A cross-board shock wave directional switch structure and its design method

Abstract

The present invention discloses a structure of an interboard shock wave directional switch, which is formed by arranging bistable superstructure units in an array along the X direction and the Y direction. The bistable superstructure unit includes four diagonal elastic members distributed in a diamond shape and connected end to end. A set of opposite nodes of the diamond structure are arranged along the Y direction, and a vertical elastic member extends outward from each of them. The other set of opposite nodes of the diamond structure are arranged along the X direction, and the two nodes are connected by an internal horizontal elastic member. The present invention also proposes a design method for the structure of the interboard shock wave directional switch, including selecting appropriate elastic stiffnesses K1, K2, and K3, determining the multi-energy barrier potential response and the equilibrium strain sites, determining the dynamic differential equation and the initial boundary conditions of the bistable discrete system, determining the implicit dynamic response law and the continuous dynamic equation of the bistable discrete system, and determining the explicit change law of the shock wave during propagation, so as to effectively achieve the directional conduction or blocking of shock waves with different energies.

Description

Technical Field

[0001] The invention relates to the technical field of underwater impact structure anti-impact, in particular to a shipboard shock wave directional switch structure under underwater impact and a design method thereof. Background Art

[0002] At present, the impact resistance of ship and marine engineering structures mainly relies on traditional means such as plastic energy absorption. Although these methods can absorb impact energy to a certain extent, their impact resistance is limited, and the structure cannot be reused after being impacted, which greatly limits its application scope and efficiency. Based on this background, bistable dynamic mechanical metamaterials have been proposed. Bistable dynamic mechanical metamaterials refer to periodic metastructures with negative stiffness characteristics but stable states that can change. Bistable dynamic mechanical metamaterials can not only automatically restore their shape after being impacted for reuse, but also accurately control the amplitude, phase and energy distribution of waves. However, most existing bistable dynamic mechanical metamaterials do not have the function of directional conduction or blocking of shock waves. Summary of the invention

[0003] The main purpose of the present invention is to provide a shipboard shock wave directional switch structure and a design method thereof. Through the design of a bistable metamaterial structure, the directional conduction or blocking of shipboard shock waves can be achieved, and it can automatically recover after being impacted and can be reused.

[0004] The technical solution adopted by the present invention is:

[0005] A directional switch structure for shock waves between ships, which is formed by arrays of bistable superstructure units along the X direction and the Y direction, wherein the Y direction is radial and the X direction is circumferential, and the bistable superstructure units include four oblique elastic members distributed in a rhombus and connected end to end, a group of nodes opposite to the rhombus structure are arranged along the Y direction, and each of them has a vertical elastic member extending outward, and another group of nodes opposite to the rhombus structure are arranged along the X direction, and the two nodes are connected by an internal transverse elastic member; the elastic stiffness of the oblique elastic member is K2 and the length is l2, the elastic stiffness of the vertical elastic member is K1 and the length is l1, and the elastic stiffness of the transverse elastic member is K3 and the length is l3. The elastic stiffness K1, K2, and K3 of the three types of elastic members in the directional switch structure for shock waves between ships can be reasonably designed to enable it to have the function of directional blocking or conducting shock waves.

[0006] In order to make the above-designed inter-ship shock wave directional switch structure have the required blocking or conducting function for shock waves of different energies, the present invention also proposes a design method for the inter-ship shock wave directional switch structure, comprising the following steps:

[0007] S1. According to the impact dynamics and bistable structure theory, the stress-strain response of the bistable superstructure unit under quasi-static compression load is calculated, and the elastic stiffness K1, K2, and K3 of the vertical elastic member, the transverse elastic member, and the oblique elastic member are selected appropriately, so that the inter-ship shock wave directional switch structure has a barrier response of multiple energy sites;

[0008] S2. For the above-mentioned inter-ship shock wave directional switch structure with potential barrier response of multiple energy sites, determine the minimum and maximum extreme points in the relationship between potential energy and strain of its bistable superstructure unit, and determine the higher energy potential energy equilibrium point and the lower energy potential energy equilibrium point of static equilibrium strain; on this basis, select a group of bistable superstructure units with a large energy barrier difference, and determine their equilibrium strain points;

[0009] S3. According to the energy barrier difference and equilibrium strain site of the bistable superstructure unit, the dynamic differential equation and initial boundary conditions of the bistable discrete system are established by discrete method, and the fourth-order Runge-Kutta method is used to solve the dynamic equilibrium position of the bistable discrete system and the potential barrier implicit dynamic response law of multiple energy sites.

[0010] S4. According to the dynamic equilibrium position of the bistable discrete system and the implicit dynamic response law of the potential barrier at multiple energy sites, two continuity boundary condition functions are introduced to interpolate the discrete boundaries, and the dynamic differential equation of the bistable discrete system is continuousized by using Taylor series to obtain the continuity dynamic equation of the bistable discrete system. The traveling wave method is used to solve the continuity dynamic equation, and the explicit change law of displacement, velocity and time of the shock wave during propagation is analyzed.

[0011] S5. According to the explicit change rules of displacement, velocity and time of shock waves during propagation, the necessary conditions for directional conduction and blocking of shock waves are clarified: the initial boundary conditions are adjusted. When all bistable superstructure units are at high energy sites at the initial moment, the directional switch structure of shock waves between the two sides will support unidirectional propagation of shock waves and will not cause loss of shock waves during propagation, thereby achieving directional conduction of shock waves between the two sides; when all bistable superstructure units are at low energy sites at the initial moment, the directional switch structure of shock waves between the two sides will not support unidirectional propagation of shock waves, and the propagation process will consume shock wave energy, thereby achieving directional blocking of shock waves between the two sides;

[0012] S6. According to the necessary conditions for directional conduction and blocking of the inter-board shock wave, the elastic stiffness K in the inter-board shock wave directional switch structure is adjusted. 1、 K 2、 K3, realizes effective directional conduction or blocking of shock waves of different energies.

