A method for determining the soft and hard core of a composite sandwich structure

Abstract

The present invention discloses a method for determining the hard and soft core of a composite sandwich structure. The present invention belongs to the technical field of multilayer composite board evaluation, and specifically discloses a method for evaluating the hard core and soft core of a composite sandwich structure. The method includes: determining the Young's modulus of the core layer and the panel, the thickness of the core layer and the panel, the length, width and thickness of the sandwich panel, and the loss factor of the core layer and the panel; introducing a dimensionless parameter χ, and calculating the dimensionless parameter χ according to the sandwich panel parameters; taking the fundamental frequency of a symmetrical sandwich panel in a vacuum as a standard, calculating the relative error ε between the ESL method and the LW method under the dimensionless parameter χ. Calculate the relative error ε between the ESL method and the LW method; and draw an ε‑χ curve based on the calculated results. Set the maximum allowable error α, calculate the intersection of the ε‑χ curve drawn in step four and the straight line ε=α, and record the horizontal coordinate χ=χ of the intersection. α When ε≤α, the ESL method is more accurate, and the core is hard. When ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft.

Description

Technical Field

[0001] The invention belongs to the technical field of multilayer composite material plate evaluation, and in particular relates to a method for determining a soft and hard core of a composite material sandwich structure. Background Art

[0002] Sandwich panels are widely used structures in modern civil, architectural, marine and aerospace industries due to their high specific strength and stiffness, good energy absorption and sound insulation performance. Therefore, it is of great significance to study the vibration and sound radiation characteristics of sandwich structures. In theoretical research, there are many two-dimensional and three-dimensional analysis methods for analyzing static and dynamic characteristics. In actual engineering calculations, three-dimensional analysis methods are more accurate, but the calculations are very complicated, while two-dimensional analysis methods have better accuracy and efficiency and have attracted great attention from relevant researchers. In previous studies, most of the existing analysis methods have focused on the vibration analysis of sandwich panels in vacuum, but there are few corresponding underwater studies. Based on the equivalent single-layer theory (ESL) and layerwise theory (LW) of FSDT, the free and forced vibrations of simply supported symmetrical sandwich panels in vacuum and water can be predicted. Compared with the LW method, the ESL method has higher computational efficiency. However, for sandwich panels with soft cores, the ESL method has a large error.

[0003] The ESL method based on FSDT is widely used in practical engineering. In order to give full play to the advantages of the ESL analysis method, it is necessary to study the application scope of the ESL method, that is, to determine a method to determine the hardness and softness of the core of a composite sandwich structure. Summary of the invention

[0004] In order to solve the technical problems existing in the background technology, the present invention aims to provide a method for determining the soft and hard core of a composite sandwich structure. According to the applicable scope of the ESL method, quantitative critical dimensionless parameters are introduced to provide an evaluation method for determining the soft and hard core of a composite sandwich structure.

[0005] In order to solve the technical problem, the technical solution of the present invention is:

[0006] A method for determining the soft and hard core of a composite sandwich structure, the method comprising:

[0007] S1: Determine the Young's modulus of the core and face sheet, the thickness of the core and face sheet, the length, width and thickness of the sandwich panel, and the loss factor of the core and face sheet;

[0008] S2: introducing the dimensionless parameter χ, and calculating the dimensionless parameter based on the sandwich plate parameters in step S1;

[0009] S3: Taking the fundamental frequency of the symmetrical sandwich plate in vacuum as the standard, calculate the relative error ε between the ESL method and the LW method under the dimensionless parameter χ in step S2;

[0010] S4: Draw the ε-χ curve based on the results calculated in S3;

[0011] S5: Set the maximum allowable error α, calculate the intersection of the ε-χ curve drawn in step S4 and the straight line ε=α, and record the horizontal coordinate of the intersection χ=χ α When ε≤α, the core is hard; when ε>α, the core is soft.

[0012] Furthermore, the material parameters of the core layer and the panel in step S1 include Young's modulus and loss factor thereof, and the dimensions of the core layer and the panel in step S1 include thickness and length and width.

