A vibration-absorbing and energy-absorbing structure with multi-stable quasi-zero stiffness

Abstract

The application discloses a kind of vibration-absorbing energy-absorbing structures with multi-stable quasi-zero stiffness, belong to mechanics metamaterial structure design and vibration-absorbing energy-absorbing technical field.The application includes adjustable compliant metamaterial unit, the adjustable compliant metamaterial unit includes three layers of upper and lower arrangement support frame: first layer support frame, second layer support frame, third layer support frame, the first layer support frame is connected between second layer support frame by flexible curve connecting rib, and second layer support frame is connected with third layer support frame by arch connecting rib.The vibration-absorbing energy-absorbing structure with multi-stable quasi-zero stiffness disclosed in the application realizes quasi-zero stiffness working interval and multi-stable energy-absorbing function by innovative geometric configuration design.

Description

Technical Field

[0001] This invention relates to the field of mechanical metamaterial structure design and vibration reduction and energy absorption technology, specifically to a vibration reduction and energy absorption structure with multi-steady-state quasi-zero stiffness. Background Technology

[0002] Metamaterials are materials that acquire physical properties not found in naturally occurring materials through artificial structural design, rather than relying on the material's inherent composition. In the field of mechanics, quasi-zero stiffness metamaterials have attracted widespread attention due to their combination of high static stiffness and low dynamic stiffness. High static stiffness ensures the structure's load-bearing capacity, while low dynamic stiffness provides the foundation for achieving excellent vibration control performance.

[0003] Traditional quasi-zero stiffness structures typically require a combination of positive and negative stiffness elements, such as complex spring-linkage mechanisms or magnetic systems. These designs often suffer from drawbacks such as cumbersome structures, large weight, significant space requirements, and high manufacturing costs. On the other hand, in the field of impact protection, while existing multistable energy-absorbing structures can absorb energy through configuration switching, they generally suffer from high initial peak forces and limited energy absorption efficiency. Furthermore, many multistable structures are based on traditional bending beam configurations, with a single deformation mode, or require a combination of rigid and soft materials to achieve the desired negative stiffness and multistable effects, increasing structural complexity and manufacturing difficulty. More importantly, existing technologies struggle to effectively control the transmission of overload during impact while achieving efficient energy absorption, failing to simultaneously meet the dual requirements of "high energy dissipation" and "low impact response." Therefore, there is an urgent need in this field for a simple, lightweight, and responsive multistable structure that can not only achieve efficient energy absorption through controllable deformation but also provide significant vibration reduction under dynamic loads to cope with complex impact and vibration environments. Summary of the Invention

[0004] This invention provides a vibration reduction and energy absorption structure with multi-stable quasi-zero stiffness. Through innovative geometric configuration design, this structure achieves a quasi-zero stiffness working range and multi-stable energy absorption function.

[0005] The technical solution of this invention is:

[0006] A vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness includes an adjustable compliant metamaterial unit. The adjustable compliant metamaterial unit includes three layers of support frames arranged vertically: a first layer support frame 1-1, a second layer support frame 1-2, and a third layer support frame 1-3. The first layer support frame 1-1 and the second layer support frame 1-2 are connected by a flexible curved connecting rib 2, and the second layer support frame 1-2 and the third layer support frame 1-3 are connected by an arched connecting rib 3.

[0007] Furthermore, the adjustable compliant metamaterial units are arranged in a three-dimensional linear array of n1×n2×n3; where n1 is the number of rows of adjustable compliant metamaterial units in each layer, n2 is the number of columns of adjustable compliant metamaterial units in each layer, and n3 is the number of layers of adjustable compliant metamaterial units along the height direction; where n1, n2, and n3 are all positive integers and all have values ​​greater than or equal to 1.

[0008] Furthermore, when the adjustable compliant metamaterial unit is multi-layered, the third layer support frame 1-3 of the i-th adjustable compliant metamaterial unit serves as the first layer support frame 1-1 of the (i+1)-th adjustable compliant metamaterial unit; where i is a positive integer and i≥1; when there are multiple adjustable compliant metamaterial units in one layer, adjacent adjustable compliant metamaterial units in the same layer share the outer rectangular contact platform 12 corresponding to the support frame.

