Asymmetric quasi-zero stiffness element structure and element structure for vibration isolation
By designing an asymmetric quasi-zero stiffness unit structure and using the periodic installation of trigonometric function curved beams, the problem of deterioration of the vibration isolation effect in the existing technology under large excitation is solved, and a larger low stiffness interval and better vibration isolation performance are achieved.
Patent Information
- Application Number
- CN202411682081.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-22
- Publication Date
- 2025-03-25
AI Technical Summary
The existing quasi-zero-stiff vibration isolation system has deteriorated vibration isolation effect under large excitation, making it difficult to take into account both high static stiffness and low dynamic stiffness.
Asymmetric quasi-zero stiffness unit structure is designed, and asymmetric quasi-zero stiffness interval is formed through the periodic installation of trigonometric function curved beams, and the low stiffness interval is increased to improve the vibration isolation performance under large excitation.
It achieves good vibration isolation effect under large excitation, expands the low stiffness range, and improves the system's load-bearing capacity and frequency range.
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Figure CN119687129A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of quasi-zero stiffness vibration isolation, and in particular to an asymmetric quasi-zero stiffness unit structure and a metastructure. Background Art
[0002] Quasi-Zero Stiffness (QZS) vibration isolation system has two stages: high stiffness and low stiffness, and has the characteristics of high static stiffness and low dynamic stiffness. High static stiffness ensures the load-bearing capacity of the system, while low dynamic stiffness reduces the natural frequency of the system and broadens the frequency range of vibration isolation, thus solving the contradiction between low stiffness and high load-bearing capacity of linear vibration isolation system.
[0003] Traditional quasi-zero stiffness structures are usually composed of positive and negative stiffness elements in parallel, for example, a buckling beam with negative stiffness characteristics is connected in parallel with a positive stiffness spring, or a cosine beam structure with negative stiffness characteristics is connected in parallel with a positive stiffness spring. These traditional quasi-zero stiffness structures involve many parameters and the design process is relatively complicated. Some quasi-zero stiffness structures are realized through single-beam design, but these structures often form symmetrical quasi-zero stiffness isolators, which have good vibration isolation effects only under small excitations. Under large excitations, the vibration isolator is prone to large jumps, resulting in a significant decrease in vibration isolation performance.
[0004] The Chinese patent publication number is "CN115217899B", and the patent name is "A quasi-zero stiffness structure and a quasi-zero stiffness sandwich structure". The structure consists of a first load-bearing plane, a second load-bearing plane, and two linear elastic core columns connected between the two load-bearing planes. The two core columns are symmetrically arranged and have the same initial bending deformation in the middle direction. However, the quasi-zero stiffness interval formed is a symmetrical quasi-zero stiffness, and the vibration isolation effect will deteriorate under large excitation. Summary of the invention
[0005] In order to solve the problem of poor vibration isolation effect under large excitation in the prior art, the present invention provides an asymmetric quasi-zero stiffness unit structure with simple design and easy implementation, which has asymmetric quasi-zero stiffness and a larger low stiffness range to solve the vibration isolation problem under large excitation.
[0006] The technical solution adopted by the present invention is:
[0007] A structure based on an asymmetric quasi-zero stiffness unit, the structure consists of an upper panel, a lower panel and multiple curved beams; the upper panel is a load-bearing surface, the lower panel is a fixed surface, the curved beam is a trigonometric curved beam, and multiple beams are periodically installed between the upper and lower panels;
[0008] The trigonometric function curved beam is a trigonometric function curve rotated around an axis to form a curved surface, and the curved surface is thickened to form the trigonometric function curved beam; during the compression process of the curved beam, the force displacement curve generated is asymmetric on the left and right sides of the quasi-zero stiffness interval, that is, an asymmetric quasi-zero stiffness beam structure is formed; the asymmetric quasi-zero stiffness unit structure is formed by periodically installing the trigonometric function curved beam.
[0009] The trigonometric function curved beam is designed based on the trigonometric function space rotation, and has five constraint parameters: the length L of the beam, the amplitude h, the thickness t, the rotation angle β, and the distance z from the rotation axis. The upper and lower base plates have two constraint parameters: the width B and the thickness T. That is, the asymmetric quasi-zero stiffness unit structure formed has a total of seven constraint parameters.