[0013] In the above scheme, in step S1, the method for calculating the stress-strain response of the bistable superstructure unit under the quasi-static compression load is:

[0014] According to the impact dynamics and bistable structure theory, for a bistable superstructure unit, it includes three types of elastic stiffness K 1、 K 2、 K3, the total potential energy of the bistable superstructure unit includes the elastic potential energy of the elastic part and the external force work:

[0015]

[0016] Where U NN is the total potential energy of the bistable superstructure unit, the elastic stiffness of the vertical elastic member is K1, the length is l1, the elastic stiffness of the oblique elastic member is K2, the length is l2, the elastic stiffness of the horizontal elastic member is K3, the length is l3, F x and F y are the constraints in the horizontal and vertical directions, U x To apply the horizontal constraint force F x The displacement under y To apply the vertical constraint force F y displacement below;

[0017] According to the principle of minimum potential energy, the horizontal constraint force F x and the vertical constraint force F y Size:

[0018]

[0019]

[0020] When F x = 0, the process of solving formulas (2) and (3) can obtain the load-displacement response of the bistable superstructure unit, and the stress-strain curve of the bistable superstructure unit can be obtained by normalizing the load-displacement.

[0021] In the above scheme, the inter-ship shock wave directional switch structure has a barrier response of multiple energy sites, which means that appropriate K1, K2, and K3 are selected so that the stress-strain curve of the bistable superstructure unit is consistent with F y / (K2*l2)=0 has multiple minimum points at the intersection.

[0022] In the above scheme, in step S2, the method for determining the higher energy potential equilibrium point and the lower energy potential equilibrium point of the static equilibrium strain is:

[0023] Integrating the stress-strain curve calculated in S1 gives the relationship between total potential energy and strain:

[0024] U NN =∫σ y dε y (4)

[0025] In the formula, σ y is the normal stress in the y direction, ε y is the normal strain in the y direction, U NN is the total potential energy of the bistable superstructure unit;

[0026] The first-order derivative is obtained by differentiating equation (4), and the second-order derivative is used to determine whether the point is a maximum or minimum point.

[0027]

[0028]

[0029] According to equations (5) and (6), the equilibrium point with higher energy potential is ε A , with a lower energy potential equilibrium site of ε B .

[0030] In the above scheme, step S3 specifically includes the following steps:

[0031] For a bistable discrete system composed of N bistable superstructure units with energy barrier difference, its Lagrangian function is:

[0032] L=TU (7)

[0033]

[0034] Where L is the Lagrangian function, T is the kinetic energy of the bistable discrete system, U is the total potential energy of the bistable discrete system, m is the mass of the bistable superstructure unit, and u is j is the vertical displacement of the jth bistable superstructure unit, ε j is the equivalent strain of the jth bistable superstructure unit, ε j-1 is the equivalent strain of the j-1th bistable superstructure unit, U NN is the total potential energy of the bistable superstructure unit, U NNS (ε j -ε j-1 ) is the potential energy effect of the adjacent j-1th bistable superstructure unit on the jth bistable superstructure unit, N is the number of bistable superstructure units in the bistable discrete system, and t represents any time;

[0035] Substituting (7) and (8) into the Lagrangian dynamics equation of the particle system, we can obtain the dynamic differential equation (9) of the bistable discrete system:

[0036]

[0037] In the formula, f NN (ε j+1 ) represents the external force of the j+1th bistable superstructure unit, f NN (ε j ) represents the external force of the jth bistable superstructure unit, f NNS (ε j -ε j-1 ) represents the internal force between the jth bistable superstructure unit and the j-1th bistable superstructure unit, f NNS (ε j+1 -ε j ) represents the internal force between the j+1th bistable superstructure unit and the jth bistable superstructure unit, f NNS (ε j+2 -ε j+1 ) represents the internal force between the j+2th bistable superstructure unit and the j+1th bistable superstructure unit;

[0038] And there is U NN (ε j ) and U NN (ε j+1 ) are the total potential energies of the jth and j+1th bistable superstructure units, ε j and ε j+1 are the strains of the jth and j+1th bistable superstructure units, respectively, U NNS (ε j -ε j-1 ) is the potential energy effect of the adjacent j-1th bistable superstructure unit on the jth bistable superstructure unit, U NNS (ε j+1 -ε j ) is the potential energy effect of the adjacent j-th bistable superstructure unit on the j+1-th bistable superstructure unit, U NNS (ε j+2 -ε j+1 ) is the potential energy effect of the adjacent j+1th bistable superstructure unit on the j+2th bistable superstructure unit;

[0039] For the jth bistable superstructure unit, its total potential energy is assumed to be the following explicit expression:

[0040]

[0041] Where U NN (ε j ) is the total potential energy of the jth bistable superstructure unit, ε jIt is expressed as the strain of the jth bistable superstructure unit, and its calculation formula is (11), B1, B2, B3 are the coefficients related to the elastic stiffness of the bistable superstructure unit, and U is obtained by solving equations (1) to (5): NN Size determines;

[0042]

[0043] Where a is the distance between adjacent bistable superstructure units, u j-1 is the vertical displacement of the j-1th bistable superstructure unit;

[0044] For the jth bistable superstructure unit, the potential energy provided by its adjacent structure is:

[0045]

[0046] Where G is a constant, greater than 0, and depends on the inherent properties of the system, ε j is expressed as the strain of the jth bistable superstructure unit, ε j-1 Expressed as the strain of the j-1th bistable superstructure unit;

[0047] For the shock wave input in the between-ship structure, the initial boundary conditions are assumed to be:

[0048]

[0049] In the formula, ε A For sites with higher energy potential equilibrium, ε B is a site with lower energy potential equilibrium; Formula (13) indicates that after the impact excitation is applied, the first 10 bistable superstructure units are in state B, and the following bistable superstructure units are still in state A because they are not affected by the impact;

[0050] By combining equations (7) to (12) and the initial boundary condition (13), the fourth-order Runge-Kutta method can be used to solve the dynamic equilibrium position of the bistable discrete system composed of N bistable superstructure units and the potential barrier implicit dynamic response law of multiple energy sites.