[0009] Furthermore, the first layer support frame 1-1, the second layer support frame 1-2, and the third layer support frame 1-3 have the same structure, each including: rectangular inclined beams 11, outer rectangular contact platforms 12, and inner contact platforms 13; wherein, one end of the four rectangular inclined beams 11 is connected to the inner contact platform 13 in a cross-shaped arrangement, and the other end of the four rectangular inclined beams 11 is respectively provided with outer rectangular contact platforms 12; in the adjustable compliant metamaterial unit, the first layer support frame 1-1 and the third layer support frame 1-3 are arranged in the same way, and the four rectangular inclined beams are concave based on the lower end face of the inner contact platform 13; the four rectangular inclined beams of the second layer support frame 1-2 are concave based on the upper end face of the inner contact platform 13.

[0010] Furthermore, the vertical distance between the inner end faces of the inner contact platforms 13 of the first layer support frame 1-1 and the second layer support frame 1-2 is less than the vertical distance between the inner end faces of the outer rectangular contact platforms 12 of the first layer support frame 1-1 and the second layer support frame 1-2; the vertical distance between the inner end faces of the inner contact platforms 13 of the second layer support frame 1-2 and the third layer support frame 1-3 is greater than the vertical distance between the inner end faces of the outer rectangular contact platforms 12 of the second layer support frame 1-2 and the third layer support frame 1-3.

[0011] Furthermore, the outer rectangular contact platforms 12 of the first layer support frame 1-1 and the second layer support frame 1-2 are connected by four concave flexible curved connecting ribs 2; the inner contact platforms 13 of the second layer support frame 1-2 and the third layer support frame 1-3 are connected by four convex arched connecting ribs 3.

[0012] Furthermore, the cross section of the flexible curved connecting rib 2 is formed by eight truncated sine curves and four circular arcs. The first sine curve L1, the first circular arc, the fourth sine curve L4, the fifth sine curve L5, the second circular arc, and the eighth sine curve L8 are connected in sequence to form the inner boundary line, and the second sine curve L2, the third circular arc, the third sine curve L3, the sixth sine curve L6, the fourth circular arc, and the seventh sine curve L7 are connected in sequence to form the outer boundary line.

[0013] Furthermore, the second sine curve L2 and the fourth sine curve L4 satisfy the following relationship in the unloaded state: ,in, Let be the coordinates of the curve along the first direction. Let be the coordinates of the curve along the second direction.

[0014] Furthermore, the arched connecting rib 3 includes a first concave arc segment, a convex arc segment, and a second concave arc segment; the first concave arc segment, the convex arc segment, and the second concave arc segment are connected sequentially.

[0015] The beneficial effects of this invention are:

[0016] 1. The structure is integrally molded and made of a single material, avoiding interface problems and manufacturing complexity caused by combining multiple materials. The process is simple and the cost is low.

[0017] 2. Through ingenious geometric design, flexible curved connecting ribs and arched connecting ribs are used to achieve multi-stable and quasi-zero stiffness characteristics based on plastic deformation, without relying on complex spring or magnetic systems, resulting in a compact and lightweight structure.

[0018] 3. It combines high static load capacity with low dynamic stiffness, enabling it to effectively reduce impact vibration and absorb energy through the damping effect generated by the plastic buckling of the structure while bearing large static loads.

[0019] 4. The structure has strong design flexibility. The trigger force value of the platform can be flexibly adjusted by adjusting the geometric parameters to adapt to application scenarios with different intensity of impact and vibration reduction requirements. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the three-dimensional structure of the adjustable compliant metamaterial unit with multi-steady-state quasi-zero stiffness vibration reduction and energy absorption structure of the present invention.

