Damping prediction method for carbon nanotube reinforced composite material laminated plate

Abstract

The invention discloses a damping prediction method for a carbon nanotube reinforced composite material laminated plate, which comprises the following steps of: firstly, deducing a stiffness matrix of a single-layer plate in a main coordinate system according to a stress-strain relationship of the carbon nanotube reinforced composite material single-layer plate in a fiber coordinate system; secondly, the bending rigidity of the carbon nano tube reinforced composite material laminated plate is obtained through the rigidity matrix, the bending rigidity is combined with the stress condition of the carbon nano tube reinforced composite material laminated plate, and the stress and strain of each single-layer plate in the laminated plate are obtained. And representing energy dissipation of the single-layer plate by adopting the specific damping capacity of the carbon nanotube reinforced composite material single-layer plate in each direction in a fiber coordinate system, and obtaining dissipation energy and strain energy of each single-layer plate by combining the stress and strain of each single-layer plate. And finally, superposing the dissipation energy and the strain energy of each single-layer plate of the carbon nanotube reinforced composite material to obtain the damping performance of the carbon nanotube reinforced composite material laminated plate.

Description

Technical Field

[0001] The present invention relates to the field of composite materials, and in particular to a method for predicting the damping of a carbon nanotube-reinforced composite laminate. Background Art

[0002] By adding carbon nanotubes to the epoxy resin matrix of carbon fiber / epoxy resin composites, a carbon nanotube-reinforced composite laminate can be made, which can enhance the interfacial effect inside the composite material, strengthen the interfacial bonding force, increase the interfacial friction, and improve the damping performance of the composite laminate during vibration. Due to the complex interaction between carbon nanotubes, carbon fibers and the epoxy resin matrix, it is difficult to predict the damping performance of carbon nanotube-reinforced composite laminates by using the microscopic mechanics analysis method.

[0003] At present, the damping of carbon nanotube-reinforced composite laminates is obtained by experimental measurement methods, and there is still a lack of theoretical and engineering prediction methods. If a macroscopic mechanics analysis method is used to establish a damping prediction method for carbon nanotube-reinforced composite laminates, at the design stage of carbon nanotube-reinforced composite laminates, by reasonably optimizing the mass fraction of carbon nanotubes and the fiber laying angle of carbon fibers, it can exert better damping performance on the premise of meeting the structural strength and stiffness, give full play to the reinforcing effect of carbon nanotubes, and greatly reduce the design cycle. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for predicting the damping of a carbon nanotube-reinforced composite laminate aiming at the defects involved in the background art.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for predicting the damping of a carbon nanotube-reinforced composite laminate, comprising the following steps:

[0007] Step 1), establish the fiber coordinate system and the principal coordinate system of the carbon nanotube-reinforced composite monolayer, and obtain the stiffness matrix of the carbon nanotube-reinforced composite monolayer in the principal coordinate system according to the stress-strain relationship of the carbon nanotube-reinforced composite monolayer in the fiber coordinate system;

[0008] Step 2), obtain the bending stiffness matrix of the carbon nanotube-reinforced composite laminate according to the stiffness matrix of the carbon nanotube-reinforced composite monolayer in the principal coordinate system;

[0009] Step 3), according to the stress condition of the carbon nanotube reinforced composite laminate, combined with the bending stiffness matrix of the carbon nanotube reinforced composite laminate, obtain the stress and strain of each monolayer of the carbon nanotube reinforced composite laminate in the principal coordinate system, and convert them to the stress and strain in the fiber coordinate system according to the stress-strain relationship of the carbon nanotube reinforced composite monolayer in the fiber coordinate system;

[0010] Step 4), according to the stress and strain of each monolayer of the carbon nanotube reinforced composite, combined with the specific damping capacity in three directions of the carbon nanotube reinforced composite monolayer in the fiber coordinate system, obtain the dissipated energy and strain energy in each carbon nanotube reinforced composite monolayer, and use the summation of each layer to obtain the dissipated energy and strain energy of the carbon nanotube reinforced composite laminate, and then obtain the damping of the carbon nanotube reinforced composite laminate.

[0011] As a further optimized scheme of the damping prediction method for a carbon nanotube reinforced composite laminate of the present invention, the detailed steps of step 1) are as follows:

[0012] Step 1.1), taking the fiber direction of the carbon nanotube reinforced composite monolayer as the x-axis, the fiber perpendicular direction as the y-axis, and the plate thickness direction as the z-axis, establish the fiber coordinate system (x, y, z) of the carbon nanotube reinforced composite monolayer;

[0013] Step 1.2), taking the length direction of the carbon nanotube reinforced composite monolayer as the 1-axis, the width direction as the 2-axis, and the plate thickness direction as the 3-axis, establish the principal coordinate system (1, 2, 3) of the carbon nanotube reinforced composite monolayer;

