Method capable of predicting shearing characteristics of aircraft MRE sandwich structure

Abstract

The invention discloses a method capable of predicting shear characteristics of an aircraft MRE sandwich structure, which comprises the following steps of: 1) constructing an aircraft simplified component MRE sandwich plate model, and clearly simplifying a geometric structure; (2) constructing an MRE mechanism model based on an ECC microstructure by utilizing the MRE sandwich plate model, so as to obtain a storage modulus G'xy (f) and a loss modulus G ''xy (f); and 3) calculating a modal loss factor of the shear characteristic index of the aircraft MRE sandwich structure based on the storage modulus and the loss modulus. According to the method, the MRE dynamic shear model based on the ECC microstructure is developed, and the shear characteristic index loss factor of the sandwich structure can be accurately predicted.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft structure design, and in particular to a method for predicting shear characteristics of an aircraft MRE sandwich structure. Background Art

[0002] With the increasing application of new composite materials and sandwich structures in aircraft structural design. Magnetorheological elastomer (MRE) sandwich structures are widely used in various engineering practices such as aircraft structural design and manufacturing, vibration and noise control, etc. due to their simple structure, light weight, and high mechanical properties such as strength and stiffness. Patent CN115798647A involves a MRE microscopic modeling method based on ECC lattice structure. Although a new MRE modeling method is proposed, the model does not conduct further shear property mechanism research on sandwich structures. For example, in 2022, Liu J et al. published a paper entitled "Failure characteristics of the active-passive damping in the functionally graded piezoelectric layers-magnetorheological elastomer sandwich structure" in the International Journal of Mechanical Sciences. Although it innovatively proposed a new compressible damping failure characteristic method for sandwich beams, this method still does not have the function of quickly predicting changes in the shear characteristics of sandwich structures. Summary of the invention

[0003] The purpose of the present invention is to provide a method for predicting the shear characteristics of an aircraft MRE sandwich structure. The present invention develops an MRE dynamic shear model based on ECC microstructure, which can accurately predict the loss factor of the shear characteristic index of the sandwich structure.

[0004] Technical solution: A method for predicting the shear properties of an aircraft MRE sandwich structure comprises the following steps:

[0005] Step 1) construct the MRE sandwich panel model of the simplified aircraft component to clarify the simplified geometric structure;

[0006] Step 2) Use the MRE sandwich plate model to construct the MRE mechanism model based on the ECC microstructure to obtain the storage modulus G′ xy (f) and loss modulus G″ xy (f);

[0007] Step 3) Calculate the modal loss factor of the shear characteristic index of the aircraft MRE sandwich structure based on the storage modulus and loss modulus.

[0008] In the aforementioned method for predicting the shear properties of an aircraft MRE sandwich structure, in step 1), a MRE sandwich panel model is constructed using 3D modeling software CATIA.

[0009] In the aforementioned method for predicting the shear properties of an aircraft MRE sandwich structure, in step 2), the storage modulus G x ' y (f) is:

[0010]

[0011] In the formula, is the static shear modulus; P is a constant that compensates for the influence of complex multipolar interactions caused by complex particle structures on material dynamics; c is the number of magnetic powders per unit volume of the network; f is the frequency of dynamic load; k B is the Boltzmann constant; is the mean absolute temperature; x (θ,β),λ y (θ,β),λ z (θ, β) is the eigenvalue spectrum function; τ0 is the minimum relaxation time associated with isotropic particles; θ is the phase shift vector; β is the anisotropy parameter; the integral part is the triple integral of the volume Ω of a cube with a side length of π.

[0012] In the aforementioned method for predicting the shear properties of an aircraft MRE sandwich structure, in step 2), the loss modulus G″ xy (f) is:

[0013]

[0014] In the formula, is the initial loss modulus.