[0021] Figure 2 This is a schematic diagram of the two-dimensional structure of the adjustable compliant metamaterial unit of the present invention. Figure 1 ;

[0022] Figure 3 This is a schematic diagram of the two-dimensional structure of the adjustable compliant metamaterial unit of the present invention. Figure 2 ;

[0023] Figure 4 This is a front view of a vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness provided according to an embodiment;

[0024] Figure 5 This is a top view of a vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness provided according to an embodiment;

[0025] Figure 6 This is a force-displacement curve diagram of an embodiment of the present invention;

[0026] Figure 7 This is a structural diagram of the modified straight inclined rib of the present invention;

[0027] Figure 8 This is a structural diagram of the modified sinusoidal rib of the present invention;

[0028] Figure 9 for Figure 7 Force-displacement curves of the corresponding structure;

[0029] Figure 10 for Figure 8 Force-displacement curves of the corresponding structure;

[0030] Figure 11 This is a comparison of force-displacement curves of arched connecting ribs of different thicknesses in the vibration reduction and energy absorption structure with multi-steady-state quasi-zero stiffness of the present invention.

[0031] Figure 12 This is a diagram showing the specific energy absorption of the vibration-damping and energy-absorbing structure with multi-steady-state quasi-zero stiffness according to the present invention.

[0032] The labels in the diagram are as follows: 1-1, first layer support frame; 1-2, second layer support frame; 1-3, third layer support frame; 11, rectangular inclined beam; 12, outer rectangular contact platform; 13, inner contact platform; 2, flexible curved connecting rib; 3, arched connecting rib. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0034] Example 1: As Figures 1-12As shown, a vibration reduction and energy absorption structure with multi-steady-state quasi-zero stiffness includes an adjustable compliant metamaterial unit whose geometry is distributed in a mirror-symmetric manner along the vertical (height) direction. The adjustable compliant metamaterial unit includes three layers of support frames arranged vertically: a first layer support frame 1-1, a second layer support frame 1-2, and a third layer support frame 1-3. The first layer support frame 1-1 and the second layer support frame 1-2 are connected by a flexible curved connecting rib 2, and the second layer support frame 1-2 and the third layer support frame 1-3 are connected by an arched connecting rib 3.

[0035] Furthermore, the adjustable compliant metamaterial units are arranged in a three-dimensional linear array of n1×n2×n3; where n1 is the number of rows of adjustable compliant metamaterial units in each layer, n2 is the number of columns of adjustable compliant metamaterial units in each layer, and n3 is the number of layers of adjustable compliant metamaterial units along the height direction; where n1, n2, and n3 are all positive integers and all have values ​​greater than or equal to 1. The height direction is used as the layer sequence reference, with the top layer being the first layer, and the layer numbers increasing sequentially downwards. Figure 4 and Figure 5 The images show front and top views of an array structure composed of 3×3×3 adjustable compliant metamaterial units. The 3×3×3 indicates that there are three layers along the height direction, with three rows and three columns in each layer.

[0036] Furthermore, when the adjustable compliant metamaterial unit is multi-layered, the third layer support frame 1-3 of the i-th layer adjustable compliant metamaterial unit serves as the first layer support frame 1-1 of the (i+1)-th layer adjustable compliant metamaterial unit; where i is a positive integer and i≥1; when there are multiple adjustable compliant metamaterial units in one layer, adjacent adjustable compliant metamaterial units in the same layer share the outer rectangular contact platform 12 corresponding to the support frame (adjacent adjustable compliant metamaterial units in two adjacent rows / columns in the same layer share the outer rectangular contact platform 12 corresponding to the support frame).

[0037] Further, refer to Figure 1 The first layer support frame 1-1, the second layer support frame 1-2, and the third layer support frame 1-3 have the same structure, each including: rectangular inclined beams 11, outer rectangular contact platforms 12, and inner contact platforms 13; wherein, one end of the four rectangular inclined beams 11 is connected to the inner contact platform 13 in a cross-shaped arrangement, and the other end of the four rectangular inclined beams 11 is respectively provided with outer rectangular contact platforms 12; in the adjustable compliant metamaterial unit, the first layer support frame 1-1 and the third layer support frame 1-3 are arranged in the same way, and the four rectangular inclined beams are concave based on the lower end face of the inner contact platform 13; the four rectangular inclined beams of the second layer support frame 1-2 are concave based on the upper end face of the inner contact platform 13.

