A nonlinear dynamic analysis method for projectile charge partition structure

Abstract

The present invention discloses a nonlinear dynamic analysis method for a projectile charge partition structure. According to the characteristics of the projectile segmented charge, a typical projectile charge partition structure is extracted as a research object, and a mass-spring-damper system model reflecting the connection characteristics of the charge, shell, and partition is given; a two-degree-of-freedom system nonlinear dynamic theoretical analysis model considering gap and connection characteristics is established; the analysis model is subjected to time expansion and contraction transformation and dimensionless processing except for displacement, and is discretized using numerical integration to calculate the dynamic response under a given time-history load, and the nonlinear response law of the charge structure is analyzed from the perspective of structural dynamics; the normalized motion equation expressed in displacement variables obtained by dimensionless processing of mass, stiffness, load, etc. is convenient for comparing the influence of changes in each dimensionless parameter on the response of the structure, can better reflect the multi-body interaction effects caused by structural collisions, gaps, etc., and can be used to guide projectile structure design.

Description

Technical Field

[0001] The present invention relates to the technical field of nonlinear structural dynamics, and in particular to a nonlinear dynamics analysis method for a projectile charge partition structure. Background Art

[0002] To improve the projectile's safety and environmental adaptability during armor penetration, a typical projectile structure is typically assembled from multiple sections of explosives combined with partitions. During target impact and flight, the internal explosives inevitably experience multi-body interactions with the charge shell and partitions, such as interstitial collisions and friction. This can lead to problems such as amplified dynamic response of the charge structure and localized premature ignition. Studying the nonlinear response patterns caused by these multi-body interactions is crucial for assessing the safety of the charge structure.

[0003] Research on armor penetration, both domestically and internationally, has primarily focused on the number of penetration layers, depth estimation, overload curves, blast damage evaluation, and target damage and protection, with a particular focus on impact dynamics. Research on armor penetration rarely considers the structural dynamic characteristics of the charge, hull, and barrier structure. However, the amplification of the local dynamic response of the charge can be a key factor in premature charge ignition. Therefore, the correct description of the multi-body collision process among the charge, hull, and barrier structure, as well as the amplification effects that can result from these collisions, is a key issue currently under investigation in the structural dynamics of projectiles.

[0004] Based on this, it is necessary to develop a nonlinear dynamic analysis method for the projectile charge partition structure to solve the above problems. Summary of the Invention

[0005] The purpose of the present invention is to design a nonlinear dynamic analysis method for the projectile charge partition structure in order to solve the above problems.

[0006] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0007] A nonlinear dynamic analysis method for a projectile charge partition structure comprises the following steps:

[0008] S1: Based on the segmented charge characteristics of the projectile, the charge, shell and partition structure of the typical projectile are extracted, and a mass-spring-damper two-degree-of-freedom system model reflecting its connection characteristics is established;

[0009] S2: Establish a nonlinear dynamics analysis model of a two-degree-of-freedom system considering gap and connection characteristics, and perform time expansion and contraction transformation and dimensionless processing except displacement on the analysis model;

[0010] S3: Use numerical integration to calculate the dynamic response under a given time-history load to achieve nonlinear dynamic analysis.

[0011] Step S1 includes the following sub-steps:

[0012] S11: According to the characteristics of the segmented charge of the projectile, a charge partition structure is selected as the analysis object;

[0013] S12: The lumped mass method is used for the charge partition structure to establish a mass-spring-damper two-degree-of-freedom system model that reflects the connection characteristics of the charge, shell and partition.