[0051] In the above scheme, in step S4, the method for obtaining the continuity dynamic equation of the bistable discrete system is:

[0052] First, two continuous boundary condition functions are introduced to interpolate the discrete boundaries to obtain equations (14) and (15):

[0053] ε(x=x j ,t)=ε j (t) (14)

[0054]

[0055] In the formula, ε j (t) represents the strain continuity boundary condition of the bistable discrete system, u j (t) represents the displacement continuity boundary condition of the bistable discrete system, t is any time, a is the distance between adjacent bistable superstructure units, x represents the position of any point in the ring, x j represents the position of the jth bistable superstructure unit, ε(x=x j ,t) represents the strain at the position of the jth bistable superstructure unit at any time t, represents the displacement from the position a / 2 of the jth bistable superstructure unit at any time t;

[0056] For the dynamic differential equation (9) of the bistable discrete system in ε j Taylor expansion is done to get:

[0057]

[0058] In the formula, f(ε j+1 ,t) and f(ε j-1 , t) represent the external forces of the j+1th bistable superstructure unit and the j-1th bistable superstructure unit on the jth bistable superstructure unit at any time, f'(ε j )、f”(ε j )、f”'(ε j )、f””(ε j ) respectively represent the case where x = ε j The first, second, third and fourth derivatives at j ) represents the external force of the jth bistable superstructure unit, and o represents a high-order infinitesimal;

[0059] Substituting (16) into (9), the continuous dynamic equation of the bistable discrete system is obtained as follows:

[0060]

[0061] Where m is the mass of the bistable superstructure unit, ε is the strain of the bistable discrete system, and f xx represents the second-order derivative of the external force f with respect to x, f xxxx represents the fourth-order derivative of the external force f with respect to x, G is a constant inherent to the system, greater than 0, ε xxxx represents the fourth-order derivative of strain with respect to x of the bistable discrete system;

[0062] When Gε>>af NNWhen , the shock wave propagation in the bistable discrete system is similar to the bending wave propagation phenomenon in a one-dimensional beam, and the continuity dynamic equation can be simplified to:

[0063]

[0064] In the above scheme, in step S4, the explicit variation law of displacement and time of the bistable discrete system during the propagation of the shock wave is analyzed as follows:

[0065]

[0066] Where u(x,t) represents the displacement of the bistable discrete system at any position x and any time t, c r is the propagation speed of the rarefaction front, c is the velocity pulse, is a dynamic equilibrium site with higher energy potential, ε B is the potential equilibrium site with lower energy, t is any time, t0 is the initial time of emitting the velocity pulse, and N is the number of bistable superstructure units in the bistable discrete system.

[0067] In the above scheme, in step S4, the explicit variation law of the speed and time of the bistable discrete system during the propagation of the shock wave is analyzed as follows:

[0068]

[0069] Where v(x, t) represents the velocity of the bistable discrete system at any position x and any time t, and W is determined by equation (32):

[0070]

[0071] Where a is the distance between adjacent bistable superstructure units, G is a constant inherent to the system, which is greater than 0, and B1, B2, and B3 are coefficients related to the bistable superstructure unit and the elastic stiffness.

[0072] The beneficial effects produced by the present invention are:

[0073] The structural design of the present invention can be achieved by adjusting the initial boundary conditions and the elastic stiffness K in the directional switch structure of the inter-ship shock wave. 1、 K 2、 K3, realizes effective directional conduction or blocking of shock waves of different energies, solves the problem of shock resistance and wave control in the field of shipbuilding and marine engineering, and improves the safety and reliability of shipbuilding and marine engineering structures in dynamic environments. The present invention utilizes the structural characteristics of bistable metamaterials, and by adjusting the initial boundary conditions of the bistable discrete system, it can adjust the response of the inter-ship structure under different dynamic loading conditions, and enhance the adaptability and stability of the structure to nonlinear dynamic influences.

[0074] At the same time, the inter-board shock wave directional switch structure designed based on the bistable metamaterial structure of the present invention can restore to its original state after being impacted. Through the phase change transformation in the inter-board shock wave directional switch structure, the structure can be reused, thereby greatly improving the utilization efficiency and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0076] Figure 1 It is a schematic diagram of the structure of the cross-board shock wave directional switch of the present invention;

[0077] Figure 2 It is an implementation flow chart of the design method of the inter-ship shock wave directional switch structure of the present invention;

[0078] Figure 3 is a normalized stress-strain response diagram of the bistable superstructure unit in theory and simulation according to an embodiment of the present invention;

[0079] Figure 4 is a normalized energy-strain relationship diagram of a bistable superstructure unit in an embodiment of the present invention;

[0080] Figure 5 is a schematic diagram of a bistable discrete system composed of N bistable super-structure units in an embodiment of the present invention;

[0081] Figure 6 is the potential barrier implicit dynamic response law of multiple energy sites of the bistable discrete system in the embodiment of the present invention;

[0082] Figure 7 is the potential barrier implicit dynamic response law of multiple energy sites of the bistable discrete system in the embodiment of the present invention;

[0083] Figure 8 It is the mechanical mechanism for realizing the directional switch of the inter-ship shock wave in the embodiment of the present invention. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0085] It should be noted that the illustrations provided in the embodiments of the present invention are only used to illustrate the basic concept of the present invention in a schematic manner. Therefore, the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout type may also be more complicated.

[0086] In the present invention, it is also necessary to explain that, if the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. In addition, if the terms "first" and "second" appear, they are only used for description and distinction purposes, and cannot be understood as indicating or implying relative importance.