[0038] Further, refer to Figure 2, the vertical distance A between the inner end surface of the inner contact platform 13 of the first-layer support frame 1-1 and the second-layer support frame 1-2 is less than the vertical distance C between the inner end surface of the outer rectangular contact platform 12 of the first-layer support frame 1-1 and the second-layer support frame 1-2, that is, A < C; the vertical distance B between the inner end surface of the inner contact platform 13 of the second-layer support frame 1-2 and the third-layer support frame 1-3 is greater than the vertical distance D between the inner end surface of the outer rectangular contact platform 12 of the second-layer support frame 1-2 and the third-layer support frame 1-3, that is, B > D. Among them, the inner end surface of the inner contact platform 13 of the first-layer support frame 1-1 and the second-layer support frame 1-2 is the lower end surface of the inner contact platform 13 of the first-layer support frame 1-1 and the upper end surface of the inner contact platform 13 of the second-layer support frame 1-2, and the same applies to others.

[0039] Further, the outer rectangular contact platforms 12 corresponding to the first-layer support frame 1-1 and the second-layer support frame 1-2 are connected by four concave flexible curve connecting ribs 2; the inner contact platforms 13 of the second-layer support frame 1-2 and the third-layer support frame 1-3 are connected by four convex arched connecting ribs 3. That is, the four flexible curve connecting ribs 2 and the four arched connecting ribs 3 of the same adjustable compliant metamaterial unit are arranged in vertical alignment.

[0040] Further, referring to Figure 3 , the cross-section of the flexible curve connecting rib 2 along the extension direction is surrounded by eight truncated sine curves and four arcs. The first sine curve L1, the first arc, the fourth sine curve L4, the fifth sine curve L5, the second arc, and the eighth sine curve L8 are connected in sequence to form the inner boundary line, and the second sine curve L2, the third arc, the third sine curve L3, the sixth sine curve L6, the fourth arc, and the seventh sine curve L7 are connected in sequence to form the outer boundary line (the inner boundary line and the outer boundary line are connected end to end at both ends to form the cross-section area of the flexible curve connecting rib 2).

[0041] Further, referring to Figure 3 , the second sine curve L2 and the fourth sine curve L4 satisfy the following relationship in the unloaded state: , where is the coordinate of the curve along the first direction, The coordinates of the curve along the second direction are (the length direction of the curve is the first direction, and the height direction of the curve is the second direction, which are perpendicular to each other). The first sine curve L1 is formed equidistantly from the second sine curve L2 (e.g., equidistantly 1mm apart, where 1mm is the thickness of the flexible curve connecting rib; other values ​​can be used as needed). The third sine curve L3 is formed equidistantly from the fourth sine curve L4 (the distance between the second sine curve L2 and the first sine curve L1). L5, L6, L7, L8, the second arc, and the fourth arc are formed in a mirror image symmetrically based on L1, L2, L3, L4, the first arc, and the third arc. The circle I formed by the first and third arcs located in the first layer is used as an example: the radius R of the arc is 1.5mm. A schematic diagram of the orthographic projection of the adjustable compliant metamaterial unit is shown below. Figure 3 The location of the center of circle I is explained below: Figure 3 The adjustable compliant metamaterial unit shown is used as the central axis, the right end face of the adjustable compliant metamaterial unit is used as the outer plane, the line segment between the central axis and the outer plane is used as the horizontal line segment, and the perpendicular line between the upper end face of the outer rectangular contact platform 12 of the first layer support frame 1-1 and the lower end face of the outer rectangular contact platform 12 of the second layer support frame 1-2 in the adjustable compliant metamaterial unit is used as the vertical line segment. The center O of circle I is located horizontally at 1 / 3 of the distance from the outer plane on the horizontal line segment, and vertically at 1 / 3 of the distance from the upper end face of the outer rectangular contact platform 12 of the first layer support frame 1-1 on the vertical line segment.

