V-shaped spring system, lagging and bifurcation experimental device and experimental method

Abstract

The invention belongs to the technical field of non-linear dynamics, and particularly relates to a V-shaped spring system, a lagging and bifurcation experiment device and an experiment method.The V-shaped spring system comprises a base, two telescopic arms and a spring, the two telescopic arms are the same in length, the first ends of the two telescopic arms are connected to a first connecting piece, and the second ends of the two telescopic arms are connected to a second connecting piece; at least one of the two telescopic arms is rotationally connected with the first connecting piece, the second ends of the two telescopic arms are respectively connected with a second connecting piece, the telescopic arms are rotationally connected to the base through the second connecting pieces, and the first connecting piece is movably arranged on the base along the perpendicular center line of the connecting line of the second ends of the two telescopic arms; the two telescopic arms are sleeved with springs, and the springs can stretch out and draw back along with the telescopic arms. According to the V-shaped spring system and the lagging and bifurcation experiment device applying the V-shaped spring system, the situation that the spring deviates from the axis of the spring during deformation can be reduced, and the result accuracy during theoretical verification is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nonlinear dynamics, and in particular to a V-shaped spring system, a hysteresis and bifurcation experiment device and an experiment method. BACKGROUND

[0002] Hysteresis phenomenon is manifested as path dissimilarity of the system, that is, the paths of the system from state A to state B and from state B back to state A do not coincide, and this feature is manifested as a typical ring-shaped "hysteresis loop" in the graph. The energy dissipation characteristics brought by this irreversible path are widely used in the field of structural engineering, bionics medicine and other aspects, such as using the plastic deformation of building materials in the loading and unloading process to absorb seismic energy to prevent brittle fracture, and simulating the hysteresis process of lung inflation and deflation to design a respirator. The hysteresis loop usually has two endpoints corresponding to two thresholds of the system. Due to the "dead zone" between the thresholds, the system responds slowly to changes, and is often used for noise interference and waveform shaping, such as a typical hysteresis comparator.

[0003] In most cases, hysteresis in a circuit (electronic system) is highly controllable and designable, while hysteresis in materials and physical systems is mostly inherent, a characteristic that needs to be measured and compensated, and is difficult to be designed and utilized simply by limited parameters. Christopher Ong proposed a theory in the article Hysteresis in a simple V-shape spring-mass system in 2021, which pointed out that there is a spring system including two V-shaped connected springs. When the half horizontal distance between the two ends of the spring system is less than the original length of the spring, there are maximum vertical forces on both sides of the horizontal axis with the line connecting the two ends as the horizontal axis. Assuming that the initial position is on the upper side of the horizontal axis, when the applied external force is less than the maximum vertical force, the spring system has three equilibrium points, two of which are stable equilibrium points, and the unstable equilibrium point is between the two stable equilibrium points. When the external force gradually increases, the spring system is gradually compressed downward until the downward external force is equal to the maximum vertical force provided by the spring system, the stable equilibrium point and the unstable equilibrium point coincide, and thus there are only two equilibrium points. This is the mechanism of "jump" caused by the position of the spring deviating to the opposite side, that is, when the position of the spring changes from stable equilibrium to unstable equilibrium, the spring tends to deviate to the opposite side, that is, the state with low energy is converted.

[0004] However, unlike the above theory, the spring has a serious torsion problem in the actual compression state, which will cause the spring deformation direction to deviate from the axis and affect the actual motion of the spring system. Therefore, there is an urgent need for a feasible device design to verify the theory in order to further apply it to engineering design. SUMMARY

[0005] One of the purposes of the present application is to provide a V-shaped spring system to solve the problem of the spring deformation direction deviating from its own axis and the geometric interference between two springs in the theoretical verification process.

[0006] The second purpose of the present application is to provide a hysteresis and bifurcation experimental device and experimental method for verifying the above theory.

[0007] In a first aspect, the present application provides a V-shaped spring system comprising a base, telescopic arms and springs, two telescopic arms are provided and have the same length, the first ends of the two telescopic arms are connected to a first connecting piece, and at least one of the two telescopic arms is rotatably connected to the first connecting piece, each of the second ends of the two telescopic arms is connected to a second connecting piece, the telescopic arms are rotatably connected to the base through the second connecting pieces, and the distance between the second connecting pieces is adjustable. The first connecting piece is movably arranged on the base along the vertical center line of the connecting line of the second ends of the two telescopic arms; the springs are sleeved on the two telescopic arms, and the springs can stretch and contract with the telescopic arms.

