A method for predicting shear properties of aircraft MRE sandwich structures

Abstract

This invention discloses a method for predicting the shear characteristics of aircraft MRE sandwich structures, comprising the following steps: Step 1) Constructing a simplified aircraft component MRE sandwich plate model to clarify the simplified geometry; Step 2) Using the MRE sandwich plate model to construct an MRE mechanism model based on ECC microstructures, thereby obtaining the storage modulus G′. xy (f) and loss modulus G″ xy (f); Step 3) Calculate the modal loss factor, an indicator of the shear characteristics of the aircraft MRE sandwich structure, based on the storage modulus and loss modulus. This invention develops a dynamic shear model for MRE based on ECC microstructures, which can accurately predict the loss factor, an indicator of the shear characteristics of sandwich structures.

Description

Technical Field

[0001] This invention relates to the field of aircraft structural design technology, and in particular to a method for predicting the shear characteristics of aircraft MRE sandwich structures. Background Technology

[0002] With the increasing prevalence of novel composite materials and sandwich structures in aircraft structural design, magnetorheological elastomer (MRE) sandwich structures are widely used in various engineering practices, including vibration and noise control, due to their simple structure, light weight, and high mechanical properties such as strength and stiffness. Patent CN115798647A relates to a microscopic modeling method for MRE based on ECC lattice structures. While it proposes a new MRE modeling method, it does not conduct further mechanistic research on the shear characteristics of sandwich structures. Similarly, the 2022 paper by Liu J et al., titled "Failure characteristics of the active-passive damping in the functionally graded piezoelectric layers-magnetorheological elastomer sandwich structure," published in the *International Journal of Mechanical Sciences*, innovatively proposes a novel method for the compressible damping failure characteristics of sandwich beams, but this method still lacks the ability to rapidly predict changes in the shear characteristics of sandwich structures. Summary of the Invention

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

[0004] Technical solution. A method for predicting the shear characteristics of aircraft MRE sandwich structures, comprising the following steps:

[0005] Step 1) Construct a simplified aircraft component MRE sandwich panel model to clarify the simplified geometry;

[0006] Step 2) Construct an MRE mechanism model based on an ECC microstructure using the MRE sandwich panel model, thereby obtaining the storage modulus G′. xy (f) and loss modulus G″ xy (f);

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

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

[0009] In the aforementioned method for predicting the shear characteristics of aircraft MRE sandwich structures, 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, compensating for the influence of complex multipolar interactions caused by complex particle structures on material dynamics; c is the number of magnetic particles per unit volume of the network; f is the frequency of the dynamic load; k B Boltzmann's constant; λ 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 anisotropic parameter; the integral part is a triple integral over the volume Ω of a cube with side length π.

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

[0013]

[0014] In the formula, This represents the initial loss modulus.

[0015] In the aforementioned method for predicting the shear characteristics of aircraft MRE sandwich structures, 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 particle network MRE material based on ECC microstructure is time-dependent, and the expression is:

[0017]

[0018] Step 22) Introduce the Fourier transform to convert the modulus's variation with time into its variation with frequency. The transformation formula is:

[0019]

[0020] in, It is a dynamic complex modulus, which is frequency-dependent, where ω is the angular frequency and e is the base of the natural logarithm function.

[0021] Step 23) Obtain the storage modulus and loss modulus expressed in terms of frequency from the real and imaginary parts of the dynamic complex modulus, as shown in the following expressions:

[0022]

[0023] Wherein: 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 characteristics of aircraft MRE sandwich structures, ω = 2πf, where f is the frequency of the dynamic load.

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

[0027] In the aforementioned method for predicting the shear characteristics of aircraft MRE sandwich structures, in step 3), the modal loss factor η, an indicator of the shear characteristics of aircraft MRE sandwich structures, is calculated using the following formula:

[0028]

[0029] Beneficial effects:

[0030] 1) The prediction model proposed in this invention can replace a series of cumbersome and complex theoretical derivation processes, such as constructing a dynamic model of sandwich structure using the Lagrange energy method, and can predict the shear characteristics of aircraft MRE sandwich structures more quickly and accurately.

[0031] 2) This invention proposes a microscopic model that can predict the MRE sandwich structure of aircraft, which has the function of mapping from the microscopic constitutive model of materials to the macroscopic shear properties of typical sandwich structures.

