An M-shaped low-frequency vibration isolation structure that mimics the leg structure of an arthropod

Abstract

This invention discloses an M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod, belonging to the field of vibration isolation technology. A design method for the biomimetic M-shaped structure is proposed, utilizing components such as connecting rods, bearings, springs, and guiding devices to construct the structure. The connecting rods simulate the geometry and structure of an arthropod leg, while the springs and their components approximate the leg muscle structure. A structural stiffness design method for the biomimetic M-shaped structure is proposed, including nonlinear positive stiffness and nonlinear negative stiffness design. Utilizing the unique nonlinear positive stiffness characteristics of the biomimetic M-shaped structure, it can better adapt to negative stiffness, thus significantly widening the quasi-zero stiffness range. Furthermore, the relationship between the effective vibration isolation load and structural parameters of the biomimetic M-shaped structure is given. Finally, the quasi-zero stiffness condition of the biomimetic M-shaped structure is presented, and the results show that this structure can effectively reduce the vibration isolation initiation frequency and improve low-frequency vibration isolation performance.

Description

Technical Field

[0001] This invention relates to the field of vibration isolation technology, and in particular to a biomimetic M-shaped low-frequency vibration isolation structure based on the structure of arthropod legs. Background Technology

[0002] With increasingly frequent space activities, spacecraft require ever-increasing precision and stability in pointing. Missions such as space laser communication, space-based Earth remote sensing, and space astronomical observation all demand high-precision pointing performance. The normal operation of transmission systems on spacecraft generates micro-vibrations, which are characterized by wide bandwidth, small amplitude, and difficulty in control. These micro-vibrations can significantly impact the pointing precision and stability of spacecraft. For example, in remote sensing satellites, micro-vibrations caused by moving parts excite structural vibrations that are transmitted to the sensor mounting points, leading to a decrease in image quality. Without micro-vibration interference, the camera's focusing accuracy is 5μm; after being affected by micro-vibration, the focusing accuracy exceeds 14.97μm, resulting in blurred images. Low-frequency vibration isolation technology on spacecraft primarily relies on active vibration isolation, which requires energy input and has lower stability compared to passive vibration isolation. To isolate low-frequency micro-vibrations on spacecraft, researchers have proposed a quasi-zero stiffness vibration isolator based on nonlinear dynamics theory. The principle of quasi-zero stiffness is to combine positive and negative stiffness to give the quasi-zero stiffness structure the characteristics of "high static and low dynamic", which ensures the structural load-bearing capacity while having a low vibration isolation frequency.

[0003] Existing technologies disclose a three-spring structure, where one vertical spring provides positive stiffness, and the other two inclined springs provide negative stiffness. Compared to a linear isolator consisting of a single positive stiffness spring, the three-spring structure can achieve quasi-zero stiffness at the static equilibrium position, resulting in a lower initial isolation frequency. However, its quasi-zero stiffness range is very limited, so under strong excitation conditions, the isolation initiation frequency increases rapidly. To broaden the quasi-zero stiffness range, researchers have improved upon existing quasi-zero stiffness structures. Those skilled in the art have introduced nonlinearity and pre-compression into the inclined springs of the three-spring quasi-zero stiffness system. Theoretical research results show that this method can broaden the quasi-zero stiffness range, but introducing spring pre-compression and nonlinearity is difficult to implement in practice.

[0004] In nature, arthropods such as spiders and mantises live on low-frequency vibrating webs or leaves. Compared to the arthropod's body, the leaves and webs sway more dramatically, thus their leg structures play a role in isolating large-amplitude vibrations and maintaining trunk stability. This paper proposes an M-shaped low-frequency vibration isolation structure that mimics the shape of an arthropod's leg by combining the design of an arthropod leg shape with a quasi-zero stiffness vibration isolation junction. Although the positive stiffness spring in the M-shaped structure itself is not nonlinear, the placement of the positive stiffness spring results in an equivalent stiffness that is nonlinear. After the positive and negative stiffnesses cancel each other out, the structure has a wider quasi-zero stiffness range, which can improve vibration isolation performance under large excitation conditions. Furthermore, this improvement method is easier to implement. Summary of the Invention