[0008] The V-shaped spring system can be used for theoretical verification in the background art, and the telescopic arms can make the springs stretch and contract along the length direction of the telescopic arms, effectively solving the problem of the spring deformation direction deviating from its own axis in the theoretical verification process, thereby improving the reliability of the theoretical verification.

[0009] In one embodiment, the telescopic arm comprises a first end cover, a second end cover and at least two sleeves movably sleeved in the axial direction, the first end cover is arranged on the sleeve closest to the first connecting piece, the second end cover is arranged on the sleeve closest to the second connecting piece, the ends of the spring are limited between the first end cover and the second end cover, and at least one of the first end cover and the second end cover is detachably connected to the sleeve.

[0010] In one embodiment, the first connecting piece comprises a first rotating shaft, a first connecting rod and a second connecting rod extending radially along the first rotating shaft, the outer diameters of the first connecting rod and the second connecting rod are smaller than the minimum outer diameter of the telescopic arm, one end of the first connecting rod is sleeved on the first rotating shaft and rotatably connected to the first rotating shaft, the other end of the first connecting rod is coaxially connected to one of the telescopic arms, one end of the second connecting rod is connected to the first rotating shaft, and the other end of the second connecting rod is coaxially connected to the other telescopic arm.

[0011] In one embodiment, the spring is spaced apart from the base.

[0012] In a second aspect, the present application provides a hysteresis and bifurcation experimental device, comprising the V-shaped spring system of any one of the above, further comprising a spacing adjustment mechanism, a force applying mechanism, a displacement monitoring member, a tension monitoring member, and a controller, the spacing adjustment mechanism is used to adjust the spacing between the two second connecting members, the force applying mechanism is used to apply a force to the first connecting member in a direction perpendicular to the line connecting the second end points of the two telescopic arms, the displacement monitoring member is used to monitor the linear motion spacing of the first connecting member, the tension monitoring member is used to monitor the tension applied by the force applying mechanism to the first connecting member, and the controller is in communication connection with the tension monitoring member and the displacement monitoring member, and the controller comprises a data processing module, and the data processing module is used to generate a hysteresis loop image.

[0013] In an embodiment, the spacing adjustment mechanism comprises a lead screw and a nut, the lead screw is capable of rotating around its own axis, the nut is sleeved on the lead screw and is in threaded connection with the lead screw, and the second connecting member is connected to the nut.

[0014] In an embodiment, the force applying mechanism is provided in two groups and is symmetrically arranged with the line connecting the two second connecting members as the symmetry axis, the force applying mechanism comprises a counterweight member, a connecting line, and a pulley, the counterweight member is suspended below the base and is connected to the first connecting member through the connecting line, and the connecting line is reversed through the pulley.

[0015] In an embodiment, the counterweight member comprises a water containing groove and a water tank, the water containing groove is provided with a flow monitoring member, the water tank is arranged above the water containing groove, water in the water tank can flow into the water containing groove, and the water tank is provided with a flow monitoring member.

[0016] In a third aspect, the present application provides an experimental method, which is based on the hysteresis and bifurcation experimental device of any one of the above, and the experimental method comprises the following steps:

[0017] The initial spacing between the two second connecting members is L0, the original length of the spring is S, and 1 / 2L0>S, and the spacing between the two second connecting members is gradually reduced to L, and 1 / 2L≤S;

[0018] The change in the spacing between the two second connecting members and the position of the first connecting member are tracked, and a symmetric bifurcation spacing-position curve is obtained.

[0019] In a fourth aspect, the present application provides an experimental method, which is based on the hysteresis and bifurcation experimental device of any one of the above, and the experimental method comprises the following steps:

[0020] The first connecting member applies an external force, so that the spring is in a compressed state;

[0021] gradually increase the distance between the two second connecting members until the spring jumps;

[0022] respectively decrease and increase the distance between the two second connecting members.