[0087] like Figure 1 As shown, the present invention proposes a directional switch structure for shock waves between ships, which is formed by an array of bistable superstructure units along the X direction and the Y direction, wherein the Y direction is radial and the X direction is circumferential. The bistable superstructure unit includes four oblique elastic members distributed in a rhombus shape and connected end to end, wherein the elastic stiffness of the oblique elastic members is K2 and the length is l2; a group of nodes opposite to the rhombus structure are arranged along the Y direction, and each of them extends outward with a vertical elastic member, wherein the elastic stiffness of the vertical elastic member is K1 and the length is l1; another group of nodes opposite to the rhombus structure are arranged along the X direction, and the two nodes are connected by an internal transverse elastic member, wherein the elastic stiffness of the transverse elastic member is K3 and the length is l3. The elastic stiffness K1, K2, and K3 of the three types of elastic members in the directional switch structure for shock waves between ships can be reasonably designed to enable it to have the function of directional blocking or conducting shock waves.

[0088] It should be noted that the oblique elastic member, the vertical elastic member, and the transverse elastic member may be conventional mechanical springs, or any material or structure having the same elastic stiffness K1, K2, K3.

[0089] In order to make the above-designed inter-ship shock wave directional switch structure have the required blocking or conducting function for shock waves of different energies, the present invention also proposes a design method for the inter-ship shock wave directional switch structure, see Figure 2 , including the following steps:

[0090] S1. According to the theory of impact dynamics and bistable structure, the stress-strain response of the bistable superstructure unit under quasi-static compression load is calculated, and the elastic stiffness K1, K2, and K3 of the vertical elastic parts, transverse elastic parts, and oblique elastic parts are selected appropriately, so that the inter-ship shock wave directional switch structure has a barrier response with multiple energy sites.

[0091] Specifically, the method for calculating the stress-strain response of the bistable superstructure unit under quasi-static compression load is as follows.

[0092] According to the impact dynamics and bistable structure theory, for a bistable superstructure unit, it includes three types of elastic stiffness K 1、 K 2、 K3, the total potential energy of the bistable superstructure unit includes the elastic potential energy of the elastic part and the external force work:

[0093]

[0094] Where U NN is the total potential energy of the bistable superstructure unit, the elastic stiffness of the vertical elastic member is K1, the length is l1, the elastic stiffness of the oblique elastic member is K2, the length is l2, the elastic stiffness of the horizontal elastic member is K3, the length is l3, F x and F y are the constraints in the horizontal and vertical directions, U x To apply the horizontal constraint force F x The displacement under y To apply the vertical constraint force F y The displacement below.

[0095] According to the principle of minimum potential energy, the horizontal constraint force F x and the vertical constraint force F y Size:

[0096]

[0097]

[0098] When F x = 0, the process of solving formulas (2) and (3) can obtain the load-displacement response of the bistable superstructure unit, and the stress-strain curve of the bistable superstructure unit can be obtained by normalizing the load-displacement.

[0099] The directional switch structure of the inter-ship shock wave has a barrier response of multiple energy sites, which means that the stress-strain curve of the bistable superstructure unit is consistent with F by selecting appropriate K1, K2, and K3. y / (K2*l2)=0 has multiple minimum points at the intersection.

[0100] In this embodiment, Figure 3 The relationship between the normalized stress and strain of the bistable superstructure unit when K1 is changed is given when specific parameters (l1 = 50mm, K2 = 200N / m, l2 / l1 = 1.4, l3 / l1 = 2, K3 / K2 = 1.5) are selected in the theoretical and simulation cases. In order to ensure the reliability of the theoretical model, finite element modeling and verification were carried out. The simulation software used ABAQUS for finite element modeling, and the theoretical solution used python theoretical numerical solution. The results show that the theoretical model can accurately capture the deformation law of the bistable superstructure unit. It is worth noting that the multi-energy site here refers to the curve and F y / (K2*l2)=0 intersects to make the energy barrier potential reach the minimum point.

[0101] S2. For the above-mentioned inter-ship shock wave directional switch structure with potential barrier response and multiple energy sites, determine the minimum and maximum extreme points in the relationship between potential energy and strain of its bistable superstructure unit, and determine the higher energy potential energy equilibrium site and the lower energy potential energy equilibrium site of the static equilibrium strain; on this basis, select a group of bistable superstructure units with a large energy barrier difference, and determine their equilibrium strain sites.

[0102] The method for determining the higher energy potential equilibrium site and the lower energy potential equilibrium site of the static equilibrium strain is as follows.

[0103] The stress-strain curve of the bistable superstructure unit calculated in S1 is integrated to obtain the relationship between the total potential energy and the strain:

[0104] U NN =∫σ y dε y (4)

[0105] Where σ y is the normal stress in the y direction, ε y is the normal strain in the y direction, U NN is the total potential energy of the bistable superstructure unit.

[0106] On this basis, the first-order derivative is obtained by differentiating equation (4), and the point is judged to be a maximum point or a minimum point according to its second-order derivative;

[0107]

[0108]

[0109] According to equations (5) and (6), the equilibrium point with higher energy potential is ε A , with a lower energy potential equilibrium site of ε B .

[0110] In this embodiment, according to Figure 3 The stress-strain curve of the bistable superstructure unit in the equation (4) to (6) can be solved as follows: Figure 4 The normalized energy-strain relationship of the bistable superstructure unit is shown, and the higher energy potential equilibrium site and the lower energy potential equilibrium site are determined as follows: ε A = -0.181 and ε B = 0. It is worth noting that Figure 4 An illustration of the energy barrier potential difference is given in FIG. 1 , which represents the normalized energy difference at the minimum value in the normalized energy versus strain curve.

