in length of the inclined spring, and y1 represents the overall vertical displacement of the prismatic vibration isolation platform. Among them, △x and △l are determined by formulas (4)-(9): Δx=2x1 (6) Δl=l1-l0 (9) In the formula, x1 represents the horizontal displacement of the half-prism vibration isolation platform, θ represents the initial rotation angle of the rotating rod, and Δh represents the change in platform height. Let l be the rotation angle of the rotating rod, L be the length of the rotating rod, l0 be the initial length of the inclined spring, and l1 be the movement length of the inclined spring. Step 4: Maintain the initial rotation angle θ of the rotating rod and the horizontal spring stiffness k as shown in Step 3. h With the spring stiffness parameter k1 unchanged, the length L of the rotating rod is changed, and step three is repeated to obtain the stiffness force curve of the prismatic vibration isolation platform under the changed length L of the rotating rod and the corresponding quasi-zero stiffness section width d1. Step 5: Evaluate the stiffness force curve under the change of the rotating rod length L in Step 4. If the quasi-zero stiffness section of the curve is optimized, proceed to the next step and obtain the optimized rotating rod length L. Otherwise, repeat Step 5. Step Six: Control the design variable values ​​corresponding to the rotation rod length L and the initial rotation angle θ and horizontal spring stiffness k of the optimization parameters in Step Five. h By keeping the spring stiffness k1 constant and changing it, i.e. changing the combined stiffness of the prismatic vibration isolation platform, a set of data on the combined stiffness values ​​of the prismatic vibration isolation platform is obtained. These data are then substituted into formulas (1)-(3) to obtain the stiffness force curves of the prismatic vibration isolation platform under different combined stiffnesses. Step 7: Evaluate the stiffness-force curves of different combinations of stiffness under the optimized parameter of the rotating rod length L in Step 6, select the optimal quasi-zero stiffness section, and obtain the corresponding optimized parameter of the inclined spring stiffness k1. Step 8: Based on the parameters obtained in Step 5 (rod length L) and Step 7 (skew spring stiffness k1), complete the optimized design of the prism-shaped vibration isolation platform under the given initial rotation angle θ of the rotating rod. Step 9: Select the initial rotation angle θ of the rotating rod, the length L of the rotating rod, and the horizontal spring stiffness k that meet the requirements. h The design variable value of the inclined spring stiffness k1 controls the length L of the rotating rod and the horizontal spring stiffness k. h With the stiffness parameter k1 of the inclined spring unchanged, change the initial rotation angle θ of the rotating rod and repeat steps four to seven to complete the optimized design of the prism-shaped vibration isolation platform with a given rotating rod length L.

2. The method for optimizing the design of a vibration damping platform based on quasi-zero stiffness according to claim 1, characterized in that: In step one, the prismatic vibration isolation platform further includes a top plate, a bottom plate, and bearings. The top plate and the bottom plate are arranged parallel to each other and spaced apart. The rotating rods are arranged between the top plate and the bottom plate. There are four sets of rotating rods, which are symmetrically arranged at the four corners of the bottom plate. Each rotating rod is composed of an upper quadrilateral and a lower quadrilateral. The top of the upper quadrilateral is connected to the top plate through a bearing, and the bottom of the lower quadrilateral is connected to the bottom plate through a bearing. The upper quadrilateral and the lower quadrilateral are hinged together. The oblique springs are respectively installed on one diagonal of the upper quadrilateral and the lower quadrilateral. The two oblique springs share an inner hinge point. A longitudinal rod is connected between the inner sides of the two sets of rotating rods. The horizontal spring and the damper are connected between the two sets of longitudinal rods. The horizontal spring and the damper are arranged parallel to each other.

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