[0014] Step 1.3), make each carbon nanotube reinforced composite monolayer in a plane stress state, that is, there is no stress in the thickness direction (z direction) of the carbon nanotube reinforced composite monolayer, and all stress components only exist in the (x, y) plane; according to the plane stress state assumption, obtain the stress-strain relationship in the carbon nanotube reinforced composite monolayer in the fiber coordinate system as follows:

[0015]

[0016] In the formula, σ xx 、σ yy 、σ xy are the stresses in the x direction, y direction, and (x, y) plane shear direction of the carbon nanotube reinforced composite monolayer respectively, and ε xx 、ε yy 、ε xy are the strains in the x direction, y direction, and (x, y) plane shear direction of the carbon nanotube reinforced composite monolayer respectively, Q xx and Q yyare the stiffnesses of the carbon nanotube reinforced composite laminate in the x and y directions respectively, Q xy is the coupling stiffness of the carbon nanotube reinforced composite laminate in the (x, y) direction, Q ss is the shear stiffness of the carbon nanotube reinforced composite laminate;

[0017] Step 1.4), according to the elastic modulus and shear modulus of the carbon nanotube reinforced composite laminate, the components of the stiffness matrix of the carbon nanotube reinforced composite laminate in the fiber coordinate system are obtained as follows:

[0018] Q ss = G xy ;

[0019] In the formula, E x and E y are the elastic moduli of the carbon nanotube reinforced composite laminate in the x and y directions respectively, G xy and v xy are the shear modulus and Poisson's ratio of the carbon nanotube reinforced composite laminate respectively;

[0020] Step 1.5), according to the stress transformation matrix and strain transformation matrix between the fiber coordinate system and the principal coordinate system of the carbon nanotube reinforced composite laminate, the stiffness matrix of the carbon nanotube reinforced composite laminate in the fiber coordinate system is transformed into the stiffness matrix in the principal coordinate system. The expression of the stiffness matrix in the principal coordinate system is

[0021]

[0022] In the formula, Q 11 and Q 22 are the stiffnesses of the nanotube reinforced composite laminate in the 1 and 2 directions in the principal coordinate system respectively, Q 66 is the stiffness of the nanotube reinforced composite laminate in the shear direction in the principal coordinate system, Q 12 is the coupling stiffness of the nanotube reinforced composite laminate in the (1, 2) direction in the principal coordinate system, Q 16 is the coupling stiffness between the 1 direction and the shear direction of the nanotube reinforced composite laminate in the principal coordinate system, Q 26 is the coupling stiffness between the 2 direction and the shear direction of the nanotube reinforced composite laminate in the principal coordinate system; [T] σ is the stress transformation matrix between the principal coordinate system and the fiber coordinate system of the nanotube reinforced composite laminate, θ is the angle between the length direction and the fiber direction of the carbon nanotube reinforced composite laminate, counterclockwise is positive; [T] ε is the strain transformation matrix between the principal coordinate system and the fiber coordinate system of the nanotube reinforced composite laminate,

[0023] As a further optimized solution for the damping prediction method of a carbon nanotube reinforced composite laminate according to the present invention, in step 2), the bending stiffness matrix components of the carbon nanotube reinforced composite laminate are obtained from the stiffness matrix of the carbon nanotube reinforced composite monolayer in the principal coordinate system as follows:

[0024]

[0025] In the formula, D ij is the bending stiffness matrix component of the carbon nanotube reinforced composite laminate. 1, 2, and 6 respectively represent the length direction, width direction, and in-plane shear direction of the carbon nanotube reinforced composite monolayer in the principal coordinate system. K is the total number of layers of the carbon nanotube reinforced composite laminate. (Q ij ) k is the stiffness matrix component of the k-th layer of carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the principal coordinate system. z k , z k-1 respectively represent the distances from the upper and lower surfaces of the k-th layer of carbon nanotube reinforced composite monolayer to the middle surface of the carbon nanotube reinforced composite laminate.

[0026] As a further optimized solution for the damping prediction method of a carbon nanotube reinforced composite laminate according to the present invention, the detailed steps of step 3) are as follows:

[0027] Step 3.1), when there is only an in-plane bending moment M in the 1 direction in the principal coordinate system for the in-plane bending moment of the carbon nanotube reinforced composite laminate, the strains of the k-th layer of carbon nanotube reinforced composite monolayer in the principal coordinate system in the carbon nanotube reinforced composite laminate are respectively obtained from the bending stiffness matrix of the laminate:

[0028]

[0029] In the formula, ε1 k , ε2 k , ε6 k are respectively the strains in the 1 direction, 2 direction, and shear direction of the k-th layer of carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the principal coordinate system. M is the in-plane moment in the 1 direction;