[0111] S3. According to the energy barrier difference and equilibrium strain site of the bistable superstructure unit, the dynamic differential equation and initial boundary conditions of the bistable discrete system are established by discrete method, and the fourth-order Runge-Kutta method is used to solve the dynamic equilibrium position of the bistable discrete system and the potential barrier implicit dynamic response law of multiple energy sites. The specific method is as follows:

[0112] For a bistable discrete system composed of N bistable superstructure units with energy barrier difference, its Lagrangian function is:

[0113] L=TU (7)

[0114]

[0115] Where L is the Lagrangian function, T is the kinetic energy of the bistable discrete system, U is the total potential energy of the bistable discrete system, m is the mass of the bistable superstructure unit, and u is j is the vertical displacement of the jth bistable superstructure unit, ε j is the equivalent strain of the jth bistable superstructure unit, ε j-1 is the equivalent strain of the j-1th bistable superstructure unit, U NN is the total potential energy of the bistable superstructure unit, U NNS (ε j -ε j-1 ) is the potential energy effect of the adjacent j-1th bistable superstructure unit on the jth bistable superstructure unit, N is the number of bistable superstructure units in the bistable discrete system, and t represents any time.

[0116] Substituting (7) and (8) into the Lagrangian dynamics equation of the particle system, we can obtain the dynamic differential equation (9) of the bistable discrete system:

[0117]

[0118] In the formula, f NN (ε j+1) represents the external force of the j+1th bistable superstructure unit, f NN (ε j ) represents the external force of the jth bistable superstructure unit, f NNS (ε j -ε j-1 ) represents the internal force between the jth bistable superstructure unit and the j-1th bistable superstructure unit, f NNS (ε j+1 -ε j ) represents the internal force between the j+1th bistable superstructure unit and the jth bistable superstructure unit, f NNS (ε j+2 -ε j+1 ) represents the internal force between the j+2th bistable superstructure unit and the j+1th bistable superstructure unit;

[0119] And there is U NN (ε j ) and U NN (ε j+1 ) are the total potential energies of the jth and j+1th bistable superstructure units, ε j and ε j+1 are the strains of the jth and j+1th bistable superstructure units, respectively, U NNS (ε j -ε j-1 ) is the potential energy effect of the adjacent j-1th bistable superstructure unit on the jth bistable superstructure unit, U NNS (ε j+1 -ε j ) is the potential energy effect of the adjacent j-th bistable superstructure unit on the j+1-th bistable superstructure unit, U NNS (ε j+2 -ε j+1 ) is the potential energy effect of the adjacent j+1th bistable superstructure unit on the j+2th bistable superstructure unit.

[0120] For the jth bistable superstructure unit, its total potential energy can be assumed to be the following explicit expression:

[0121]

[0122] Where U NN (ε j ) is the total potential energy of the jth bistable superstructure unit, ε j It is expressed as the strain of the jth bistable superstructure unit, and its calculation formula is (11), B1, B2, B3 are the coefficients related to the elastic stiffness of the bistable superstructure unit, and U is obtained by solving equations (1) to (5):NN Size determines;

[0123]

[0124] Where a is the distance between adjacent bistable superstructure units, u j-1 is the vertical displacement of the j-1th bistable superstructure unit.

[0125] For the jth bistable superstructure unit, the potential energy provided by its adjacent structure is:

[0126]

[0127] Where G is a constant, greater than 0, and depends on the inherent properties of the system, ε j is expressed as the strain of the jth bistable superstructure unit, ε j-1 Expressed as the strain of the j-1th bistable superstructure unit.

[0128] For the shock wave input in the between-ship structure, the initial boundary conditions are assumed to be:

[0129]

[0130] In the formula, ε A For sites with higher energy potential equilibrium, ε B is a site with lower energy potential equilibrium; Formula (13) indicates that after the impact excitation is applied, the first 10 bistable superstructure units are in state B, and the following bistable superstructure units are still in state A because they are not affected by the impact;

[0131] By combining equations (7) to (12) and the initial boundary condition (13), the fourth-order Runge-Kutta method can be used to solve the dynamic equilibrium position of the bistable discrete system composed of N bistable superstructure units and the potential barrier implicit dynamic response law of multiple energy sites.

[0132] In this embodiment, the bistable discrete system composed of N bistable superstructure units is as follows: Figure 5 As shown, steps S1-S3 are used to solve ε A = -0.181 and ε B = 0, and the specific parameters in the implementation of the dynamic response case are: B1 = 1J, B2 = 20J, B3 = 80J, G = 1J, N = 2500, m = 10g. Substituting the above parameters into equations (7) to (13), the following is obtained by numerically solving with Python: Figure 6The implicit dynamic response law of the potential barrier of the multi-energy site of the bistable discrete system shown in the figure shows that the shock wave will make the structure in a three-phase state during the propagation of the bistable discrete system. In the first 2 seconds, about 250 bistable superstructure units are in the B phase (conduction state), and about 1500 bistable superstructure units are in the transition process from the B phase to the A phase, that is, the A* phase (transition state), indicating that the shock wave is traversing the bistable discrete system in a directional manner, and about 250 are in the A phase (blocking state), indicating that the shock wave has not reached the tail of the bistable discrete system. It is worth noting that the phase change here refers to the transformation of the equilibrium site, and the transformation process will conduct energy or block energy.

[0133] S4. According to the dynamic equilibrium position of the bistable discrete system and the implicit dynamic response law of the potential barrier at multiple energy sites, two continuity boundary condition functions are introduced to interpolate the discrete boundaries, and the dynamic differential equation of the bistable discrete system is continuousized by using Taylor series to obtain the continuity dynamic equation of the bistable discrete system. The traveling wave method is used to solve the continuity dynamic equation, and the explicit change law of displacement, velocity and time of the shock wave during propagation is analyzed. The specific method is as follows:

[0134] First, two continuous boundary condition functions are introduced to interpolate the discrete boundaries to obtain equations (14) and (15):

[0135] ε(x=x j ,t)=ε j (t) (14)

[0136]

[0137] In the formula, ε j (t) represents the strain continuity boundary condition of the bistable discrete system, u j (t) represents the displacement continuity boundary condition of the bistable discrete system, t is any time, a is the distance between adjacent bistable superstructure units, x represents the position of any point in the ring, x j represents the position of the jth bistable superstructure unit, ε(x=x j ,t) represents the strain at the position of the jth bistable superstructure unit at any time t, represents the displacement from the position a / 2 of the jth bistable superstructure unit at any time t.