[0005] This invention, based on the shape of the leg structure of arthropods such as spiders and mantises, designs a quasi-zero stiffness structure with a large quasi-zero stiffness range. For classic quasi-zero stiffness vibration isolation structures, when the excitation amplitude is large, the displacement of the isolated object will exceed the quasi-zero stiffness range. This leads to a significant increase in the structure's equivalent stiffness under large excitation, resulting in a decrease in the structure's low-frequency vibration isolation performance. The reason for the limited quasi-zero stiffness range of classic quasi-zero stiffness structures is that the positive stiffness is provided by the vertical spring at a constant value, while the tilting spring can only provide negative stiffness within a limited range near the equilibrium position. Outside this range, the tilting spring provides positive stiffness, making the structure's equivalent stiffness even higher than that of the vertical spring.

[0006] To address the issues of limited quasi-zero stiffness range in classical structures and the difficulty in implementing existing improvement methods, this invention proposes a biomimetic M-shaped quasi-zero stiffness structure. In this structure, negative stiffness is provided by a tilting spring, while positive stiffness is provided by a horizontal spring. The placement of the horizontal spring allows the M-shaped structure to possess nonlinear positive stiffness. As the negative stiffness of the M-shaped structure increases with displacement, the positive stiffness decreases, thus expanding the range of positive and negative stiffness cancellation and broadening the quasi-zero stiffness range. Furthermore, achieving quasi-zero stiffness in the proposed M-shaped biomimetic structure requires defining the relationship between structural parameters, i.e., the quasi-zero stiffness design criteria.

[0007] This invention is implemented as follows:

[0008] An M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod is disclosed. This invention improves vibration isolation performance by mimicking the geometric nonlinearity of arthropod structures to broaden the range of quasi-zero stiffness. The structure is an arthropod-like structure comprising four interconnected rods: rod one, rod two, rod three, and rod four. A horizontal spring connects the connection points of rods one and two, and the connection points of rods three and four. The two ends of the horizontal spring are a first spring guide device and a second spring guide device.

[0009] The first inclined spring is located between the first and second rods; the second inclined spring is located between the third and fourth rods; the two ends of the first inclined spring are the third and fourth spring guide devices; the two ends of the second inclined spring are the fifth and sixth spring guide devices.

[0010] One rod, two rods, three rods, and four rods are hinged in sequence to form an M shape. One rod, two rods, three rods, and four rods constitute the leg structure of the arthropod. Horizontal springs constitute the back muscles of the arthropod. The first inclined spring and the second inclined spring constitute the leg muscles of the arthropod.

[0011] Furthermore, the first and fourth rods are respectively connected to the first base and the second base. The third spring guide device is connected to the hinge joint between the first base and the first rod; the fourth spring guide device is connected to the hinge joint between the second and third rods; the second inclined spring is fixed to the fifth and sixth spring guide devices, the fifth spring guide device is connected to the hinge joint between the second and third rods, and the sixth spring guide device is connected to the hinge joint between the fourth rod and the second base.

[0012] Furthermore, the first spring guide device, the second spring guide device, the third spring guide device, the fourth spring guide device, the fifth spring guide device, and the sixth spring guide device constitute three sets of spring guide devices; the rod, the spring guide device, and the base all have holes drilled at the connection points to install bearings, and bolts are used to pass through the inner ring of the bearings to connect the various components.

[0013] Furthermore, the stiffness of the first and second inclined springs is k1; the stiffness of the horizontal spring is k2; the load mass simulates the weight of an arthropod's body and is located at the hinge of the two middle rods of the M-shaped structure, namely the second and third rods; the vibration-isolated object of the M-shaped structure is the load mass with a mass of m, and the low-frequency vibration originates from the first and second bases of the foundation, which are on the same horizontal plane.

[0014] The length between the hinge points at both ends of rods one, two, three, and four is l, and the distance from one end support to the axis of symmetry of the M-shaped structure is s. Due to geometric constraints, the relationship between s and l must satisfy l <s<2l;

[0015] When the structure is unloaded and under load, the horizontal spring, the first tilting spring, and the second tilting spring are all at their original lengths. The lengths of the first tilting spring and the second tilting spring are l1; the length of the horizontal spring is l2; the relationship between l1 and l2 is:

[0016]

[0017] In the M-type structure, the dimensions of l, s, and l1 can be determined according to the installation environment, and l2 can be calculated according to formula (1).