[0042] Further, refer to Figure 2 The arched connecting rib 3 includes a first concave arc segment, a convex arc segment, and a second concave arc segment; the first concave arc segment, the convex arc segment, and the second concave arc segment are connected sequentially. For example, the outer arc radius r1 of the first and second concave arc segments, which are transitionally connected, is 1.81 mm, and the inner arc radius r2 is 3.31 mm; the outer arc radius R1 of the convex arc segment is 6.2 mm, and the inner arc radius R2 is 4.7 mm.

[0043] Furthermore, the external support frame 1, flexible curved connecting ribs 2, and arched connecting ribs 3 can all be made of Al6061 and integrally formed through 3D printing. The width and thickness of the flexible curved connecting ribs 2 and arched connecting ribs 3 are significantly smaller than the cross-sectional dimensions of the rectangular inclined beam 11, thus giving it lower bending stiffness and making it prone to elastic buckling, acting as an "elastic hinge" to guide the structure to achieve multi-level deformation response. The entire unit cell structure is made of Al6061 material and integrally manufactured through metal 3D printing technology, balancing structural integrity and forming precision.

[0044] As can be seen from the above technical solution, the support frame 1 forms a cross-shaped support structure through four rectangular inclined beams, which provides constraint boundaries for the internal flexible units while ensuring overall stability. The flexible curved connecting rib 2 and the arched connecting rib 3 are located in the internal space of the frame, forming a double-layer deformation system (i.e., forming upper and lower layered, independent yet cooperative deformation paths). The flexible curved connecting rib 2 adopts an equation-driven transition curve design. Due to its extremely low bending stiffness, it will first reach the buckling critical force, resulting in an elastic jump and forming the first force plateau and the first stable state. This stage is mainly used to cope with low-energy vibrations or impacts. When compression continues, the load is fully transferred to the arched connecting rib 3. At this time, the arched connecting rib 3 buckles, producing a second jump and forming a second force plateau with a higher force value. This stage is used to absorb higher-energy impacts. Under the action of external vertical loads, this invention can generate multi-level quasi-zero stiffness plates and irreversible configuration switching through sequential plastic buckling, thereby simultaneously achieving excellent vibration reduction and energy absorption effects in impact events. This structure can be used in high-intensity impact protection scenarios such as spacecraft landing buffers, vehicle collision protection, and equipment impact-resistant bases.

[0045] The working principle of this invention is as follows: When the cellular structure is subjected to a quasi-static compressive load in the vertical direction, the load is first transferred to the upper flexible curved connecting rib 2 via the external support frame 1. Due to the small cross-sectional size and low stiffness of this connecting rib, it undergoes large-deflection elastic bending deformation under load, generating a negative stiffness effect. This negative stiffness couples with the positive stiffness provided by the other rigid parts in the structure, forming the first quasi-zero stiffness platform on a macroscopic scale, achieving preliminary vibration reduction and energy distribution. As the compressive displacement further increases, the deformation of the upper flexible curved connecting rib 2 tends to saturate, and the load is effectively transferred to the lower arched connecting rib 3 through the inner contact platform 13. When the axial pressure on the arched connecting rib 3 reaches its buckling critical value, elastic buckling behavior occurs, activating its inherent negative stiffness characteristics, thereby forming a second quasi-zero stiffness platform in the force-displacement response, achieving a higher level of vibration reduction and energy absorption.

[0046] Furthermore, a 3×3×3 cubic array will be used as a typical example for illustration below.

[0047] By precisely designing the cross-sectional dimensions and spatial tilt angle of the upper flexible curved connecting rib 2, as well as the curvature radius and cross-sectional moment of inertia of the lower arched connecting rib 3, independent control of the force levels and occurrence ranges of the two platforms can be achieved, thereby adapting to the customized requirements of structural performance in different engineering scenarios.