[0023] collect the distance change between the two second connecting members and the position of the first connecting member, and obtain a distance-position curve of asymmetric fork bifurcation.

[0024] The hysteresis and bifurcation experiment device and experiment method in the application can be used for verifying the theory mentioned in the background art, and provide a basis for the application of hysteresis behavior in the non-circuit electronic field. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a structural schematic diagram of a V-shaped spring system in an embodiment of the application;

[0026] Figure 2 is a partial structural schematic diagram of a telescopic arm and a first connecting member in an embodiment of the application;

[0027] Figure 3 is a partial structural schematic diagram of a telescopic arm and a second connecting member in an embodiment of the application;

[0028] Figure 4 is a structural schematic diagram of a hysteresis and bifurcation experiment device in an embodiment of the application

[0029] In the drawings:

[0030] 1, V-shaped spring system; 11, telescopic arm; 111, sleeve; 112, first end cover; 113, second end cover; 12, spring; 13, first connecting member; 131, first rotating shaft; 132, first pad; 133, first limiting member; 134, first connecting rod; 135, second connecting rod; 14, second connecting member; 141, second rotating shaft; 142, second pad; 143, second limiting member; 144, third connecting rod; 2, distance adjusting mechanism; 21, screw rod; 22, stepping motor; 3, force applying mechanism; 31, connecting wire; 32, pulley; 33, water tank; 34, water containing groove; 4, controller; 5, displacement monitoring member. DETAILED DESCRIPTION

[0031] The application will be further described in detail below in combination with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the application, and not to limit the application. In addition, it should be noted that, in order to facilitate the description, only the parts related to the application are shown in the drawings, not all the structures.

[0032] In the description of the present application, unless otherwise explicitly specified and limited, the terms "connected", "connected", "fixed" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0033] In the present application, unless otherwise explicitly specified and limited, the first feature "on" or "under" the second feature can include that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, the first feature "on", "above" and "above" the second feature includes that the first feature is directly above and obliquely above the second feature, or only indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature "below", "below" and "below" the second feature includes that the first feature is directly below and obliquely below the second feature, or only indicates that the horizontal height of the first feature is less than that of the second feature.

[0034] In the description of the present embodiment, the terms "up", "down", "left", "right" and other orientation or position relationships are based on the orientation or position relationship shown in the drawings, and are only for the convenience of description and simplification of operation, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first" and "second" are only used to distinguish in description and have no special meaning.

[0035] Reference Figures 1-3 As shown in the drawings, the embodiment of the present application proposes a V-shaped spring system 1, which comprises a base and two telescopic arms 11, the lengths of the two telescopic arms 11 are the same, the first ends of the two telescopic arms 11 are connected to a first connecting piece 13, and at least one of the two telescopic arms 11 is rotatably connected to the first connecting piece 13 to realize the angle change between the two telescopic arms 11, the second ends of the two telescopic arms 11 are respectively connected to a second connecting piece 14, the telescopic arm 11 is rotatably connected to the base through the second connecting piece 14, and the spacing between the second connecting pieces 14 is adjustable, the first connecting piece 13 is movably arranged on the base along the vertical center line of the connecting line of the second end points of the two telescopic arms 11, and the spring 12 is sleeved on the telescopic arm 11, and the spring 12 can be synchronously telescoped with the telescopic arm 11.

[0036] The telescopic arm 11 in the V-shaped spring system 1 can make the spring 12 stretch and contract along the length direction of the telescopic arm 11, effectively solve the problem that the deformation direction of the spring 12 deviates from the axis of the spring 12 in the theoretical verification process, and thus improve the reliability of the theoretical verification. It can be understood that the V-shaped spring system can be used for teaching demonstration and can also be applied to mechanical switches such as water pressure and air pressure. When the pressure difference on both sides of the first connecting member 13 reaches a threshold value (the pressure difference on both sides is used as an external force applied to the first connecting member 13, and when the external force reaches the maximum elastic force of the spring 12), the state is automatically switched, which will not be described here.