[0138] For the dynamic differential equation (9) of the bistable discrete system in ε j Taylor expansion is done to get:

[0139]

[0140] In the formula, f(εj+1 ,t) and f(ε j-1 , t) represent the external forces of the j+1th bistable superstructure unit and the j-1th bistable superstructure unit on the jth bistable superstructure unit at any time, f'(ε j )、f”(ε j )、f”'(ε j )、f””(ε j ) respectively represent the case where x = ε j The first, second, third and fourth derivatives at j ) represents the external force of the jth bistable superstructure unit, and o represents a high-order infinitesimal.

[0141] Substituting (16) into (9), the continuous dynamic equation of the bistable discrete system is obtained as follows:

[0142]

[0143] Where m is the mass of the bistable superstructure unit, ε is the strain of the bistable discrete system, and f xx represents the second-order derivative of the external force f with respect to x, f xxxx represents the fourth-order derivative of the external force f with respect to x, G is a constant inherent to the system, greater than 0, ε xxxx represents the fourth-order derivative of strain with respect to x of the bistable discrete system;

[0144] When Gε>>af NN When , the shock wave propagation in the bistable discrete system is similar to the bending wave propagation phenomenon in a one-dimensional beam, and the continuity dynamic equation can be simplified to:

[0145]

[0146] The traveling wave method is used to solve the continuity dynamic equation, and ζ = x-ct, where c is the velocity pulse. Substituting it into equation (18) yields:

[0147]

[0148] In the formula, f represents the external force;

[0149] Integrating ζ in equation (19) twice yields:

[0150]

[0151] In the formula, C1 and C2 are integral constants. Since the energy barrier potential changes from state B to state A during the propagation of the shock wave, the boundary condition is:

[0152] ε(ζ→∞)=ε B (twenty one)

[0153] Formula (21) indicates that when ζ = x-ct tends to infinity, the strain of the bistable discrete system is equal to ε B .

[0154] Combining equations (20) and (21) we get:

[0155]

[0156] Where U NN Expressed as the total potential energy of the bistable superstructure unit.

[0157] The pseudo potential energy of the bistable discrete system can be calculated from formula (22):

[0158]

[0159] From formula (23), we can get: The necessary and sufficient conditions for the directional conduction shock wave of the bistable discrete system are:

[0160]

[0161]

[0162] Where V pseudo represents the pseudo potential energy of the bistable discrete system, A* is the dynamic equilibrium position of point A, Indicates the dynamic equilibrium site with higher energy potential, ε B Indicates a potential equilibrium site with lower energy.

[0163] Combining equations (8), (23) to (25) yields:

[0164]

[0165]

[0166] Combining (26) and (27) we can obtain:

[0167]

[0168]

[0169] Substituting equations (28) and (29) into (20) and then into the initial boundary conditions (13) to simplify, we obtain:

[0170]

[0171] Integrating equation (30) and substituting it into the initial boundary condition (13) yields:

[0172]

[0173] Where W is determined by formula (32):

[0174]

[0175] Integrating formula (32) yields:

[0176]

[0177] Where u(x, t) is the displacement of the bistable discrete system at any position x and any time t, and C4 is the rigid body motion displacement.

[0178] Substituting the displacement boundary condition u(c r (t-t0), t) = 0, and C4 is calculated as:

[0179]

[0180] Where c is the speed pulse, c r is the propagation speed of the sparse front, which is determined by (35):

[0181]

[0182] Combining (33) to (35) and Taylor expansion, the displacement equation of the bistable discrete system is:

[0183]

[0184] Where u(x,t) represents the displacement of the bistable discrete system at any position x and any time t, c r is the propagation speed of the rarefaction front, c is the velocity pulse, is a dynamic equilibrium site with higher energy potential, ε B is the potential equilibrium site with lower energy, t is any time, t0 is the initial time of emitting the velocity pulse, and N is the number of bistable superstructure units in the bistable discrete system.

[0185] The explicit expression of velocity is obtained by differentiating equation (36):

[0186]

[0187] Where v(x,t) represents the velocity of the bistable discrete system at any position x and any time t.

[0188] In this embodiment, the parameter settings in S3 are used, and the propagation law of the shock wave in the bistable discrete system can be solved by combining equations (14) to (37). Figure 7The implicit dynamic response law of the potential barrier at multiple energy sites of the bistable discrete system is given. The figure shows that at the time 1.2s, the displacement u at each position x of the bistable discrete system is changing. The results show that the shock wave can propagate losslessly in the inter-ship shock wave directional switch structure and is in a state of directional conduction.

[0189] S5. According to the explicit change rules of displacement, velocity and time of shock wave in the process of propagation, the necessary conditions for directional conduction and blocking of shock wave are clarified: the initial boundary conditions are adjusted. When all bistable superstructure units are at high energy positions at the initial moment, the directional switch structure of shock wave between the sides will support unidirectional propagation of shock wave and will not cause loss of shock wave in the process of propagation, thereby realizing directional conduction of shock wave between the sides; when all bistable superstructure units are at low energy positions at the initial moment, the directional switch structure of shock wave between the sides will not support unidirectional propagation of shock wave and the propagation process will consume shock wave energy, thereby realizing directional blocking of shock wave between the sides. It should be noted that the orientation is achieved based on the previous phase change. When the B phase is transformed into the A* phase, the inter-board shock wave directional switch structure will block the energy. When the A* phase is transformed into the B phase, the inter-board shock wave directional switch structure will conduct the energy. Therefore, when the shock wave passes through the inter-board shock wave directional switch structure, the structure will be in the mutual transformation process between the B phase and the A* phase, thereby realizing the directional conduction or blocking of the shock wave.