[0018] Furthermore, the structural bearing capacity is determined by the horizontal spring; the coordinate y is defined as the displacement of the mass block in the vertical direction, and the coordinate z is the displacement of the foundation in the vertical direction. The origin of both coordinates is the midpoint of the two supports, and the positive direction is upward; the displacement of the load mass relative to the foundation can be expressed as x = yz.

[0019] The restoring force f2 in the vertical direction generated by the horizontal spring is:

[0020]

[0021] The system is in static equilibrium at x = 0. The weight of the structural load is supported by a horizontal spring, i.e., mg = f² (x = 0). The mass m that the structure can bear is:

[0022]

[0023] After the mass m of the vibration isolation object is determined, the correspondence between the mass m of the vibration isolation object bearing the structure and the stiffness k2 of the horizontal spring is obtained according to formula (2), thereby determining the stiffness k1 of the horizontal spring.

[0024] Furthermore, near x = 0, the first and second tilting springs provide equivalent negative stiffness, while the horizontal spring of the M-shaped structure provides equivalent positive stiffness; combining the two, the total stiffness of the system at x = 0 approaches zero; the equivalent stiffness K of the structure is:

[0025]

[0026] At the equilibrium position x = 0, setting K = 0 yields...

[0027]

[0028] When the ratio of the stiffness of the first inclined spring, the second inclined spring and the horizontal spring satisfies the relationship given in formula (5) with the structural parameters, the equivalent stiffness of the system in the equilibrium position and the surrounding area of ​​the object being isolated is close to 0, thereby achieving the effect of low-frequency vibration isolation; according to formula (5), the corresponding relationship between k1 and k2 can be obtained, thereby determining the stiffness k1 of the inclined spring.

[0029] The advantages of this invention compared to the prior art are as follows:

[0030] The biomimetic M-shaped quasi-zero stiffness structure of this invention provides negative stiffness through a tilting spring and positive stiffness through a horizontal spring. The placement of the horizontal spring allows the M-shaped structure to possess nonlinear positive stiffness. As the negative stiffness of the M-shaped structure increases with displacement, the positive stiffness decreases, thus expanding the range of positive and negative stiffness cancellation and broadening the range of quasi-zero stiffness. Simultaneously, achieving quasi-zero stiffness in the proposed M-shaped biomimetic structure requires addressing the relationship between structural parameters, i.e., establishing quasi-zero stiffness design criteria.

[0031] This invention broadens the quasi-zero stiffness range, lowers the vibration isolation initiation frequency, and improves vibration isolation performance in the operating frequency band. The specific effects can be determined by comparing and analyzing the stiffness-displacement curves and transmissibility curves of the biomimetic M-shaped quasi-zero stiffness structure and the traditional quasi-zero stiffness structure. When the rod length *l* of the M-shaped structure is 80 mm, the distance *s* between the support and the axis of symmetry of the M-shaped structure is 120 mm, the tilt spring stiffness *k1* is 400 N / m, its length is 123.7 mm, and the horizontal spring length is 144.6 mm, the horizontal spring stiffness is calculated to be 31.7 N / mm according to the quasi-zero stiffness design criteria for the M-shaped structure. The structure can bear a mass of 70.1 g, corresponding to a 23.45% increase in the quasi-zero stiffness range of the M-shaped structure. When the excitation acceleration is 1 m / s²... 2 At f = 3Hz, the peak response of the biomimetic M-shaped quasi-zero stiffness structure is located at 2.448Hz, which is 16.45% lower than that of the traditional quasi-zero stiffness structure. This verifies that the M-shaped quasi-zero stiffness structure reduces the initial vibration isolation frequency. At the same time, the M-shaped structure has better vibration isolation performance in the operating frequency band. For example, at f = 3Hz, the transmissibility of the M-shaped quasi-zero stiffness structure is -42.085dB, which is 6.6dB lower than that of the traditional quasi-zero stiffness structure. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the structure provided for an embodiment of the present invention;