[0037] Specifically, the telescopic arm 11 includes at least two sleeve 111 axially slidingly sleeved, and the number of the sleeve 111 can be adjusted according to the length of the spring 12 used, which is not specifically limited here. Taking any telescopic arm 11 including three sleeves 111 as an example, the three sleeves 111 are a first sleeve, a second sleeve and a third sleeve arranged in the first end to the second end direction of the telescopic arm 11 in sequence, the inner diameters of the first sleeve, the second sleeve and the third sleeve increase in sequence, and one end of the first sleeve connected with the second sleeve and one end of the second sleeve connected with the third sleeve are provided with a limiting part, the limiting part is limited to be movably arranged in the next sleeve (the limiting part of the first sleeve is arranged in the second sleeve, and the limiting part of the second sleeve is arranged in the third sleeve), so as to prevent the first sleeve and the second sleeve, and the second sleeve and the third sleeve from being separated when the telescopic arm 11 is elongated.

[0038] In order to make the spring 12 stretch and contract with the telescopic arm 11, and to facilitate the disassembly and assembly of the spring 12, in some embodiments, the telescopic arm 11 further includes a first end cover 112 and a second end cover 113, the first end cover 112 is arranged on the sleeve 111 closest to the first connecting member 13, and the second end cover 113 is arranged on the sleeve 111 closest to the second connecting member 14, the both ends of the spring 12 are limited between the first end cover 112 and the second end cover 113, and at least one of the first end cover 112 and the second end cover 113 is detachably connected with the sleeve 111. Exemplarily, the first end cover 112 and the second end cover 113 are both threadedly connected with the sleeve 111.

[0039] In other embodiments, the both ends of the spring 12 are fixedly connected to the both ends of the telescopic arm 11 in length.

[0040] Reference Figure 2As shown, the first connecting member 13 comprises a first rotating shaft 131, at least one of the two telescopic arms 11 is capable of rotating relative to the first rotating shaft 131. The first connecting member 13 further comprises a first connecting rod 134 and a second connecting rod 135 extending radially from the first rotating shaft 131, the outer diameter of the first connecting rod 134 and the second connecting rod 135 is smaller than the minimum outer diameter of the telescopic arm 11, one end of the first connecting rod 134 is sleeved on the first rotating shaft 131 and is rotationally connected with the first rotating shaft 131, the other end of the first connecting rod 134 is coaxially connected to the first end cover 112, one end of the second connecting rod 135 is fixedly connected with the first rotating shaft 131, and the other end of the second connecting rod 135 is coaxially connected to the other first end cover 112.

[0041] Similarly, referring to Figure 3 As shown, the second connecting member 14 comprises a second rotating shaft 141 and a third connecting rod 144 extending radially from the second rotating shaft 141, the outer diameter of the third connecting rod 144 is smaller than the minimum outer diameter of the telescopic arm 11, one end of the third connecting rod 144 is sleeved on the second rotating shaft 141 and is rotationally connected with the second rotating shaft 141, and the other end is coaxially connected with the second end cover 113.

[0042] The first connecting rod 134 and the second connecting rod 135 increase the distance between the first ends of the two telescopic arms 11, provide space for the mutual approach of the two springs 12, and can avoid geometric interference between the springs 12 sleeved on the telescopic arms 11 when the two telescopic arms 11 approach relative to rotation. It can be understood that the above-mentioned V-shaped spring 12 system is particularly suitable for springs 12 with large length and diameter, and the length of the first connecting rod 134 and the second connecting rod 135 is small, so the increase in the overall length of the V-shaped spring system 1 caused by the first connecting rod 134 and the second connecting rod 135 can be ignored, which is beneficial to improve the accuracy of theoretical verification.

[0043] Further, in order to guide the first connecting member 13 to move along the vertical center line of the second end points of the two telescopic arms 11, a sliding block or a roller is arranged at the bottom of the first connecting member 13, and a sliding groove or a sliding rail is correspondingly arranged on the base.