[0014] Step S2 includes the following sub-steps:

[0015] S21: Establish the two-degree-of-freedom system motion equation corresponding to the mass-spring-damper two-degree-of-freedom system model in S12 to form a theoretical analysis model:

[0016] In the above formula, m 1: Extract the total mass of the shell and partition; m 2: Mass of charge in charge partition structure; k 1: Extract the stiffness of the shell and partition; k 2: The rigidity of the charge part in the charge partition structure; c 1: Extract the damping of the shell and partition; c 2: Damping of the charge part in the charge partition structure; x 1: Extract the displacement of the shell and partition; : Extract the acceleration of the shell and partition; : Extraction speed of the shell and partition part; x 2: Displacement of the charge part; : acceleration of the charge part; : speed of the charging part; F : dynamic load borne by the projectile; : gap collision force function describing nonlinear characteristics;

[0017] Furthermore, the gap collision force is:

[0018] In the above formula, k 3: Contact connection stiffness between charge and partition; c 3: Damping between charge and partition; b : The gap between the charge and the partition;

[0019] when x 2- x 1> b When , there is no gap. At this time, formula (1) becomes:

[0020] when x 2- x 1≤ b When , there is a gap. At this time, formula (1) becomes:

[0021] S22: Time Stretch Transformation , respectively substitute into formula (3) and formula (4), and record , , , the dimensionless processing equation except displacement is obtained; τ: transformation time; ω1: natural circular frequency of the extracted shell and partition part; ω2: natural circular frequency of the charge part; ω3: nonlinear circular frequency of the extracted shell and partition part; where:

[0022] The equation of motion for the gapless case becomes:

[0023] Where, ξ1: modal damping ratio of the extraction shell and partition part; ξ2: modal damping ratio of the charge part; ξ3: nonlinear damping ratio of the extraction shell and partition part; : dynamic load borne by the projectile after time transformation; α: dimensionless parameter of natural frequency; β: dimensionless parameter of stiffness; μ: dimensionless parameter of mass;

[0024] The equation of motion for the clearance case becomes:

[0025] Furthermore, the values ​​of the parameters in formula (5) and formula (6) are:

[0026] Step S3 includes the following sub-steps:

[0027] S31: Reduce the order of the motion equations (5) and (6) in step S22, and let , , , ,in:

[0028] For the gapless case, the reduced-order equation is:

[0029] For the gap case, the reduced-order equation is:

[0030] S32: The fourth-order Runge-Kutta method is used to discretize and numerically solve the equations of motion (8) and (9). The discrete recursive expression from time τ to time τ+Δτ is:

[0031] Where Δτ is the discrete time interval;

[0032] Furthermore, for the case of no gap, the expressions of the parameters in formula (10) are:

[0033] (12),

[0034] (14),

[0035] For the case of gaps, the parameter expressions of equations (11) and (13) still hold, and equation (12) becomes:

[0036] Formula (14) becomes:

[0037] S33: The discrete moments obtained according to the discrete relation expression in step S32 u 1. u 2. u 3. u 4. And use Time transformation relationship to obtain the structural displacement, velocity, acceleration and other responses at each real moment:

[0038] The beneficial effects of the present invention are:

[0039] (1) By extracting the characteristics of typical projectile charge partition structures, a structural dynamics theoretical model considering the nonlinear effect of gaps was established. The nonlinear dynamic response of typical charge components was analyzed and explored from the perspective of structural dynamics.

[0040] (2) The dynamic motion equation of the warhead charge partition structure was obtained, and the normalized motion equation expressed in displacement variables was obtained by dimensionlessly processing the mass, stiffness, load, etc., which facilitates the comparison of the effects of the changes in each dimensionless parameter on the structural response;

[0041] (3) The normalized equation of motion was reduced in order and solved discretely by using a numerical integration algorithm. A specific calculation method for discrete parameters was given, and finally a nonlinear dynamic analysis method for the projectile charge partition structure was formed. The relevant calculation method is very easy to implement in a program, and the corresponding calculation program can be easily constructed based on the recursive formula and solution process, which is highly practical.