[0048] To verify the structural performance of this invention, a three-dimensional model of the 3×3×3 array structure was established using SolidWorks software and imported into the finite element analysis software Abaqus for numerical simulation. Specific model parameters are as follows: the overall structural dimensions are 112mm (length) × 112mm (width) × 119mm (height). Four flexible curved connecting ribs 2 are symmetrically arranged on the upper layer of each cell, with the thickness of the flexible curved connecting ribs gradually varying between 1 and 3mm. The lower layer of arched connecting ribs 3 is a semi-circular arc beam structure, with a transition connection zone between the arc segment and the contact platform to optimize stress distribution; the outer arc radius R1 is 6.2mm, the inner arc radius R2 is 4.7mm, and the outer arc radius r1 of the transition connection is 1.81mm, while the inner arc radius r2 is 3.31mm. The material model is defined as an elastoplastic model of Al6061.

[0049] A vertical displacement load of 65 mm was applied to the model. The thickness of the lower arched connecting rib 3 was 1.5 mm. The support reactions were extracted, and the macroscopic force-displacement curve was calculated, as shown below. Figure 6 As shown in the figure. Simulation results indicate that the structure exhibits two distinct force plateaus during compression: the first plateau is located in the displacement range of 2mm to 30mm, with an average plateau force of approximately 550N, corresponding to the bending-dominant deformation stage of the upper flexible curved connecting rib; the second plateau is located in the range of 32mm to 59mm, with an average plateau force of approximately 1338N, corresponding to the buckling response stage of the lower arched connecting rib. Calculations of the curve slope show that the equivalent dynamic stiffness of the structure is close to zero within both displacement ranges, indicating that it possesses typical bi-stage quasi-zero stiffness characteristics.

[0050] Regarding the design of the flexible curved ribs in the upper layer of this unit cell structure, this invention provides a comparative analysis. Figure 7 The straight inclined rib shown is Figure 8 The sinusoidal curve rib is shown. By arraying the modified unit cell structure into a 3×3×3 array and applying the same displacement load to the model using the above method, the force-displacement curve is obtained, as shown. Figure 9 , Figure 10 As shown. Simulation results show that using... Figure 7 The structure shown with straight inclined ribs does not have the double-plateau characteristic, so it is replaced with... Figure 8 The sinusoidal rib structure shown cannot form a stable first quasi-zero stiffness plateau. That is, only the flexible curved rib used in this invention can form two stable quasi-zero stiffness plateaus.

[0051] To further investigate the influence of geometric parameters on structural performance, keeping other parameters constant, only the thickness of the lower arched connecting rib 3 was changed. Simulation analyses were conducted using three different thicknesses: 1.0 mm, 1.5 mm, and 1.8 mm. The results are as follows: Figure 11As shown, with the increase of the thickness of the connecting arch rib 3, the triggering force of the second force platform increases significantly, while the mechanical behavior of the first force platform remains basically unchanged. This indicates that by adjusting the cross-sectional dimensions of the connecting arch rib 3, the load-bearing capacity of the second force platform can be independently controlled, demonstrating the flexibility and adjustability of the structural design.

[0052] Figure 12 The specific energy absorption-displacement curve of this embodiment is shown. As illustrated, the structure exhibits graded specific energy absorption characteristics: the specific energy absorption in the first plateau region reaches approximately 150 J / kg, while the specific energy absorption in the second plateau region reaches a maximum of approximately 600 J / kg. This value is significantly superior to traditional polymer foams and many homogeneous metal structures, and comparable to the performance of current advanced porous metamaterials. This indicates that the flexible curved connecting rib 2 and the arched connecting rib 3 work synergistically to effectively achieve efficient energy dissipation under a multi-level deformation mechanism. More importantly, combined with its unique dual-plateau and quasi-zero stiffness characteristics, this invention achieves adaptive, efficient, and stable energy absorption across a wide range of impact energy levels, solving the traditional structural challenge of balancing "high energy dissipation" and "low impact response." This performance advantage makes it highly promising for applications in adaptive shock and vibration protection for extreme conditions.

[0053] In summary, this invention utilizes Al6061 material and employs an integrated molding process to construct a flexible curved connecting rib and arched connecting rib structure with symmetrical distribution characteristics, successfully achieving multi-steady-state response and dual-stage quasi-zero stiffness characteristics. Simultaneously, this structure achieves a balance between instantaneous vibration reduction and efficient energy absorption, providing an innovative lightweight solution for critical impact protection scenarios such as aerospace landings and vehicle collisions.