[0044] In order to prevent the spring 12 from rubbing against the base during movement, the spring 12 is spaced apart from the base. On this basis, the first connecting member 13 includes a first pad 132 arranged at the lower end of the first rotating shaft 131, a sliding block or a roller is arranged on the first pad 132, the first pad 132 is in contact with the base through the sliding block or the roller, the outer diameter of the first pad 132 is greater than the outer diameter of the first rotating shaft 131 and a first limiting step is formed between the first pad 132 and the first rotating shaft 131, the first limiting step limits the falling of the first connecting rod 134, and the sliding block or the roller cooperates to raise the first rotating shaft 131, the second connecting member 14 includes a second pad 142 arranged at the lower end of the second rotating shaft 141 and abutting against the base, the outer diameter of the second pad 142 is greater than the outer diameter of the second rotating shaft 141 and a second limiting step is formed between the second pad 142 and the second rotating shaft 141, the second limiting step limits the falling of the third connecting rod 144.

[0045] Referring to Figure 2 and Figure 3 In order to prevent the first connecting rod 134 from disengaging from the first rotating shaft 131 and the third connecting rod 144 from disengaging from the second rotating shaft 141, the first connecting member 13 further includes a first limiting member 133 fixed to the top end of the first rotating shaft 131, that is, the first limiting member 133 and the first pad 132 are arranged at the two axial ends of the first rotating shaft 131 respectively, the first connecting rod 134 is limited on the first rotating shaft 131 between the first pad 132 and the first limiting member 133, and the second connecting rod 135 is connected to the first rotating shaft 131 by connecting the first pad 132 or the first limiting member 133, the second connecting member 14 further includes a second limiting member 143 fixed to the top end of the second rotating shaft 141, that is, the second limiting member 143 and the second pad 142 are arranged at the two axial ends of the second rotating shaft 141 respectively, and the third connecting rod 144 is limited on the second rotating shaft 141 between the second pad 142 and the second limiting member 143. Exemplarily, the first limiting member 133 is threadedly connected with the first rotating shaft 131, and the second limiting member 143 is threadedly connected with the second rotating shaft 141.

[0046] In order to reduce the damping between the first connecting rod 134 and the first rotating shaft 131 and between the third connecting rod 144 and the second rotating shaft 141, the first connecting member 13 further includes a first bearing arranged between the first connecting rod 134 and the first rotating shaft 131, and the second connecting member 14 further includes a second bearing arranged between the third connecting rod 144 and the second rotating shaft 141.

[0047] Referring to Figure 4As shown, the embodiment of the present application also proposes a hysteresis and bifurcation experiment device for generating and recording saddle-node bifurcation and corresponding hysteresis loop for teaching demonstration or providing reference for applying the V-shaped spring system to engineering design related to water pressure and air pressure. The experiment device comprises the V-shaped spring system 1, further comprises a spacing adjustment mechanism 2, a force applying mechanism 3, a displacement monitoring member 5, a tension monitoring member and a controller 4, wherein the spacing adjustment mechanism 2 is used to adjust the spacing between the second end points of the two telescopic arms 11, the force applying mechanism 3 is used to apply force to the first connecting member 13 to move the first connecting member 13 in the direction of the vertical center line of the line connecting the second end points of the two telescopic arms 11, and the displacement monitoring member 5 is used to monitor the linear motion spacing of the first connecting member 13. The tension monitoring member is used to monitor the tension applied by the force applying mechanism 3 to the first connecting member 13. The controller 4 is in communication connection with the tension monitoring member and the displacement monitoring member 5, and the controller 4 comprises a data processing module, which is used to generate a hysteresis loop image (external force-position curve, where the external force refers to the tension applied by the force applying mechanism 3 to the first connecting member 13, and the position refers to the position of the first connecting member 13).

[0048] Specifically, the displacement monitoring member 5 can adopt a laser displacement sensor, and the tension monitoring member can adopt a tension sensor.

[0049] In some embodiments, the spacing adjustment mechanism 2 comprises a lead screw 21 and a nut, the lead screw 21 is provided with two opposite threads, the nut is sleeved on the lead screw 21 and is in threaded connection with the lead screw 21, and when the lead screw 21 rotates, the nut can move along the length direction of the lead screw 21. The nut is also provided with two nuts, and the two nuts are respectively connected with the corresponding second connecting members 14. In order to realize automatic adjustment of the spacing between the two second connecting members 14 and improve the accuracy of spacing adjustment, the spacing adjustment mechanism 2 further comprises a stepping motor 22 in communication connection with the controller 4, and the stepping motor 22 is connected to the lead screw 21 to drive the lead screw 21 to rotate.