[0010] The parameters of the trigonometric function curved beam are calculated by joint simulation of Comsol and Matlab according to the objective function of forming quasi-zero stiffness.
[0011] The upper and lower panels and the trigonometric function curved beam are all made of materials with high strength and toughness and have the characteristics of large bearing capacity.
[0012] A structure based on an asymmetric quasi-zero stiffness element is characterized in that it comprises a single-layer plane, a second-layer plane, a third-layer plane, a fourth-layer plane and a plurality of asymmetric quasi-zero stiffness unit structures superimposed between the planes.
[0013] Beneficial effects of the present invention: The present invention forms a curved surface by rotating a trigonometric function curve around an axis, and thickens the curved surface to form a trigonometric function curved beam, which can achieve asymmetric quasi-zero stiffness. The curved beam is periodically arranged to form an asymmetric quasi-zero stiffness unit structure and element structure. Due to its asymmetric quasi-zero stiffness characteristic, it has a larger low stiffness range and can achieve good vibration isolation effect under large excitation. BRIEF DESCRIPTION OF THE DRAWINGS
[0014] Figure 1 A schematic diagram of forming a trigonometric function curved beam provided in Example 1 of the present invention;
[0015] Figure 2 Comsol and Matlab joint simulation flow chart provided in Example 1 of the present invention;
[0016] Figure 3 A schematic diagram of the asymmetric quasi-zero stiffness unit structure provided in Example 1 of the present invention;
[0017] Figure 4 A force-displacement curve diagram of the asymmetric quasi-zero stiffness unit structure provided in Example 1 of the present invention;
[0018] Figure 5 A schematic diagram of the structure of an asymmetric quasi-zero stiffness element provided in Example 2 of the present invention;
[0019] Figure 6 A force-displacement curve diagram of the asymmetric quasi-zero stiffness element structure provided in Example 2 of the present invention;
[0020] Figure 7 A schematic diagram of the frequency domain response of an asymmetric quasi-zero stiffness element structure provided in Example 2 of the present invention;
[0021] Figure 8 A schematic diagram of the time domain response of an asymmetric quasi-zero stiffness element structure provided in Example 2 of the present invention; Figure 8 (a) is the time domain response diagram for 5 Hz frequency excitation; Figure 8 (b) is the time domain response diagram for 10 Hz frequency excitation; Figure 8 (c) is the time domain response diagram for 20 Hz frequency excitation; Figure 8 (d) is the time domain response diagram for 30Hz frequency excitation.
[0022] Among them, 1. asymmetric zero stiffness unit structure, 2. upper panel, 3. trigonometric function curved beam, 4. lower panel, 10. asymmetric zero stiffness unit structure, 11. first floor plane, 12. second floor plane, 13. third floor plane, 14. fourth floor plane. DETAILED DESCRIPTION
[0023] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
[0024] A structure based on an asymmetric quasi-zero stiffness unit, which consists of an upper panel, a lower panel and multiple curved beams; the upper panel is a load-bearing surface, the lower panel is a fixed surface, the curved beam is a trigonometric function curved beam, and multiple beams are periodically installed between the upper and lower panels.
[0025] The trigonometric function curved beam is a curved surface formed by rotating a trigonometric function curve around an axis, and the curved surface is thickened to form a trigonometric function curved beam. During the compression process of the curved beam, the force displacement curve generated is asymmetric on the left and right sides of the quasi-zero stiffness interval, that is, an asymmetric quasi-zero stiffness beam structure is formed; the asymmetric quasi-zero stiffness unit structure is formed by periodically installing the trigonometric function curved beam.
[0026] Furthermore, the trigonometric function curved beam has load-bearing capacity and its deformation is reversible.
[0027] Furthermore, the upper panel, the lower panel and the trigonometric function curved beam are all made of materials with strength and toughness.
[0028] Furthermore, the present application also provides an asymmetric quasi-zero stiffness element structure, comprising a single-layer plane, a second-layer plane, a third-layer plane, a fourth-layer plane and multiple asymmetric quasi-zero stiffness unit structures between the planes, and the asymmetric quasi-zero stiffness unit structure adopts the above-mentioned asymmetric quasi-zero stiffness unit structure.
[0029] Embodiment 1:
[0030] Trigonometric function curves mainly include sine function curves, cosine function curves and tangent function curves.