[0054] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness, characterized in that, The system includes an adjustable compliant metamaterial unit, which comprises three layers of integrally formed support frames arranged vertically: a first support frame (1-1), a second support frame (1-2), and a third support frame (1-3). The first support frame (1-1) and the second support frame (1-2) are connected by an integrally formed flexible curved connecting rib (2), and the second support frame (1-2) and the third support frame (1-3) are connected by an integrally formed arched connecting rib (3). The first layer support frame (1-1), the second layer support frame (1-2), and the third layer support frame (1-3) have the same structure, each including: a rectangular inclined beam (11), an outer rectangular contact platform (12), and an inner contact platform (13); wherein, one end of the four rectangular inclined beams (11) is connected to the inner contact platform (13) in a cross-shaped arrangement, and the other end of the four rectangular inclined beams (11) is respectively provided with an outer rectangular contact platform (12); in the adjustable compliant metamaterial unit, the first layer support frame (1-1) and the third layer support frame (1-3) are arranged in the same way, and the four rectangular inclined beams are concave based on the lower end face of the inner contact platform (13); the four rectangular inclined beams of the second layer support frame (1-2) are concave based on the upper end face of the inner contact platform (13); The outer rectangular contact platforms (12) of the first layer support frame (1-1) and the second layer support frame (1-2) are connected by four concave flexible curved connecting ribs (2); the inner contact platforms (13) of the second layer support frame (1-2) and the third layer support frame (1-3) are connected by four convex arched connecting ribs (3). The flexible curve connecting rib (2) is formed by eight truncated sine curves and four circular arcs. The first sine curve L1, the first circular arc, the fourth sine curve L4, the fifth sine curve L5, the second circular arc, and the eighth sine curve L8 are connected in sequence to form the inner boundary line. The second sine curve L2, the third circular arc, the third sine curve L3, the sixth sine curve L6, the fourth circular arc, and the seventh sine curve L7 are connected in sequence to form the outer boundary line. The second sine curve L2 and the fourth sine curve L4 satisfy the following relationship in the unloaded state: ,in, Let be the coordinates of the curve along the first direction. Let be the coordinates of the curve along the second direction; The arched connecting rib (3) includes a first concave arc segment, a convex arc segment, and a second concave arc segment; the first concave arc segment, the convex arc segment, and the second concave arc segment are connected in sequence.

2. The vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness according to claim 1, characterized in that, The adjustable compliant metamaterial units are arranged in a three-dimensional linear array of n1×n2×n3; where n1 is the number of rows of adjustable compliant metamaterial units in each layer, n2 is the number of columns of adjustable compliant metamaterial units in each layer, and n3 is the number of layers of adjustable compliant metamaterial units along the height direction; where n1, n2, and n3 are all positive integers and all have values ​​greater than or equal to 1.

3. The vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness according to claim 2, characterized in that, When the adjustable compliant metamaterial unit is multi-layered, the third layer support frame (1-3) of the i-th adjustable compliant metamaterial unit serves as the first layer support frame (1-1) of the (i+1)-th adjustable compliant metamaterial unit; where i is a positive integer and i≥1; when there are multiple adjustable compliant metamaterial units in one layer, adjacent adjustable compliant metamaterial units in the same layer share the outer rectangular contact platform (12) corresponding to the support frame.

4. The vibration damping and energy absorption structure with multi-steady-state quasi-zero stiffness according to claim 1, characterized in that, The vertical distance between the inner end faces of the inner contact platforms (13) of the first layer support frame (1-1) and the second layer support frame (1-2) is less than the vertical distance between the inner end faces of the outer rectangular contact platforms (12) of the first layer support frame (1-1) and the second layer support frame (1-2); the vertical distance between the inner end faces of the inner contact platforms (13) of the second layer support frame (1-2) and the third layer support frame (1-3) is greater than the vertical distance between the inner end faces of the outer rectangular contact platforms (12) of the second layer support frame (1-2) and the third layer support frame (1-3).

Images