[0015] In the aforementioned method for predicting the shear properties of an aircraft MRE sandwich structure, in step 2), the storage modulus G′ xy (f) and loss modulus G″ xy The construction process of (f) is as follows:

[0016] Step 21) In the normal coordinate mode, the shear modulus of the isotropic ECC microstructure-based particle network MRE material is time-dependent and is expressed as:

[0017]

[0018] Step 22) Fourier transform is introduced to convert the modulus change with time into the modulus change with frequency. The conversion formula is:

[0019]

[0020] in, is the dynamic complex modulus, which is related to frequency, ω is the angular frequency; e is the base of the natural logarithm function.

[0021] Step 23) The storage modulus and loss modulus expressed in terms of frequency are obtained from the real and imaginary parts of the dynamic complex modulus, and the expressions are as follows:

[0022]

[0023] Where: G′ xy (ω) is the storage modulus, G″ xy (ω) is the loss modulus;

[0024] Step 24) Obtain the storage modulus G′ based on the MRE mechanism model of the ECC microstructure xy (f) and loss modulus G″ xy (f).

[0025] In the aforementioned method for predicting the shear properties of aircraft MRE sandwich structures, ω = 2πf, where f is the frequency of the dynamic load.

[0026] In the aforementioned method for predicting the shear properties of aircraft MRE sandwich structures, φ represents the volume fraction of CIP in MRE, and v is the unit lattice volume.

[0027] In the aforementioned method for predicting the shear characteristics of an aircraft MRE sandwich structure, in step 3), the modal loss factor η, an index of the shear characteristics of the aircraft MRE sandwich structure, is calculated as follows:

[0028]

[0029] Beneficial effects:

[0030] 1) The prediction model proposed in the present invention can replace a series of tedious and complex theoretical derivation processes such as constructing a sandwich structure dynamics model through the Lagrangian energy method, and can predict the shear characteristics of the aircraft MRE sandwich structure more quickly and accurately.

[0031] 2) The present invention proposes a microscopic model that can predict the aircraft MRE sandwich structure, which has the mapping function from the material microscopic constitutive model to the macroscopic shear performance of the typical sandwich structure.

[0032] 3) The present invention expands the application scope of the MRE mechanism model based on the ECC (edge-centered cubic lattice) microstructure, and broadens the path for the application of constitutive models of composite materials.

[0033] 4) The error range of the loss factor solved by the microscopic model proposed in the present invention compared with the experimental true value solution result is 0.01% to 2%, which is significantly lower than the error range of 0.9% to 4.23% of the loss factor obtained by constructing the sandwich structure dynamic model using the Lagrange energy method. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flowchart for predicting the shear properties of aircraft MRE sandwich structures based on the constitutive model of ECC microstructure;

[0035] Figure 2 Schematic diagram of MRE sandwich panel for simplified aircraft components.

[0036] Figure 3 Schematic diagram of the isotropic ECC microstructure geometric model. DETAILED DESCRIPTION

[0037] Example 1. A method for predicting the shear properties of an aircraft MRE sandwich structure, see Figure 1-Figure 3 ,include:

[0038] 1) Use 3D modeling software CATIA to build aircraft simplified component MRE sandwich panels ( Figure 2 ), clarify and simplify the geometric structure.

[0039] 2) In normal coordinate mode, isotropic ECC microstructure ( Figure 3 ) The shear modulus of the particle network MRE material is time-dependent and can be expressed as:

[0040]

[0041] in, φ represents the volume fraction of CIP in MRE, v is the unit lattice volume, and the integral part can be understood as the triple integral of the volume Ω of a cube with a side length of π.

[0042] 2.1) To simplify the formula, Fourier transform is introduced to convert the modulus change with time into the modulus change with frequency. The conversion formula is:

[0043]

[0044] in, is the dynamic complex modulus, which is frequency-dependent, ω is the angular frequency, and e is the base of the natural logarithm function.

[0045] ω=2πf

[0046] Where f is the frequency of the dynamic load.