[0013] Further, the dimensionless parameter x in step S2 is expressed as:

[0014]

[0015] Furthermore, the relative error ε in step S3 refers to the relative error of the fundamental frequency of the symmetrical sandwich plate in vacuum calculated by the ESL method and the LW method, that is:

[0016]

[0017] Where f ESL is the fundamental frequency calculated by the ESL method, f LW is the fundamental frequency calculated by the LW method.

[0018] Further, in step S5, the evaluation method of the soft and hard core of the composite sandwich structure is determined according to the accuracy of the ESL method, that is, when ε≤α, the ESL method is more accurate, and the core is hard; when ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft.

[0019] Compared with the prior art, the advantages of the present invention are:

[0020] The present invention takes into account the influence of the Young's modulus ratio of the core layer and the face plate, the thickness ratio of the core layer and the face plate, the length-to-thickness ratio and the length-to-width ratio of the sandwich plate, and can determine whether a simple ESL method can be used while maintaining a certain accuracy, that is, to judge the softness and hardness of the core of a composite sandwich structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a schematic diagram of the evaluation process of the present invention;

[0022] Figure 2 It is a schematic diagram of an example of the present invention;

[0023] Figure 3 It is a coordinate system and deformation diagram of the ESL method of the present invention;

[0024] Figure 4 It is a coordinate system and deformation diagram of the LW method of the present invention;

[0025] Figure 5 It is a schematic diagram of calculation results of an example of the present invention. DETAILED DESCRIPTION

[0026] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0027] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0028] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0029] Embodiment 1:

[0030] The present invention takes the fundamental frequency of a symmetrical sandwich plate in vacuum as a standard and introduces the critical dimensionless parameter χ and the dimensionless parameter threshold χ α , and determine the maximum allowable error α and relative error ε. When ε≤α, the ESL method is accurate, convenient and fast, that is, the core is hard at this time. When ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft. Therefore, the complex and inefficient LW method must be used to obtain accurate results. The evaluation method mainly includes the following steps:

[0031] Step 1: Determine the Young's modulus of the core layer and the face sheet, the thickness of the core layer and the face sheet, the length, width and thickness of the sandwich panel, and the loss factor of the core layer and the face sheet.

[0032] Step 2: Introduce the dimensionless parameter χ and calculate the dimensionless parameter χ based on the sandwich plate parameters in step 1.

[0033] Step 3: Taking the fundamental frequency of the symmetrical sandwich plate in vacuum as the standard, calculate the relative error ε between the ESL method and the LW method under the dimensionless parameter χ in step 1.

[0034] Step 4: Draw the ε-χ curve based on the results calculated in step 3.

[0035] Step 5: Set the maximum allowable error α, calculate the intersection of the ε-χ curve drawn in step 4 and the straight line ε = α, and record the horizontal coordinate of the intersection point as χ = χ α When ε≤α, the ESL method is more accurate, and the core is hard. When ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft.

[0036] Embodiment 2:

[0037] Combination Figure 1 Flowchart, the present invention comprises the following steps:

[0038] Step 1: Determine the Young's modulus E of the core layer and the panel c 、E p , the thickness of the core layer and the face sheet t c ,t p , the length of the sandwich panel is L x 、Width L y , core layer and panel loss factor η c , η p .

[0039] Step 2: Set the maximum allowable error α and introduce the critical dimensionless parameter χ. The dimensionless parameter χ is expressed as:

[0040]

[0041] Step 3: Taking the fundamental frequency of the symmetrical sandwich plate in vacuum as the standard, calculate the relative error ε between the ESL method and the LW method under the dimensionless parameter χ in step 2. The relative error ε is expressed as:

[0042]

[0043] Where f ESL is the fundamental frequency calculated by the ESL method, f LW is the fundamental frequency calculated by the LW method.