[0030] Step 3.2), the stresses in the three directions of the k-th layer of carbon nanotube reinforced composite monolayer in the principal coordinate system are obtained from the stiffness matrix of the carbon nanotube reinforced composite monolayer in the principal coordinate system:

[0031]

[0032] In the formula, are respectively the stresses of the k-th carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the 1-direction, 2-direction, and shear direction in the principal coordinate system;

[0033] Step 3.3), obtain the stresses and strains of the k-th carbon nanotube reinforced composite monolayer in the fiber coordinate system according to the stress transformation matrix and strain transformation matrix between the principal coordinate system and the fiber coordinate system of the carbon nanotube reinforced composite monolayer:

[0034]

[0035] In the formula, are respectively the stresses of the k-th carbon nanotube reinforced composite monolayer in the fiber direction, perpendicular to the fiber direction, and shear direction in the fiber coordinate system in the carbon nanotube reinforced composite laminate, are respectively the strains of the k-th carbon nanotube reinforced composite monolayer in the fiber direction, perpendicular to the fiber direction, and shear direction in the fiber coordinate system in the carbon nanotube reinforced composite laminate.

[0036] As a further optimization scheme of the damping prediction method for a carbon nanotube reinforced composite laminate of the present invention, the detailed steps of step 4) are as follows:

[0037] Step 4.1), use the specific damping capacities of the carbon nanotube reinforced composite monolayer in the fiber direction, perpendicular to the fiber direction, and shear direction to characterize the energy dissipation of the monolayer, and obtain the dissipated energy and strain energy of the carbon nanotube reinforced composite monolayer per unit width according to the specific damping capacities in the three directions as follows:

[0038]

[0039] In the formula, ΔU k and U k are respectively the dissipated energy and strain energy of the k-th monolayer in the carbon nanotube reinforced composite laminate per unit width, ψ x and ψ y are respectively the specific damping capacities of the carbon nanotube reinforced composite monolayer along the fiber direction and perpendicular to the fiber direction, ψ xy is the specific damping capacity of the carbon nanotube reinforced composite monolayer in the shear direction, and L and h are respectively the length and thickness of the carbon nanotube reinforced composite laminate;

[0040] Step 4.2), sum up the dissipated energy and strain energy of each carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate to obtain the damping of the carbon nanotube reinforced composite laminate in one vibration period as

[0041]

[0042] In the formula, ξ and K are the damping and the total number of plies of the carbon nanotube reinforced composite laminate, respectively.

[0043] Compared with the prior art by adopting the above technical solution, the present invention has the following technical effects:

[0044] By using the method of the present invention, the damping of the carbon nanotube reinforced composite laminate with a carbon nanotube mass fraction of 3% and a carbon fiber ply arrangement of [0° / 90° / 0°] 2s is calculated to be 1.73%, which is within the damping range of general composite laminates, indicating that the method can predict the damping of the composite laminate with added carbon nanotubes, and provides an engineering prediction method for the damping prediction of carbon nanotube reinforced composite laminates. Brief Description of the Drawings

[0045] Figure 1 Schematic diagram of the fiber coordinate system and the principal coordinate system of a single layer of carbon nanotube reinforced composite;

[0046] Figure 2 Schematic diagram of the plane stress of a single layer of carbon nanotube reinforced composite;

[0047] Figure 3 Schematic diagram of the force on a carbon nanotube reinforced composite laminate. Detailed Description of the Invention

[0048] The technical solution of the present invention will be further described in detail below with reference to the drawings:

[0049] The present invention can be implemented in many different forms and should not be construed as limited to the embodiments described herein. On the contrary, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0050] The present invention provides a method for predicting the damping of a carbon nanotube reinforced composite laminate. Taking the application of this method to a terminal as an example, it includes the following steps:

[0051] Step 1), as Figure 1 shown, taking the fiber direction of a single layer of carbon nanotube reinforced composite as the x-axis, the direction perpendicular to the fiber as the y-axis, and the plate thickness direction as the z-axis, establish the fiber coordinate system (x, y, z) of a single layer of carbon nanotube reinforced composite; taking the length direction of a single layer of carbon nanotube reinforced composite as the 1-axis, the width direction as the 2-axis, and the plate thickness direction as the 3-axis, establish the principal coordinate system (1, 2, 3) of a single layer of carbon nanotube reinforced composite.