[0050] Of course, the spacing adjustment mechanism 2 can also be provided with only one lead screw 21, and the threads at the two ends of the lead screw 21 are opposite, and two nuts are respectively sleeved on the two ends of the lead screw 21 with opposite threads and connected with the second connecting members 14.

[0051] Specifically, the force applying mechanism 3 is provided with two groups and is symmetrically arranged with the line connecting the second end points of the two telescopic arms 11 as the symmetry axis, and the force applying mechanism 3 comprises a counterweight, a connecting line 31 and a pulley 32. The counterweight is suspended below the base and connected with the first connecting member 13 through the connecting line 31, the connecting line 31 passes through the pulley 32 to adjust the force applying direction from the vertical direction to the horizontal direction, and by changing the weight of the counterweight, the size of the external force applied by the force applying mechanism 3 to the first connecting member 13 can be changed.

[0052] In some embodiments, the counterweight includes a water tank 34, and a flow monitoring device is arranged in the water tank 34 to monitor the water flow change. The magnitude of the external force applied to the first connecting member 13 can be changed by discharging water into or from the water tank 34.

[0053] In order to facilitate the water discharge into the water tank 34, the counterweight further includes a water tank 33 arranged above the water tank 34 through a support base. The water in the water tank 33 can flow into the water tank 34. The water tank 33 is also provided with a flow monitoring device. In addition, the water outlet of the water tank 33 is provided with an on-off valve, which is in communication connection with the controller 4. The controller 4 can open or close the on-off valve in time according to the feedback of the flow monitoring device.

[0054] When there is no tension, the spring 12 is in the original length state (assuming that the first connecting member 13 is located at the rear side of the line connecting the second end points of the two telescopic arms 11). When the water tank 33 located at the front side slowly injects water into the corresponding water tank 34, the external force provided by the connecting line 31 gradually increases, so that the spring 12 is gradually compressed. During this process, the elastic force of the spring 12 itself is upward and balances with the downward external force. Since the positions of the second end points of the two telescopic arms 11 are fixed, the V-shaped spring system 1 has two maximum force points in the direction perpendicular to the line connecting the second end points of the two telescopic arms 11. When the external force is less than the maximum force of the V-shaped spring system 1 at the rear side of the line, the spring 12 is slowly compressed as the tension increases. When the external force is equal to the maximum force of the V-shaped spring system 1 at the rear side of the line, the balance point of the spring 12 changes from stable balance to unstable balance, and the spring 12 jumps to the balance point at the front side corresponding to the external force value.

[0055] After the spring 12 reaches the balance point at the front side (at this time, the spring 12 is in the stretched state), the water in the water tank 34 is gradually discharged, and the tension provided by the connecting line 31 to the V-shaped spring system 1 decreases. When the water is discharged, the spring 12 is in the original length state (the first connecting member 13 is located at the front side of the line connecting the second end points of the two telescopic arms 11). At this time, the external force is reversely increased (i.e., the tension of the connecting line 31 is backward), and the spring 12 is gradually compressed. Similarly, when the external force is equal to the maximum force of the V-shaped spring system 1 at the front side of the line, the spring 12 jumps to the balance point at the rear side. This cycle is repeated. During this process, the three balance points become two balance points, and the saddle bifurcation occurs. At each moment, the position coordinates of the first connecting member 13 collected by the displacement monitoring device 5 and the external force data collected by the tension monitoring device are transmitted to the data processing module, so that the hysteresis loop image (external force-position curve) is obtained in real time. By adjusting the distance between the two second connecting members 14, different shapes of hysteresis loops can be obtained.

[0056] In other embodiments, the counterweight can also use multiple weights. The magnitude of the external force can be changed by increasing or decreasing the weights.

[0057] The embodiment of the present application also provides an experimental method, which is based on the above-mentioned hysteresis and bifurcation experimental device and used for studying symmetric fork bifurcation, and mainly comprises the following steps.

[0058] The initial interval of the two second connecting members 14 is L0, the original length of the spring 12 is S, 1 / 2L0>S, and the interval between the two second connecting members 14 is gradually reduced to L, 1 / 2L=S.