[0032] 3) This invention expands the applicability of the MRE mechanism model based on ECC (edge-centered cubic lattice) microstructures, paving the way for the application of constitutive models of composite materials.

[0033] 4) The loss factor obtained by the microscopic model proposed in this invention has an error range of 0.01% to 2% compared with the experimental true value solution, which is significantly lower than the loss factor obtained by the Lagrange energy method by constructing the dynamic model of sandwich structure with an error range of 0.9% to 4.23%. Attached Figure Description

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

[0035] Figure 2 A schematic diagram of MRE sandwich panels for simplified aircraft components.

[0036] Figure 3 This is a schematic diagram of the geometric model of an isotropic ECC microstructure. Detailed Implementation

[0037] Example 1. A method for predicting the shear characteristics of aircraft MRE sandwich structures, see [link to example]. Figures 1-3 ,include:

[0038] 1) Use the 3D modeling software CATIA to construct the MRE sandwich panel, a simplified component for aircraft. Figure 2 ), clearly simplifying the geometric structure.

[0039] 2) In the normal coordinate mode, isotropic microstructures are based on ECC microstructures ( Figure 3 The shear modulus of the particle network MRE material is time-dependent, expressed as:

[0040]

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

[0042] 2.1) To simplify the formula, a Fourier transform is introduced, which converts the time-varying modulus into a frequency-varying modulus. The transformed formula is as follows:

[0043]

[0044] in, It is a dynamic complex modulus, which is frequency-dependent, where 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 terms of frequency, can be obtained from the real and imaginary parts of the dynamic complex modulus, as shown in the following expressions:

[0048]

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

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

[0051]

[0052] In the formula, 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 particles per unit volume of the network, and f is the frequency of the dynamic load. k is the mean absolute temperature. B Boltzmann's constant, This is the static shear modulus. Let λ be the initial loss modulus, and τ0 be 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, with a value range of [0,π]; β is the anisotropy parameter, and β=1 for the isotropic case.

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

[0054]

Claims

1. A method for predicting the shear characteristics of aircraft MRE sandwich structures, characterized in that, Includes the following steps: Step 1) Construct a simplified aircraft component MRE sandwich panel model to clarify the simplified geometry; Step 2) Construct an MRE mechanism model based on an ECC microstructure using the MRE sandwich panel model, thereby obtaining the storage modulus. and loss modulus ; Step 3) Calculate the modal loss factor, an indicator of the shear characteristics of the aircraft MRE sandwich structure, based on the storage modulus and loss modulus; In step 2), the storage modulus for: ； In the formula, It is the static shear modulus; The constant is used to compensate for the influence of complex multipolar interactions caused by complex particle structures on material dynamics; The number of magnetic particles per unit volume of the network; For the frequency of dynamic load; Boltzmann's constant; Mean absolute temperature; , , For eigenvalue spectral functions; The minimum relaxation time associated with isotropic particles; It is the phase shift vector; Let be the anisotropic parameter; the integral part is the side with length . The volume of the cube Perform triple integrals; In step 2), the loss modulus for: ； In the formula, This is the initial loss modulus; In step 2), the storage modulus and loss modulus The construction process is as follows: Step 21) In the normal coordinate mode, the shear modulus of the isotropic particle network MRE material based on the ECC microstructure is time-dependent, and the expression is: ； Step 22) Introduce the Fourier transform to convert the time-varying modulus into a frequency-varying modulus. The transformation formula is: ； in, It is a dynamic complex modulus, which is frequency-dependent. Angular frequency; is the base of the natural logarithm function; Step 23) Obtain the storage modulus and loss modulus expressed in terms of frequency from the real and imaginary parts of the dynamic complex modulus, as shown in the following expressions: ； in: For storing modulus, For loss modulus; Step 24) Obtain the storage modulus based on the MRE mechanism model of the ECC microstructure. and loss modulus .

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

3. The method for predicting the shear characteristics of an aircraft MRE sandwich structure according to claim 1, characterized in that, , The frequency of the dynamic load.

4. The method for predicting the shear characteristics of an aircraft MRE sandwich structure according to claim 1, characterized in that, , Represents the CIP volume fraction in MRE. It refers to the size of a unit crystal lattice volume.

5. The method for predicting the shear characteristics of an aircraft MRE sandwich structure according to claim 1, characterized in that, In step 3), the modal loss factor η, an indicator of the shear characteristics of the aircraft MRE sandwich structure, is calculated using the following formula: 。

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