[0033] Figure 2 Structural dimension diagrams provided for embodiments of the present invention;

[0034] Figure 3 For detailed diagrams of the hinge;

[0035] Figure 4 Equivalent stiffness-displacement curves for traditional quasi-zero stiffness structures and M-type quasi-zero stiffness structures;

[0036] Figure 5 Transmission rate curves for a traditional quasi-zero stiffness structure and an M-type quasi-zero stiffness structure;

[0037] Among them, 1-one rod, 2-two rods, 3-three rods, 4-four rods, 5-horizontal spring, 6-first tilting spring, 7-second tilting spring, 8-load mass, 9-first base, 10-second base, 11-first spring guide device, 12-second spring guide device, 13-third spring guide device, 14-fourth spring guide device, 15-fifth spring guide device, 16-sixth spring guide device, 17-bearing, 18-bolt. Detailed Implementation

[0038] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the following examples provide a more detailed description of the invention. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0039] This invention improves vibration isolation performance by mimicking the geometric nonlinearity of arthropod structures to broaden the range of quasi-zero stiffness. A biomimetic M-shaped quasi-zero stiffness structure, such as... Figures 1-2 As shown, it mainly consists of four rods: rod 1, rod 2, rod 3, rod 4; one horizontal spring 5; two inclined springs (first inclined spring 6, second inclined spring 7); a load mass 8; and a first base 9 and a second base 10 connecting to the foundation. It also comprises three sets of spring guide devices: first spring guide device 11, second spring guide device 12, third spring guide device 13, fourth spring guide device 14, fifth spring guide device 15, and sixth spring guide device 16, as well as bearings and bolts for connection. Bearings are installed at the joints of the rods, spring guide devices, and bases, and bolts are used to connect the components through the inner rings of the bearings.

[0040] The specific connection method of the biomimetic M-shaped quasi-zero stiffness structure is as follows: Figure 3 As shown, at the connection of rod 1, rod 2 and the first spring guide device 11, the rods and the spring guide device are drilled to install bearings respectively. The bearing 17 contains 5 coaxial bearings. Finally, the rod 1, rod 2 and the first spring guide device 11 are connected by bolts 18.

[0041] The first rod 1, the second rod 2, the third rod 3, and the fourth rod 4 of this invention simulate the leg structure of a spider, and the four rods are hinged together in sequence to form an M-shape. The horizontal spring 5 simulates the back muscles of the spider, and the first inclined spring 6 and the second inclined spring 7 simulate the leg muscles of the springs. The stiffness of the first inclined spring 6 and the second inclined spring 7 is k1, and the stiffness of the horizontal spring 5 is k2. The load mass 8 simulates the weight of an arthropod's body and is located at the hinge of the two middle rods in the M-shaped structure. The vibration-isolated object of the M-shaped structure is the load mass 8, with a mass of m. The low-frequency vibration originates from the first base 9 and the second base 10, which are on the same horizontal plane.

[0042] like Figure 1As shown, the lengths between the hinge points at both ends of the first rod 1, the second rod 2, the third rod 3, and the fourth rod 4 are all l. The distance between one end support and the symmetry axis of the M-shaped structure is s. Due to geometric relationship limitations, the size relationship between s and l needs to satisfy l < s < 2l. When the structure has no load mass, the horizontal spring 5, the first inclined spring 6, and the second inclined spring 7 are all in their original length states. The length of the first inclined spring 6 and the second inclined spring 7 is l1; the length of the horizontal spring is l2. The relationship between l1 and l2 is:

[0043]

[0044] In the M-shaped structure, l, s, and l1 can be determined according to the installation environment, and l2 can be calculated according to formula (1).

[0045] The bearing capacity of the structure of the present invention is determined by the horizontal spring. Define the coordinate y as the displacement of the mass block in the vertical direction, the coordinate z as the displacement of the foundation in the vertical direction, with the origin of coordinates being the midpoint between the two supports and the positive direction being upward. The displacement of the load mass relative to the foundation can be expressed as x = y - z.