[0031] See also Figure 1 This embodiment provides a method for forming a trigonometric function curved beam 3, taking a cosine function curve as an example. The trigonometric function curved beam has five constraint parameters: beam length L, amplitude h, thickness t, rotation angle β, and distance z from the rotation axis. In this embodiment, the trigonometric function curved beam 3 is made of a material similar to polylactic acid (PLA) material with good strength and toughness, but is not limited to polylactic acid material. The use of polylactic acid (PLA) material has low cost and is recyclable.
[0032] In an exemplary embodiment 1, the material parameters of the trigonometric function curved beam 3 are shown in Table 1:
[0033] Table 1
[0034] Material <![CDATA[Density (Kg / m 3 )]]> Young's modulus(Mpa) Poisson's ratio Polylactic acid (PLA) 1250 1174 0.4
[0035] See also Figure 2 , according to the desired quasi-zero stiffness range and load, the objective function is established, a finite element model of a curved beam with trigonometric functions is created in Comsol, and a static solution is performed. The solution is brought into the objective function error study, and the parameters are output if the error satisfies the requirement. If the error does not satisfy the requirement, the optimization algorithm is established in Matlab to update the parameters and continuously iterate the solution to obtain the geometric parameters that meet the objective function. Finally, the parameters are output and a three-dimensional solid structure is constructed for verification. The objective function created is The maximum vertical restoring force Fy generated during compression max and the minimum vertical restoring force Fy min When the index Π min When it is close to zero, it means that the vertical restoring force of the trigonometric function curved beam 3 remains almost constant in the entire deformation range and does not change significantly with the change of deformation. This almost constant restoring force corresponds to an extremely low stiffness value, which is a quasi-zero stiffness state.
[0036] The geometric parameters of the trigonometric function curved beam 3 are shown in Table 2.
[0037] Table 2
[0038] L h t β z 100mm 3.5mm 1.01mm 50.035° 18.1mm
[0039] See also Figure 3 This embodiment provides an asymmetric quasi-zero stiffness unit structure 1, which is composed of four trigonometric function curved beams 3, an upper panel 2 and a lower panel 4, and the four trigonometric function curved beams 3 are symmetrically arranged.
[0040] The upper panel 2, the lower panel 4 and the trigonometric function curved beam 3 are all made of materials with certain strength and toughness, ensuring that the deformation of the trigonometric function curved beam 3 is reversible, so that the structure has certain bearing performance without large geometric deformation.
[0041] In this embodiment, the upper panel 2, the lower panel 4 and the trigonometric function curved beam 3 are made of materials such as polylactic acid (PLA) material having good strength and toughness, but are not limited to polylactic acid material.
[0042] The force displacement curve of the asymmetric quasi-zero stiffness unit structure 1 is obtained by ABAQUS numerical simulation as shown in Figure 4 As shown. Figure 4 It can be seen that the asymmetric quasi-zero stiffness unit structure 1 has an asymmetric stiffness on the left and right sides near zero stiffness, and has a larger low stiffness range.
[0043] Embodiment 2:
[0044] See also Figure 5 This embodiment provides an asymmetric quasi-zero stiffness unit structure 10, which includes a first plane 11, a second plane 12, a third plane 13, a fourth plane 14 and a plurality of asymmetric quasi-zero stiffness unit structures 1 between the planes. The asymmetric quasi-zero stiffness unit structure 1 adopts the asymmetric quasi-zero stiffness unit structure 1 described in Example 1.
[0045] By periodically arranging multiple asymmetric quasi-zero stiffness unit structures 1, an asymmetric quasi-zero stiffness element structure 10 is formed. A first-layer plane 11, a second-layer plane 12, a third-layer plane 13 and a fourth-layer plane 14 are respectively arranged at the upper and lower ends of the multiple asymmetric quasi-zero stiffness unit structures 1 to assemble and constrain them, which can not only greatly improve the bearing capacity of the system, but also widen the asymmetric quasi-zero stiffness range; the bearing capacity of the asymmetric quasi-zero stiffness element structure 10 is the bearing capacity of a single asymmetric quasi-zero stiffness unit structure 1 multiplied by the number of asymmetric quasi-zero stiffness unit structures 1.
[0046] The first layer plane 11, the second layer plane 12, the third layer plane 13, and the fourth layer plane 14 are made of alloy planes, and the asymmetric quasi-zero stiffness element structure 10 is made of PLA material.