[0190] In this embodiment, Figure 8 A mechanical mechanism for realizing the directional switch of the inter-board shock wave is given. When the B phase transforms to the A* phase, the inter-board shock wave directional switch structure will block the energy because the pseudo-potential energy of the B equilibrium strain site is lower than the pseudo-potential energy of the A* dynamic equilibrium strain site; when the A* phase transforms to the B phase, the inter-board shock wave directional switch structure will conduct the energy because the pseudo-potential energy of the A* dynamic equilibrium strain site is higher than the pseudo-potential energy of the B equilibrium strain site, which satisfies the energy minimum potential principle.

[0191] S6. According to the necessary conditions for directional conduction and blocking of the inter-board shock wave, the elastic stiffness K in the inter-board shock wave directional switch structure is adjusted. 1、 K 2、 K3, realizes effective directional conduction or blocking of shock waves of different energies.

[0192] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0193] The order of execution of each step in the above embodiment does not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0194] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A design method for a directional switch structure for a blast wave between two sides of a ship, wherein the directional switch structure for a blast wave between two sides of a ship is formed by an array of bistable superstructure units along the X direction and the Y direction, wherein the Y direction is radial and the X direction is circumferential, and wherein: The bistable superstructure unit includes four oblique elastic members distributed in a diamond shape and connected end to end, a group of nodes opposite to the diamond structure are arranged along the Y direction, and each of them has a vertical elastic member extending outward, and another group of nodes opposite to the diamond structure are arranged along the X direction, and the two nodes are connected by an internal transverse elastic member; the elastic stiffness of the oblique elastic member is K2 and the length is l2, the elastic stiffness of the vertical elastic member is K1 and the length is l1, and the elastic stiffness of the transverse elastic member is K3 and the length is l3; The design method comprises the following steps: S1. According to the impact dynamics and bistable structure theory, the stress-strain response of the bistable superstructure unit under quasi-static compression load is calculated, and the elastic stiffness K1, K2, and K3 of the vertical elastic member, the transverse elastic member, and the oblique elastic member are selected so that the inter-ship shock wave directional switch structure has a barrier response of multiple energy sites; S2. For the above-mentioned inter-ship shock wave directional switch structure with potential barrier response of multiple energy sites, determine the minimum and maximum extreme points in the relationship between potential energy and strain of its bistable superstructure unit, and determine the higher energy potential energy equilibrium point and the lower energy potential energy equilibrium point of static equilibrium strain; on this basis, select a group of bistable superstructure units with a large energy barrier difference, and determine their equilibrium strain points; S3. According to the energy barrier difference and equilibrium strain site of the bistable superstructure unit, the dynamic differential equation and initial boundary conditions of the bistable discrete system are established by discrete method, and the fourth-order Runge-Kutta method is used to solve the dynamic equilibrium position of the bistable discrete system and the potential barrier implicit dynamic response law of multiple energy sites. S4. According to the dynamic equilibrium position of the bistable discrete system and the implicit dynamic response law of the potential barrier at multiple energy sites, two continuity boundary condition functions are introduced to interpolate the discrete boundaries, and the dynamic differential equation of the bistable discrete system is continuousized by using Taylor series to obtain the continuity dynamic equation of the bistable discrete system. The traveling wave method is used to solve the continuity dynamic equation, and the explicit change law of displacement, velocity and time of the shock wave during propagation is analyzed. S5. According to the explicit change rules of displacement, velocity and time of shock waves during propagation, the necessary conditions for directional conduction and blocking of shock waves are clarified: the initial boundary conditions are adjusted. When all bistable superstructure units are at high energy sites at the initial moment, the directional switch structure of shock waves between the two sides will support unidirectional propagation of shock waves and will not cause loss of shock waves during propagation, thereby achieving directional conduction of shock waves between the two sides; when all bistable superstructure units are at low energy sites at the initial moment, the directional switch structure of shock waves between the two sides will not support unidirectional propagation of shock waves, and the propagation process will consume shock wave energy, thereby achieving directional blocking of shock waves between the two sides; S6. According to the necessary conditions for directional conduction and blocking of the inter-board shock wave, the elastic stiffness K in the inter-board shock wave directional switch structure is adjusted. 1、 K 2、 K3, realizes effective directional conduction or blocking of shock waves of different energies.

2. The design method of the shipboard shock wave directional switch structure according to claim 1 is characterized in that: In step S1, the method for calculating the stress-strain response of the bistable superstructure unit under the quasi-static compression load is: According to the impact dynamics and bistable structure theory, for a bistable superstructure unit, it includes three types of elastic stiffness K 1、 K 2、 K3, the total potential energy of the bistable superstructure unit includes the elastic potential energy of the elastic part and the external force work: Where U NN is the total potential energy of the bistable superstructure unit, F x and F y are the constraints in the horizontal and vertical directions, U x To apply the horizontal constraint force F x The displacement under y To apply the vertical constraint force F y displacement below; According to the principle of minimum potential energy, the horizontal constraint force F x and the vertical constraint force F y Size: When F x = 0, the process of solving formulas (2) and (3) can obtain the load-displacement response of the bistable superstructure unit, and the stress-strain curve of the bistable superstructure unit can be obtained by normalizing the load-displacement.

3. The design method of the shipboard shock wave directional switch structure according to claim 2 is characterized in that: The directional switch structure of the inter-ship shock wave has a barrier response of multiple energy sites, which means that the selected K1, K2, and K3 make the stress-strain curve of the bistable superstructure unit and F y / (K2*l2)=0 has multiple minimum points at the intersection.

4. The design method of the shipboard shock wave directional switch structure according to claim 2 is characterized in that: In step S2, the method for determining the higher energy potential equilibrium point and the lower energy potential equilibrium point of the static equilibrium strain is: Integrating the stress-strain curve calculated in S1 gives the relationship between total potential energy and strain: You NN =∫σ y dε y (4) In the formula, σ y is the normal stress in the y direction, ε y is the positive strain in the y direction; The first-order derivative is obtained by differentiating equation (4), and the maximum or minimum point is determined according to its second-order derivative. According to equations (5) and (6), the equilibrium point with higher energy potential is ε A , with a lower energy potential equilibrium site of ε B .