[0046] The restoring force f2 generated by the horizontal spring 5 in the vertical direction is:

[0047]

[0048] When x = 0, the system is in the static equilibrium position. The gravity of the vibration isolation object 8 is borne by the horizontal spring, that is, mg = f2(0). The mass m that the structure can bear is

[0049]

[0050] After the mass m of the vibration isolation object is determined, according to formula (3), the corresponding relationship between the mass m of the vibration isolation object borne by the structure and the stiffness k2 of the horizontal spring can be obtained, and thus the stiffness k2 of the horizontal spring is determined.

[0051] In order to achieve quasi-zero stiffness at the equilibrium position of the vibration isolation object, the quasi-zero stiffness design criterion for the M-shaped structure of the present invention is: near x = 0, the first inclined spring 6 and the second inclined spring 7 provide equivalent negative stiffness, while the horizontal spring 5 of the M-shaped structure provides equivalent positive stiffness. After combining the two, the total stiffness of the system at x = 0 is close to zero. The equivalent stiffness K of the structure is:

[0052]

[0053] At the equilibrium position x = 0, setting K = 0 can obtain

[0054]

[0055] When the ratio of the stiffness of the first inclined spring 6, the second inclined spring 7, and the horizontal spring 5 satisfies the relationship given in formula (5) with the structural parameters, the equivalent stiffness of the system in the equilibrium position and surrounding area of ​​the object being isolated is close to 0, thereby achieving the effect of low-frequency vibration isolation. According to formula (5), the corresponding relationship between k1 and k2 can be obtained, thereby determining the stiffness k1 of the inclined spring.

[0056] When the length l of the M-shaped structure is taken as 80mm, the distance s between the support and the axis of symmetry of the M-shaped structure is taken as 120mm, the stiffness k1 of the inclined spring is taken as 400N / m, the length l1 is taken as 123.7mm, and the length l2 of the horizontal spring is taken as 144.6mm. According to the quasi-zero stiffness design criterion for the M-shaped structure, the stiffness of the horizontal spring k2 is calculated to be 31.7N / mm, and the mass borne by the structure is 70.1g.

[0057] Figure 4 Stiffness-displacement curves for the M-type quasi-zero stiffness structure and the traditional quasi-zero stiffness structure are presented. The length and stiffness of the inclined spring in the M-type structure are consistent with those in the traditional quasi-zero stiffness structure. The displacement range corresponding to when the equivalent stiffness of the system is less than 1 / 50 of the inclined spring stiffness (i.e., 8 N / m) is defined as the quasi-zero stiffness range. At this point, the quasi-zero stiffness range of the traditional three-spring quasi-zero stiffness structure is [-9.69 9.68] mm, and the quasi-zero stiffness width is 19.37 mm; while the quasi-zero stiffness range of the M-type structure is [-14.23 9.684] mm, and the quasi-zero stiffness width is 23.914 mm, an increase of 23.45%, verifying that the M-type quasi-zero stiffness structure has a wider quasi-zero stiffness range.

[0058] Figure 5 The following is given when the excitation acceleration is 1 m / s² 2 The transmissivity curves of the M-shaped quasi-zero stiffness structure and the traditional quasi-zero stiffness structure are shown. The peak response of the traditional quasi-zero stiffness structure is at 2.93Hz, while the peak response of the biomimetic M-shaped quasi-zero stiffness structure is at 2.448Hz, a decrease of 16.45% compared to the former. This verifies that the M-shaped quasi-zero stiffness structure reduces the initial vibration isolation frequency. Furthermore, within the frequency band where both exhibit vibration isolation effects, taking f=3Hz as an example, the transmissivity of the traditional quasi-zero stiffness structure is -35.476dB, while the transmissivity of the M-shaped quasi-zero stiffness structure is -42.085dB, a decrease of 6.6dB compared to the former. This indicates that the M-shaped structure has better vibration isolation performance in the operating frequency band.