[0044] The ESL method is as follows:

[0045] For a sandwich plate with four simply supported sides, the displacement is expanded in the form of a double trigonometric series:

[0046]

[0047] Where m and n are half-wave numbers. ψ x =cosαx,ψ y =cosβy.w 0mn ,θ xmn With θ ymn is the displacement amplitude. α=mπ / Lx ,β=nπ / L y The external force can be expressed as:

[0048]

[0049] in The equation of motion can be expressed as:

[0050]

[0051] In the formula is the elastic stiffness coefficient, and the elastic constant is It is expressed as:

[0052]

[0053] In formula (5), D ij and It is expressed as:

[0054]

[0055] In formula (5), C 55 With C 44 is the shear stiffness coefficient, expressed as:

[0056]

[0057] in:

[0058]

[0059] When the sandwich panel is in a vacuum, ρ 0 = 0. During free vibration, q z = 0. Using the Navier method, the three motion equations are in orthogonal modal form cos(pπx / L x )sin(qπy / L y ), sin(pπx / L x )cos(qπy / L y ) and sin(pπx 0 / L x )sin(qπy 0 / L y ), where p,q=1,2...+∞. To obtain the mode (m,n), let p=m,q=n, then the free vibration equation is:

[0060]

[0061] Where R ij (i,j=1,2,3) is expressed as:

[0062]

[0063] in:

[0064]

[0065] Assuming the determinant of the coefficient matrix of equation (10) is 0, the natural frequency of mode (m,n) can be calculated. The LW method is as follows:

[0066] Under the condition of four-side simple support, the displacement equation of the sandwich plate is:

[0067]

[0068] Using the Navier method, the free vibration equation is transformed into:

[0069]

[0070] In the formula for:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Assuming the determinant of the coefficient matrix of equation (14) is 0, the natural frequency of mode (m, n) can be calculated.

[0079] Step 4: Draw the ε-χ curve based on the results calculated in step 3. The results are shown in the attached Figure 5 .

[0080] Step 5: Set the maximum allowable error α, calculate the intersection of the ε-χ curve drawn in step 4 and the straight line ε = α, and record the horizontal coordinate of the intersection point as χ = χ α When ε≤α, the ESL method is more accurate, and the core is hard. When ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft.

[0081] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0082] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for determining the soft and hard core of a composite sandwich structure, characterized in that: The method comprises: S1: Determine the Young's modulus of the core and face sheet, the thickness of the core and face sheet, the length, width and thickness of the sandwich panel, and the loss factor of the core and face sheet; S2: introducing the dimensionless parameter χ, and calculating the dimensionless parameter based on the sandwich plate parameters in step S1; S3: Taking the fundamental frequency of the symmetrical sandwich plate in vacuum as the standard, calculate the relative error ε between the ESL method and the LW method under the dimensionless parameter χ in step S2; S4: Draw the ε-χ curve based on the results calculated in S3; S5: Set the maximum allowable error α, calculate the intersection of the ε-χ curve drawn in step S4 and the straight line ε=α, and record the horizontal coordinate of the intersection χ=χ α When ε≤α, the core is hard; when ε>α, the core is soft.

2. A method for determining the soft and hard core of a composite sandwich structure according to claim 1, characterized in that: The material parameters of the core layer and the panel in step S1 include Young's modulus and loss factor thereof, and the dimensions of the core layer and the panel in step S1 include thickness and length and width.

3. The method for determining the soft and hard core of a composite sandwich structure according to claim 1, characterized in that: The dimensionless parameter x in step S2 is expressed as:

4. The method for determining the soft and hard core of a composite sandwich structure according to claim 1, characterized in that: The relative error ε in step S3 refers to the relative error of the fundamental frequency of the symmetrical sandwich plate in vacuum calculated by the ESL method and the LW method, that is: Where f ESL is the fundamental frequency calculated by the ESL method, f LW is the fundamental frequency calculated by the LW method.

5. The method for determining the soft and hard core of a composite sandwich structure according to claim 1, characterized in that: In step S5, the evaluation method of the soft and hard core of the composite sandwich structure is determined according to the accuracy of the ESL method, that is, when ε≤α, the ESL method is more accurate, and the core is hard; when ε>α, the fundamental frequency error of the ESL method is large, that is, the core is soft.

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