[0047] In an exemplary embodiment 2, the material parameters are shown in Table 3:
[0048] Table 3
[0049] Material <![CDATA[Density (Kg / m 3 )]]> Young's modulus(Mpa) Poisson's ratio Polylactic acid (PLA) 1250 1174 0.4 Aluminum Alloy 2750 70000 0.33
[0050] The force displacement curve of the asymmetric quasi-zero stiffness element structure 10 is obtained by ABAQUS numerical simulation as shown in Figure 6 As shown. Figure 6 It can be seen that after the periodic arrangement, the asymmetric quasi-zero stiffness range and load of the asymmetric quasi-zero stiffness element structure 10 are improved to a certain extent.
[0051] The asymmetric quasi-zero stiffness element structure of this embodiment is analyzed for transmissibility using the linear dynamics method. The transmissibility formula is:
[0052]
[0053] Where K is the linear stiffness and c is the damping of the material. In fact, the asymmetric quasi-zero stiffness interval is also approximately linear, with a relatively small stiffness K2. Therefore, the transmissibility of the asymmetric quasi-zero stiffness element structure 10 can be obtained by equation (1), where K is replaced by K2. Comparison with an equivalent linear isolator is an effective method to verify the vibration isolation performance of the newly designed QZS structure.
[0054] The transmissibility of the asymmetric quasi-zero stiffness element structure 10 and the equivalent linear system when the load is M = 36 kg is obtained by formula (1), and the transmissibility is expressed as 20log10(T). Figure 7 Compared with the equivalent linear system, the asymmetric quasi-zero stiffness element structure 10 provides a wider vibration isolation frequency band and a better vibration isolation effect.
[0055] See also Figure 8 , shows the response curve of the quasi-asymmetric quasi-zero stiffness element structure 10 in the time domain, using an acceleration excitation with an amplitude of A = 0.2g, and excitation at frequencies of 5Hz, 10Hz, 20Hz and 30Hz. The results show that the structure exhibits good vibration isolation effect at all frequencies and is consistent with Figure 7 The frequency domain response characteristics are roughly consistent.
[0056] The above content describes the preferred embodiments of the present invention in detail, but the specific implementation of the present invention cannot be limited to these descriptions. Without departing from the concept of the present invention, ordinary technicians in this field can also make some simple deductions and substitutions, and these changes should be considered to fall within the scope of protection of the present invention.
Claims
1. A structure based on an asymmetric quasi-zero stiffness unit, characterized in that: The asymmetric quasi-zero stiffness unit structure is composed of an upper panel, a lower panel and a plurality of curved beams; the upper panel is a bearing surface, the lower panel is a fixed surface, the curved beam is a trigonometric curved beam, and the plurality of curved beams are periodically installed between the upper and lower panels; The trigonometric function curved beam is a trigonometric function curve rotated around an axis to form a curved surface, and the curved surface is thickened to form the trigonometric function curved beam; during the compression process of the curved beam, the force displacement curve generated is asymmetric on the left and right sides of the quasi-zero stiffness interval, that is, an asymmetric quasi-zero stiffness beam structure is formed; the asymmetric quasi-zero stiffness unit structure is formed by periodically installing the trigonometric function curved beam.
2. The asymmetric quasi-zero stiffness unit structure according to claim 1, characterized in that: The trigonometric function curved beam is designed based on the trigonometric function space rotation, and has five constraint parameters: the length L of the beam, the amplitude h, the thickness t, the rotation angle β, and the distance z from the rotation axis. The upper and lower base plates have two constraint parameters: the width B and the thickness T. That is, the asymmetric quasi-zero stiffness unit structure formed has a total of seven constraint parameters.
3. The asymmetric quasi-zero stiffness unit structure according to claim 1, characterized in that: The parameters of the trigonometric function curved beam are calculated by joint simulation of Comsol and Matlab according to the objective function of forming quasi-zero stiffness.
4. The asymmetric quasi-zero stiffness unit structure according to claim 1, characterized in that: The upper and lower panels and the trigonometric function curved beam are all made of materials with high strength and toughness and have the characteristics of large bearing capacity.
5. A structure based on an asymmetric quasi-zero stiffness element, characterized in that: It includes a first-layer plane, a second-layer plane, a third-layer plane, a fourth-layer plane and a plurality of asymmetric quasi-zero stiffness unit structures superimposed between the planes.