[0059] The following are specific examples:

[0060] This embodiment specifically provides a biomimetic M-shaped quasi-zero stiffness low-frequency vibration isolation structure, such as... Figure 1As shown, the structure includes: rod 1, rod 2, rod 3, rod 4, horizontal spring 5, first tilting spring 6, second tilting spring 7, load mass 8, first base 9, second base 10 of the connecting foundation, three sets of spring guide devices (first spring guide device 11, second spring guide device 12, third spring guide device 13, fourth spring guide device 14, fifth spring guide device 15, and sixth spring guide device 16), and bearings and bolts for connection. The rods, spring guide devices, and bases are manufactured using 3D printing with resin as the material. The springs need to be customized according to the required length and stiffness. The bolts and bearings use standard parts; therefore, when designing the pre-drilled holes at the hinges, attention should be paid to matching the hole diameter with the selected bearings.

[0061] like Figure 1 As shown, rod 1, rod 2, rod 3, and rod 4 are connected sequentially, and the other ends of rod 1 and rod 4 are connected to the first base 9 and the second base 10 of the foundation. One end of the horizontal spring 5 is fixed to the first spring guide device 11, and the other end is fixed to the second spring guide device 12.

[0062] The first spring guide device 11 is connected to the hinge of rod 1 and rod 2, and the second spring guide device 12 is connected to the hinge of rod 3 and rod 4. The first tilting spring 6 is fixed to the third spring guide device 13 and the fourth spring guide device 14. The third spring guide device 13 is connected to the hinge of the first base 9 and rod 1, and the fourth spring guide device 14 is connected to the hinge of rod 2 and rod 3. The second tilting spring 7 is fixed to the fifth spring guide device 15 and the sixth spring guide device 16. The fifth spring guide device 15 is connected to the hinge of rod 2 and rod 3, and the sixth spring guide device 16 is connected to the hinge of rod 4 and the second base 10. The load mass 8 is installed at the hinge of rod 2 and rod 3. The connection method of the biomimetic M-shaped structure is as follows... Figure 2 As shown, holes are pre-drilled at the hinge and bearings are installed in the holes. Shims are placed between each contact surface to reduce the contact area, and finally bolts are used for connection.

[0063] like Figure 1As shown, the lengths between the hinge points of the first rod 1, the second rod 2, the third rod 3, and the fourth rod 4 are all l, and the distance between one end support and the symmetry axis of the M-shaped structure is s. Due to the limitation of geometric relationships, the size relationship between s and l needs to satisfy l < s < 2l; when the structure has no load mass, the horizontal spring 5, the first inclined spring 6, and the second inclined spring 7 are all in their original length states. The lengths of the first inclined spring 6 and the second inclined spring 7 are l1; the length of the horizontal spring is l2. After the installation environment and the vibration isolation object are determined, l, s, l1, and m in the structural parameters are determined fixed values. The stiffness k2 of the horizontal spring 5 is calculated according to formula (3) based on the determined structural parameters. The stiffness k1 of the first inclined spring 6 and the second inclined spring 7 is calculated according to formula (5).

[0064] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements can be made, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. An M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod, characterized in that, The structure is an arthropod-like structure; it includes four rods connected in sequence, namely rod (1), rod (2), rod (3), and rod (4). The connection points of rod (1), rod (2), rod (3), and rod (4) are connected by a horizontal spring (5). The two ends of the horizontal spring (5) are a first spring guide device (11) and a second spring guide device (12). The first spring guide device (11) is connected to the hinge of the first rod (1) and the second rod (2), and the second spring guide device (12) is connected to the hinge of the third rod (3) and the fourth rod (4); the first inclined spring (6) is between the first rod (1) and the second rod (2); the second inclined spring (7) is between the third rod (3) and the fourth rod (4). The first inclined spring (6) has a third spring guide device (13) and a fourth spring guide device (14) at both ends; The two ends of the second tilting spring (7) are the fifth spring guide device (15) and the sixth spring guide device (16); The load mass (8) is installed at the hinge between the second rod (2) and the third rod (3); One rod (1), two rods (2), three rods (3), and four rods (4) constitute the M-shaped leg structure of the arthropod; horizontal spring (5) constitutes the back muscles of the arthropod; first inclined spring (6) and second inclined spring (7) constitute the leg muscles of the arthropod. The length between the hinge points at both ends of rods (1), (2), (3), and (4) is l. The distance from one end support to the axis of symmetry of the M-shaped structure is s. Due to geometric constraints, the relationship between s and l must satisfy l. <s<2l。 2. The M-type low-frequency vibration isolation structure mimicking the leg structure of an arthropod, as described in claim 1, is characterized in that... The other ends of the rod (1) and the four rods (4) are respectively connected to the first base (9) and the second base (10); the third spring guide device (13) is connected to the hinge of the first base (9) and the rod (1); the fourth spring guide device (14) is connected to the hinge of the two rods (2) and the three rods (3); the second inclined spring (7) is fixed to the fifth spring guide device (15) and the sixth spring guide device (16), the fifth spring guide device (15) is connected to the hinge of the two rods (2) and the three rods (3), and the sixth spring guide device (16) is connected to the hinge of the four rods (4) and the second base (10).