[0042] (4) In addition, the projectile charge partition structure analyzed using nonlinear methods can correctly describe the multi-body collision process and the amplification effect that may be caused by collisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flow chart of the steps for implementing the present invention;

[0044] Figure 2 It is a schematic diagram of the process of extracting a charge partition structure based on the typical projectile structure characteristics;

[0045] Figure 3 It is a mass-spring-damper two-degree-of-freedom system model established based on the charge partition structure and connection characteristics;

[0046] Figure 4 The response of the charge structure to the change of the natural frequency ratio (α) at ​​each initial value ( x 2) Impact over time;

[0047] Figure 5 The response of the charge structure to the change of different stiffness ratios (β) under different initial values ​​( x 2) Impact over time;

[0048] Figure 6 The response of different mass ratios (μ) to the charge structure under different initial values ​​( x 2) Impact over time;

[0049] Figure 7 is the gap between the different initial values ​​( b ) to the charge structure response ( x 2) Impact over time.

[0050] In the figure: 1-projectile body; 2-charge partition structure; 21-first partition; 22-gap; 23-charge; 24-shell; 25-second partition. DETAILED DESCRIPTION

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings of the embodiments of the present invention. It should be understood that the described embodiments are only a portion of the embodiments of the present invention, not all of them. Generally, the components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations.

[0052] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0053] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0054] In the description of the present invention, it should be understood that the terms "upper", "lower", "inside", "outside", "left", "right", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, or are the orientations or positional relationships in which the inventive product is conventionally placed when in use, or are the orientations or positional relationships conventionally understood by those skilled in the art. These are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0055] Furthermore, the terms “first”, “second”, etc. are merely used for distinguishing descriptions and should not be understood as indicating or implying relative importance.

[0056] In the description of the present invention, it should also be noted that, unless otherwise expressly specified or limited, terms such as "disposed" and "connected" should be understood in a broad sense. For example, "connected" can mean a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can also mean internal communication between two components. Those skilled in the art will be able to understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0057] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0058] like Figure 1 As shown, a nonlinear dynamic analysis method for a projectile charge partition structure includes the following steps:

[0059] S1: Based on the segmented charge characteristics of the projectile, the charge, shell and partition structure of the typical projectile are extracted, and a mass-spring-damper two-degree-of-freedom system model reflecting its connection characteristics is established;

[0060] Step S1 includes the following sub-steps:

[0061] S11: According to the characteristics of the segmented charge of the projectile, a charge partition structure is selected as the analysis object; Figure 2 As shown, a projectile 1 and a charge partition structure 2 on the projectile 1 are shown; the charge partition structure 2 includes a first partition 21, a gap 22, a charge 23, a shell 24, and a second partition 25. A placement cavity is provided inside the shell 24, and the first partition 21 and the second partition 25 are respectively provided at both ends of the shell 24 for blocking. The gap 22 is provided between the charge 23 and the first partition 21.

[0062] S12: The lumped mass method is used for the charge partition structure to establish a mass-spring-damper two-degree-of-freedom system model that reflects the connection characteristics of the charge, shell and partition, such as Figure 3 shown.

[0063] S2: Establish a nonlinear dynamics analysis model of a two-degree-of-freedom system considering gap and connection characteristics, and perform time expansion and contraction transformation and dimensionless processing except displacement on the analysis model;

[0064] Step S2 includes the following sub-steps:

[0065] S21: Establish the two-degree-of-freedom system motion equation corresponding to the mass-spring-damper two-degree-of-freedom system model in S12 to form a theoretical analysis model:

[0066] In the above formula, m 1: Extract the total mass of the shell and partition; m 2: Mass of charge in charge partition structure; k 1: Extract the stiffness of the shell and partition; k 2: The rigidity of the charge part in the charge partition structure; c 1: Extract the damping of the shell and partition; c 2: Damping of the charge part in the charge partition structure; x 1: Extract the displacement of the shell and partition; : Extract the acceleration of the shell and partition; : Extraction speed of the shell and partition part; x 2: Displacement of the charge part; : acceleration of the charge part; : speed of the charging part; F : dynamic load borne by the projectile; : gap collision force function describing nonlinear characteristics;