[0047] 2.2) The storage modulus and loss modulus expressed in frequency can be obtained from the real and imaginary parts of the dynamic complex modulus, as shown in the following expressions:

[0048]

[0049] Where: G′ xy (ω) is the storage modulus, G″ xy (ω) is the loss modulus.

[0050] 2.3) Storage modulus G′ obtained based on the MRE mechanism model of ECC microstructure xy (f) and loss modulus G″ xy The expression of (f) is:

[0051]

[0052] Where P is a constant that can compensate for the influence of complex multipolar interactions caused by complex particle structures on material dynamics, c is the number of magnetic powders per unit volume of the network, and f is the frequency of the dynamic load. is the mean absolute temperature, k B is the Boltzmann constant, is the static shear modulus, is the initial loss modulus, and τ0 is the minimum relaxation time associated with isotropic particles. x (θ,β),λ y (θ,β),λ z (θ, β) is the eigenvalue spectrum function; θ is the phase shift vector, and its value range is [0, π]; β is the anisotropy parameter, and for the isotropic case, β = 1.

[0053] 3) The modal loss factor of the shear characteristic index of the aircraft MRE sandwich structure is:

[0054]

Claims

1. A method for predicting the shear properties of an aircraft MRE sandwich structure, characterized in that: The steps include: Step 1) construct the MRE sandwich panel model of the simplified aircraft component to clarify the simplified geometric structure; Step 2) Use the MRE sandwich plate model to construct the MRE mechanism model based on the ECC microstructure to obtain the storage modulus G′ xy (f) and loss modulus G″ xy (f); Step 3) Calculate the modal loss factor of the shear characteristic index of the aircraft MRE sandwich structure based on the storage modulus and loss modulus.

2. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 1, characterized in that: In step 1), the MRE sandwich panel model is constructed using 3D modeling software CATIA.

3. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 1, characterized in that: In step 2), the storage modulus G′ xy (f) is: In the formula, is the static shear modulus; P is a constant that compensates for the influence of complex multipolar interactions caused by complex particle structures on material dynamics; c is the number of magnetic powders per unit volume of the network; f is the frequency of dynamic load; k B is the Boltzmann constant; is the mean absolute temperature; x (θ,β),λ y (θ,β),λ z (θ, β) is the eigenvalue spectrum function; τ0 is the minimum relaxation time associated with isotropic particles; θ is the phase shift vector; β is the anisotropy parameter; the integral part is the triple integral of the volume Ω of a cube with a side length of π.

4. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 3, characterized in that: In step 2), the loss modulus G″ xy (f) is: In the formula, is the initial loss modulus.

5. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 4, characterized in that: In step 2), the storage modulus G′ xy (f) and loss modulus G″ xy The construction process of (f) is as follows: Step 21) In the normal coordinate mode, the shear modulus of the isotropic ECC microstructure-based particle network MRE material is time-dependent and is expressed as: Step 22) Fourier transform is introduced to convert the modulus change with time into the modulus change with frequency. The conversion formula is: in, is the dynamic complex modulus, which is related to frequency, ω is the angular frequency; e is the base of the natural logarithm function. Step 23) The storage modulus and loss modulus expressed in terms of frequency are obtained from the real and imaginary parts of the dynamic complex modulus, and the expressions are as follows: Where: G′ xy (ω) is the storage modulus, G″ xy (ω) is the loss modulus; Step 24) Obtain the storage modulus G′ based on the MRE mechanism model of the ECC microstructure xy (f) and loss modulus G″ xy (f).

6. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 5, characterized in that: ω=2πf, f is the frequency of the dynamic load.

7. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 3, characterized in that: φ represents the volume fraction of CIP in MRE, and v is the unit lattice volume.

8. The method for predicting the shear properties of an aircraft MRE sandwich structure according to claim 1, characterized in that: In step 3), the modal loss factor η of the shear characteristic index of the aircraft MRE sandwich structure is calculated as follows:

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