3. The M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod, as described in claim 1, is characterized in that... The first spring guide device (11), the second spring guide device (12), the third spring guide device (13), the fourth spring guide device (14), the fifth spring guide device (15), and the sixth spring guide device (16) constitute three sets of spring guide devices; the rod, the spring guide device, and the base are all drilled at the connection point to install bearings (17), and bolts (18) are used to pass through the inner ring of the bearing to connect each component.

4. The M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod, as described in claim 1, is characterized in that... The stiffness of the first inclined spring (6) and the second inclined spring (7) is k1; the stiffness of the horizontal spring (5) is k2; the load mass (8) simulates the weight of an arthropod's body and is located at the hinge of the two middle rods of the M-shaped structure, namely the second rod (2) and the third rod (3); the object isolated by the vibration of the M-shaped structure is the load mass (8), with a mass of m, and the low-frequency vibration originates from the first base (9) and the second base (10) on the same horizontal plane; When the structure is unloaded and has no load mass, the horizontal spring (5), the first inclined spring (6), and the second inclined spring (7) are all in their original lengths, and the lengths of the first inclined spring (6) and the second inclined spring (7) are l1. The length of the horizontal spring (5) is l2; the relationship between l1 and l2 is: In the M-type structure, the dimensions of l, s, and l1 can be determined according to the installation environment, and l2 can be calculated according to formula (1).

5. The M-shaped low-frequency vibration isolation structure mimicking the leg structure of an arthropod, as described in claim 1, is characterized in that... The structural bearing capacity is determined by the horizontal spring (5); the coordinate y is defined as the displacement of the mass block in the vertical direction, and the coordinate z is the displacement of the foundation in the vertical direction. The origin of both coordinates is the midpoint of the two supports, and the positive direction is upward; the displacement of the load mass (8) relative to the foundation can be expressed as x = yz; The restoring force f2 in the vertical direction generated by the horizontal spring (5) is: The system is in static equilibrium at x = 0. The weight of the structural load mass (8) is borne by a horizontal spring, i.e., mg = f2 (0). The mass m that the structure can bear is: After the mass m of the vibration isolation object is determined, the correspondence between the mass m of the vibration isolation object bearing the structure and the stiffness k2 of the horizontal spring is obtained according to formula (3), thereby determining the stiffness k2 of the horizontal spring.

6. The M-type low-frequency vibration isolation structure mimicking the leg structure of an arthropod, as described in claim 1, is characterized in that... Near x = 0, the first tilting spring (6) and the second tilting spring (7) provide equivalent negative stiffness, while the horizontal spring (5) of the M-shaped structure provides equivalent positive stiffness; combining the two, the total stiffness of the system at x = 0 is close to zero; the equivalent stiffness K of the structure is: At the equilibrium position x = 0, setting K = 0 yields... When the ratio of the stiffness of the first tilting spring (6), the second tilting spring (7) and the horizontal spring (5) satisfies the relationship given in formula (5) with the structural parameters, the equivalent stiffness of the system in the equilibrium position and the surrounding area of ​​the object being isolated is close to 0, thereby achieving the effect of low-frequency vibration isolation; according to formula (5), the corresponding relationship between k1 and k2 can be obtained, thereby determining the stiffness k1 of the tilting spring.

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