5. The design method of the shipboard shock wave directional switch structure according to claim 4 is characterized in that: Step S3 specifically includes the following steps: For a bistable discrete system composed of N bistable superstructure units with energy barrier difference, its Lagrangian function is: L=TU (7) Where L is the Lagrangian function, T is the kinetic energy of the bistable discrete system, U is the total potential energy of the bistable discrete system, m is the mass of the bistable superstructure unit, and u is j is the vertical displacement of the jth bistable superstructure unit, ε j is the equivalent strain of the jth bistable superstructure unit, ε j-1 is the equivalent strain of the j-1th bistable superstructure unit, U NNS (ε j -ε j-1 ) is the potential energy effect of the adjacent j-1th bistable superstructure unit on the jth bistable superstructure unit, N is the number of bistable superstructure units in the bistable discrete system, and t represents any time; Substituting (7) and (8) into the Lagrangian dynamics equation of the particle system, we can obtain the dynamic differential equation (9) of the bistable discrete system: In the formula, f NN (ε j+1 ) represents the external force of the j+1th bistable superstructure unit, f NN (ε j ) represents the external force of the jth bistable superstructure unit, f NNS (ε j -ε j-1 ) represents the internal force between the jth bistable superstructure unit and the j-1th bistable superstructure unit, f NNS (ε j+1 -ε j ) represents the internal force between the j+1th bistable superstructure unit and the jth bistable superstructure unit, f NNS (ε j+2 -ε j+1 ) represents the internal force between the j+2th bistable superstructure unit and the j+1th bistable superstructure unit; And there is U NN (ε j ) and U NN (ε j+1 ) are the total potential energies of the jth and j+1th bistable superstructure units, ε j+1 is the strain of the j+1th bistable superstructure unit, U NNS (ε j+1 -ε j ) is the potential energy effect of the adjacent j-th bistable superstructure unit on the j+1-th bistable superstructure unit, U NNS (ε j+2 -ε j+1 ) is the potential energy effect of the adjacent j+1th bistable superstructure unit on the j+2th bistable superstructure unit; For the jth bistable superstructure unit, its total potential energy is assumed to be the following explicit expression: In the formula, ε j The calculation formula is (11), B1, B2, B3 are the coefficients related to the elastic stiffness of the bistable superstructure unit, and U is obtained by solving equations (1) to (5): NN Size determines; Where a is the distance between adjacent bistable superstructure units, u j-1 is the vertical displacement of the j-1th bistable superstructure unit; For the jth bistable superstructure unit, the potential energy provided by its adjacent structure is: Where G is a constant, greater than 0, and depends on the inherent properties of the system; For the shock wave input in the between-ship structure, the initial boundary conditions are assumed to be: Formula (13) indicates that after the impact excitation is applied, the first 10 bistable superstructure units are in state B, and the following bistable superstructure units are still in state A because they are not affected by the impact; By combining equations (7) to (12) and the initial boundary condition (13), the fourth-order Runge-Kutta method can be used to solve the dynamic equilibrium position of the bistable discrete system composed of N bistable superstructure units and the potential barrier implicit dynamic response law of multiple energy sites.

6. The design method of the shipboard shock wave directional switch structure according to claim 5 is characterized in that: In step S4, the method for obtaining the continuity dynamic equation of the bistable discrete system is: First, two continuous boundary condition functions are introduced to interpolate the discrete boundaries to obtain equations (14) and (15): ε(x=x j ,t)=e j (t) (14) In the formula, ε j (t) represents the strain continuity boundary condition of the bistable discrete system, u j (t) represents the displacement continuity boundary condition of the bistable discrete system, x represents the position of any point in the ring, and x j represents the position of the jth bistable superstructure unit, ε(x=x j ,t) represents the strain at the position of the jth bistable superstructure unit at any time t, represents the displacement from the position a / 2 of the jth bistable superstructure unit at any time t; For the dynamic differential equation (9) of the bistable discrete system in ε j Taylor expansion is done to get: In the formula, f(ε j+1 ,t) and f(ε j-1 , t) represent the external forces of the j+1th bistable superstructure unit and the j-1th bistable superstructure unit on the jth bistable superstructure unit at any time, f'(ε j )、f”(ε j )、f”'(ε j )、f””(ε j ) respectively represent the case where x = ε j The first, second, third and fourth derivatives at j ) represents the external force of the jth bistable superstructure unit, and o represents a high-order infinitesimal; Substituting (16) into (9), the continuous dynamic equation of the bistable discrete system is obtained as follows: Where ε is the strain of the bistable discrete system, f xx represents the second-order derivative of the external force f with respect to x, f xxxx represents the fourth-order derivative of the external force f with respect to x, ε xxxx represents the fourth-order derivative of strain with respect to x of the bistable discrete system; When Gε>>af NN When , the shock wave propagation in the bistable discrete system is similar to the bending wave propagation phenomenon in a one-dimensional beam, and the continuity dynamic equation can be simplified to:

7. The design method of the shipboard shock wave directional switch structure according to claim 6 is characterized in that: In step S4, the explicit variation law of displacement and time of the bistable discrete system during the propagation of the shock wave is analyzed as follows: Where u(x,t) represents the displacement of the bistable discrete system at any position x and any time t, c r is the propagation speed of the rarefaction front, c is the velocity pulse, ε A* is the dynamic equilibrium point with higher energy potential, and t0 is the initial moment of emitting the velocity pulse.

8. The design method of the shipboard shock wave directional switch structure according to claim 7 is characterized in that: In step S4, the explicit variation law of the velocity and time of the bistable discrete system during the propagation of the shock wave is analyzed as follows: Where v(x, t) represents the velocity of the bistable discrete system at any position x and any time t, and W is determined by equation (32):

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