[0059] During the interval change of the two second connecting members 14, the interval change of the two second connecting members 14 and the position of the first connecting member 13 are collected, and the interval-position curve of the symmetric fork bifurcation is obtained through the data processing module. The interval refers to the interval of the two second connecting members 14, and the position refers to the position of the first connecting member 13.

[0060] When the external force applied to the V-shaped spring system 1 is equal to zero, if the interval of the two second connecting members 14 is greater than the original length of the spring 12 (at this time, the two springs 12 are in a stretched state when they are on the same straight line), the spring 12 has only one balance point when the axis of the spring 12 coincides with the above-mentioned connecting line. When the interval of the two second connecting members 14 is less than or equal to the original length of the spring 12 (the initial two springs 12 are in a compressed or original length state when they are on the same straight line), the spring 12 has two balance points (stable) symmetrically distributed on both sides of the connecting line in addition to the balance point (unstable) on the connecting line. In this way, as the interval of the two second connecting members 14 is continuously reduced to twice the original length of the spring 12, the spring 12 randomly jumps to one of the two stable balance points, which triggers the symmetric fork bifurcation of the V-shaped spring system 1 from one balance point to three balance points.

[0061] The embodiment of the present application also provides an experimental method, which is based on the above-mentioned hysteresis and bifurcation experimental device and used for studying symmetric fork bifurcation, and mainly comprises the following steps.

[0062] An external force is applied to the first connecting member 13, so that the spring 12 is in a compressed state.

[0063] Then the interval between the two second connecting members 14 is gradually increased until the spring 12 jumps.

[0064] The interval between the two second connecting members 14 is respectively reduced and increased.

[0065] During the interval change of the two second connecting members 14, the interval change of the two second connecting members 14 and the position of the first connecting member 13 are collected, and the interval-position curve of the symmetric fork bifurcation is obtained through the data processing module. The interval refers to the interval of the two second connecting members 14, and the position refers to the position of the first connecting member 13.

[0066] When the external force applied to the first connecting member 13 is not zero, the V-shaped spring system 1 is initially in a compressed state at the equilibrium point. Since the distance between the two second connecting members 14 is determined, the maximum resultant force of the V-shaped spring system 1 in the direction perpendicular to the connecting line of the end points of the two second ends of the telescopic arms 11 is unique, so when the distance between the two second connecting members 14 is increased to the corresponding value of the external force, the V-shaped spring system 1 will trigger asymmetric fork bifurcation, and the asymmetric fork bifurcation distance-position curve can be obtained in the data processing module. It should be noted that the V-shaped spring system 1 has an energy barrier at different equilibrium points, and once a mutation occurs, it will move along a new path, at this time no matter how to change the distance between the two second connecting members 14, the first connecting member 13 will not mutate to the opposite side again. If the V-shaped spring system 1 described above needs to depict a complete path curve, after the V-shaped spring system 1 jumps, the distance between the two second connecting members 14 should be respectively reduced and increased to verify the irreversibility of the equilibrium point path and the complete state of the V-shaped spring system 1 at the new path.

[0067] Obviously, the above embodiments of the present application are only examples for clear illustration of the present application, and are not intended to limit the embodiments of the present application. For those skilled in the art, various obvious changes, readjustments and substitutions can be made without departing from the scope of the present application. It is not necessary and impossible to enumerate all the embodiments. Any modification, equivalent substitution and improvement within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A V-type spring system, characterized in that, include: Base; Two telescopic arms (11) of the same length are provided. The first ends of both telescopic arms (11) are connected to a first connector (13), and at least one of the two telescopic arms (11) is rotatably connected to the first connector (13). The second ends of the two telescopic arms (11) are each connected to a second connector (14). The telescopic arms (11) are rotatably connected to the base through the second connectors (14). The spacing between the second connectors (14) is adjustable. The first connector (13) is movably disposed on the base along the vertical centerline of the line connecting the second ends of the two telescopic arms (11). Spring (12) is fitted on both of the telescopic arms (11), and the spring (12) can extend and retract together with the telescopic arms (11).