[0067] Furthermore, the nonlinear gap collision force is:

[0068] In the above formula, k 3: Contact connection stiffness between charge and partition; c 3: Damping between charge and partition; b : The gap between the charge and the partition;

[0069] The load borne by the projectile is in the form of: ;

[0070] According to the dynamic load of the charge and the partition part F ( t ) under the action of gap or not, combined with the above gap collision force values, the motion equations with and without gap are constructed respectively:

[0071] when x 2- x 1> b When , there is no gap. At this time, formula (1) becomes:

[0072] when x 2- x 1≤ b When , there is a gap. At this time, formula (1) becomes:

[0073] S22: Perform time expansion and contraction transformation for the above two cases with and without gaps , respectively substitute into formula (3) and formula (4), and record , , , the dimensionless processing equation except displacement is obtained; τ: transformation time; ω1: natural circular frequency of the extracted shell and partition part; ω2: natural circular frequency of the charge part; ω3: nonlinear circular frequency of the extracted shell and partition part; where:

[0074] The equation of motion for the gapless case becomes:

[0075] Where, ξ1: modal damping ratio of the extraction shell and partition part; ξ2: modal damping ratio of the charge part; ξ3: nonlinear damping ratio of the extraction shell and partition part; : dynamic load borne by the projectile after time transformation; α: dimensionless parameter of natural frequency; β: dimensionless parameter of stiffness; μ: dimensionless parameter of mass;

[0076] The equation of motion for the clearance case becomes:

[0077] Furthermore, the values ​​of the parameters in formula (5) and formula (6) are:

[0078] S3: Use numerical integration to calculate the dynamic response under a given time-history load to achieve nonlinear dynamic analysis.

[0079] Step S3 includes the following sub-steps:

[0080] S31: Reduce the order of the motion equations (5) and (6) in step S22, and let , , , , we obtain the reduced-order equations of motion with and without clearance, where:

[0081] For the gapless case, the reduced-order equation is:

[0082] For the gap case, the reduced-order equation is:

[0083] S32: The fourth-order Runge-Kutta method is used to discretize and numerically solve the equations of motion (8) and (9). The discrete recursive expression from time τ to time τ+Δτ is:

[0084] Where Δτ is the discrete time interval;

[0085] Furthermore, for the case of no gap, the expressions of the parameters in formula (10) are:

[0086] (12),

[0087] (14),

[0088] For the case of gaps, the parameter expressions of equations (11) and (13) still hold, and equation (12) becomes:

[0089] Formula (14) becomes:

[0090] S33: Set the initial value at τ=0 u 1. u 2. u 3. u 4 are all taken as 0, ξ1 is taken as 0.001, ξ2 is taken as 0.015, ξ3 is taken as 0.015, the initial value of β is taken as 0.4, the initial value of α is taken as 1.6, and the initial value of μ is taken as 2. b The initial value is 0.03. The discrete moment values ​​obtained from the discrete relation expression in step S32 are u 1. u 2. u 3. u 4. And use Time transformation relationship to obtain the structural displacement, velocity, acceleration and other responses at each real moment:

[0091] As an example, Figure 4 The effect of the change of the natural frequency ratio (α) on the charge structure response ( x 2) Time changes; Figure 5 The response of the charge structure to the change of different stiffness ratio (β) under various initial values ​​is given. x 2) Time changes; Figure 6 The response of different mass ratios (μ) to the charge structure under different initial values ​​is given. x 2) Time changes; Figure 7 The results of different gaps ( b ) changes the response to the charge structure ( x 2) Time variation. From the above figures, we can obtain the influence of the natural frequency, specific stiffness, specific mass, and gap size between the charge and the shell partition on the dynamic response of the charge, thereby evaluating the impact of each variable on the charge response and guiding the design of the projectile structure.