2. The V-shaped spring system according to claim 1, characterized in that, The telescopic arm (11) includes a first end cap (112), a second end cap (113), and at least two sleeves (111) that are axially movably sleeved together. The first end cap (112) is disposed on the sleeve (111) closest to the first connector (13), and the second end cap (113) is disposed on the sleeve (111) closest to the second connector (14). The two ends of the spring (12) are constrained between the first end cap (112) and the second end cap (113), and at least one of the first end cap (112) and the second end cap (113) is detachably connected to the sleeve (111).

3. The V-shaped spring system according to claim 1, characterized in that, The first connector (13) includes a first rotating shaft (131), a first connecting rod (134) and a second connecting rod (135) extending radially along the first rotating shaft (131). The outer diameters of the first connecting rod (134) and the second connecting rod (135) are both smaller than the minimum outer diameter of the telescopic arm (11). One end of the first connecting rod (134) is sleeved on the first rotating shaft (131) and rotatably connected to the first rotating shaft (131). The other end of the first connecting rod (134) is coaxially connected to one of the telescopic arms (11). One end of the second connecting rod (135) is connected to the first rotating shaft (131), and the other end of the second connecting rod (135) is coaxially connected to another telescopic arm (11).

4. The V-shaped spring system according to claim 1, characterized in that, The spring (12) is spaced apart from the base.

5. A hysteresis and bifurcation experimental apparatus, characterized in that, The system includes a V-shaped spring system (1) as described in any one of claims 1-4, and further includes a spacing adjustment mechanism (2), a force application mechanism (3), a displacement monitoring device (5), a tension monitoring device, and a controller (4). The spacing adjustment mechanism (2) is used to adjust the spacing between the two second connecting members (14). The force application mechanism (3) is used to apply a force to the first connecting member (13) in a direction perpendicular to the line connecting the second end points of the two telescopic arms (11). The displacement monitoring device (5) is used to monitor the linear motion spacing of the first connecting member (13). The tension monitoring device is used to monitor the tension applied to the first connecting member (13) by the force application mechanism (3). The controller (4) is communicatively connected to both the tension monitoring device and the displacement monitoring device (5). The controller (4) includes a data processing module, which is used to generate a hysteresis loop image.

6. The hysteresis and bifurcation experimental apparatus according to claim 5, characterized in that, The spacing adjustment mechanism (2) includes a lead screw (21) and a nut. The lead screw (21) is rotatable around its own axis. The nut is sleeved on the lead screw (21) and threadedly connected to the lead screw (21). The second connecting piece (14) is connected to the nut.

7. The hysteresis and bifurcation experimental apparatus according to claim 5, characterized in that, The force application mechanism (3) is provided in two sets and is symmetrically arranged with the line connecting the two second connecting parts (14) as the axis of symmetry. The force application mechanism (3) includes a counterweight, a connecting line (31) and a pulley (32). The counterweight is suspended below the base and connected to the first connecting part (13) through the connecting line (31). The connecting line (31) is reversed through the pulley (32).

8. The hysteresis and bifurcation experimental apparatus according to claim 5, characterized in that, The counterweight includes a water tank (34) and a water tank (33). A flow monitoring device is installed in the water tank (34). The water tank (33) is located above the water tank (34). Water in the water tank (33) can flow into the water tank (34). A flow monitoring device is installed in the water tank (33).

9. The experimental method, characterized in that, The experiment is conducted using the hysteresis and bifurcation experimental apparatus according to any one of claims 5-8, and the experimental method includes the following steps: Let the initial distance between the two second connecting parts (14) be L0, and the original length of the spring (12) be S. 1 / 2 L0>S. Gradually reduce the distance between the two second connecting parts (14) to L, 1 / 2L≤S; The spacing changes of the two second connectors (14) and the position of the first connector (13) are collected to obtain a symmetrically bifurcated spacing-position curve.

10. The experimental method, characterized in that, The experiment is conducted using the hysteresis and bifurcation experimental apparatus according to any one of claims 5-8, and the experimental method includes the following steps: An external force is applied to the first connector (13) to compress the spring (12); Gradually increase the distance between the two second connectors (14) until the spring (12) jumps; Decrease and increase the distance between the two second connectors (14) respectively; The spacing change between the two second connectors (14) and the position of the first connector (13) are collected to obtain a spacing-position curve with an asymmetrical forked shape.

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