[0092] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A nonlinear dynamic analysis method for a projectile charge partition structure, characterized in that: The following steps are involved: S1: Based on the segmented charge characteristics of the projectile, the charge, shell and partition structure of the typical projectile are extracted, and a mass-spring-damper two-degree-of-freedom system model reflecting its connection characteristics is established; S2: Establish a nonlinear dynamics analysis model of a two-degree-of-freedom system taking into account gap and connection characteristics, and perform time expansion and contraction transformation and dimensionless processing on the analysis model except displacement; Step S2 includes the following sub-steps: S21: Establish the two-degree-of-freedom system motion equation corresponding to the mass-spring-damper two-degree-of-freedom system model to form a theoretical analysis model: (1)， In the above formula, m1: the total mass of the extraction shell and partition; m2: the mass of the charge in the charge partition structure; k1: the stiffness of the extraction shell and partition; k2: the stiffness of the charge part in the charge partition structure; c1: the damping of the extraction shell and partition; c2: the damping of the charge part in the charge partition structure; x1: the displacement of the extraction shell and partition; : Extract the acceleration of the shell and partition; : The speed of extracting the shell and the partition part; x2: The displacement of the charging part; : acceleration of the charge part; : velocity of the charge part; F: dynamic load borne by the projectile; : gap collision force function describing nonlinear characteristics; Furthermore, the gap collision force is: (2)， In the above formula, k3: contact connection stiffness between charge and diaphragm; c3: damping between charge and diaphragm; b: the size of the gap between the charge and the partition; S3: Use numerical integration to calculate the dynamic response under a given time-history load to achieve nonlinear dynamic analysis.

2. The nonlinear dynamic analysis method of a projectile charge partition structure according to claim 1, characterized in that: Step S1 includes the following sub-steps: S11: According to the characteristics of the segmented charge of the projectile, a charge partition structure is selected as the analysis object; S12: The lumped mass method is used for the charge partition structure to establish a mass-spring-damper two-degree-of-freedom system model that reflects the connection characteristics of the charge, shell and partition.

3. The nonlinear dynamic analysis method of a projectile charge partition structure according to claim 2, characterized in that: when When , there is no gap. At this time, formula (1) becomes: (3)， when When , there is a gap. At this time, formula (1) becomes: (4)， S22: Time Stretch Transformation , respectively substitute into formula (3) and formula (4), and record , , , we get the dimensionless processing equation except displacement; : Transformation time; : Extract the natural circular frequency of the shell and partition part; : natural circular frequency of the charge part; : Extract the nonlinear circular frequency of the shell and partition; where: The equation of motion for the gapless case becomes: (5)， in, : Extract the modal damping ratio of the shell and partition; : modal damping ratio of the charge part; : Extract the nonlinear damping ratio of the shell and partition; : dynamic load borne by the projectile after time transformation; α: dimensionless parameter of natural frequency; β: dimensionless parameter of stiffness; µ: dimensionless parameter of mass; The equation of motion for the clearance case becomes: (6)， Furthermore, the values ​​of the parameters in formula (5) and formula (6) are: (7)。 4. The nonlinear dynamic analysis method of a projectile charge partition structure according to claim 3, characterized in that: Step S3 includes the following sub-steps: S31: Reduce the order of the motion equations (5) and (6) in step S22, and let , , , ,in: For the gapless case, the reduced-order equation is: (8)， For the gap case, the reduced-order equation is: (9)， S32: The fourth-order Runge-Kutta method is used to discretize and numerically solve the equations of motion (8) and (9), from Time has come The discrete recursive expression of the moment is: (10)， in, is a discrete time interval; Furthermore, for the case of no gap, the expressions of the parameters in formula (10) are: (11)， (12)， (13)， (14)， For the case of gaps, the parameter expressions of equations (11) and (13) still hold, and equation (12) becomes: (15)， Formula (14) becomes: (16)， S33: The discrete moments obtained according to the discrete relation expression in step S32 , and use Time transformation relationship to obtain the structural displacement, velocity, and acceleration responses at each real moment: (17)。

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