[0052] As Figure 2As shown, according to the classical laminated plate theory, since the single layer of carbon nanotube-reinforced composite material is thin enough, it is assumed that there is a plane stress state within each layer, that is, there is no stress in the thickness direction (z direction) of the single layer of carbon nanotube-reinforced composite material, and all stress components exist only in the (x, y) plane. Based on the plane stress state assumption, the stress-strain relationship of the single layer of carbon nanotube-reinforced composite material in the fiber coordinate system is obtained, and the expression of the stress-strain relationship is

[0053]

[0054] In the formula, σ xx 、σ yy 、σ xy are the stresses of the single layer of carbon nanotube-reinforced composite material in the x direction, y direction, and shear direction in the (x, y) plane respectively, ε xx 、ε yy 、ε xy are the strains of the single layer of carbon nanotube-reinforced composite material in the x direction, y direction, and shear direction in the (x, y) plane respectively, Q xx and Q yy are the stiffnesses of the single layer of carbon nanotube-reinforced composite material in the x and y directions respectively, Q xy is the coupling stiffness of the single layer of carbon nanotube-reinforced composite material in the (x, y) direction, and Q ss is the shear stiffness of the single layer of carbon nanotube-reinforced composite material.

[0055] According to the elastic modulus and shear modulus of the single layer of carbon nanotube-reinforced composite material, each component of the stiffness matrix of the single layer of carbon nanotube-reinforced composite material in the fiber coordinate system is obtained, and the expression of each component of the stiffness matrix is

[0056] Q ss =G xy ;

[0057] In the formula, E x and E y are the elastic moduli of the single layer of carbon nanotube-reinforced composite material in the x and y directions respectively, G xy and v xy are the shear modulus and Poisson's ratio of the single layer of carbon nanotube-reinforced composite material respectively.

[0058] According to the stress transformation matrix and strain transformation matrix between the fiber coordinate system and the principal coordinate system of the single layer of carbon nanotube-reinforced composite material, the stiffness matrix of the single layer of carbon nanotube-reinforced composite material in the fiber coordinate system is transformed into the stiffness matrix in the principal coordinate system, and the expression of the stiffness matrix in the principal coordinate system is

[0059]

[0060] In the formula, Q 11 and Q 22 are the stiffnesses of the nanotube-reinforced composite laminate in the 1 and 2 directions in the principal coordinate system respectively, Q 66 is the stiffness of the nanotube-reinforced composite laminate in the shear direction in the principal coordinate system, Q 12 is the coupling stiffness of the nanotube-reinforced composite laminate in the (1, 2) direction in the principal coordinate system, Q 16 is the coupling stiffness between the 1 direction and the shear direction of the nanotube-reinforced composite laminate in the principal coordinate system, Q 26 is the coupling stiffness between the 2 direction and the shear direction of the nanotube-reinforced composite laminate in the principal coordinate system. [T] σ is the stress transformation matrix between the principal coordinate system and the fiber coordinate system of the nanotube-reinforced composite laminate, [T] ε is the strain transformation matrix between the principal coordinate system and the fiber coordinate system of the nanotube-reinforced composite laminate, and its specific expression is

[0061]

[0062] In the formula, θ is the angle between the length direction and the fiber direction of the carbon nanotube-reinforced composite laminate, and it is stipulated that counterclockwise is positive.

[0063] Step 2), according to the stiffness matrix of the carbon nanotube-reinforced composite laminate in the principal coordinate system, obtain the bending stiffness matrix components of the carbon nanotube-reinforced composite laminate. The expression of the bending stiffness matrix components is

[0064]

[0065] In the formula, D ij is the bending stiffness matrix component of the carbon nanotube-reinforced composite laminate. 1, 2, and 6 respectively represent the length direction, width direction, and in-plane shear direction of the carbon nanotube-reinforced composite laminate in the principal coordinate system. K is the total number of layers of the carbon nanotube-reinforced composite laminate. (Q ij ) k is the stiffness matrix component of the k-th layer of carbon nanotube-reinforced composite laminate in the carbon nanotube-reinforced composite laminate in the principal coordinate system. z k , z k-1 respectively represent the distances from the upper and lower surfaces of the k-th layer of carbon nanotube-reinforced composite laminate to the middle surface of the carbon nanotube-reinforced composite laminate.

[0066] Step 3), as Figure 3As shown, when there is only an in-plane bending moment in the 1-direction in the carbon nanotube-reinforced composite laminate, according to the classical Kirchhoff hypothesis, the normal of the undeformed plane in the laminate remains normal and undeformed in the deformed plane, the thickness of the laminate remains unchanged during the deformation process, the thickness of the plate is much smaller than its deflection, and the geometric nonlinear effect during the deformation can be ignored. At this time, the in-plane strain in the carbon nanotube-reinforced composite laminate is a linear function of the thickness. To facilitate the analysis of the strain in each layer, the middle strain of each layer is taken as the average strain of that layer. According to the bending stiffness matrix of the carbon nanotube-reinforced composite laminate, the strains of the k-th layer of carbon nanotube-reinforced composite single-ply in the carbon nanotube-reinforced composite laminate are respectively

[0067]

[0068] In the formula, are respectively the strains of the k-th layer of carbon nanotube-reinforced composite single-ply in the carbon nanotube-reinforced composite laminate in the 1-direction, 2-direction, and shear direction in the principal coordinate system, and M is the in-plane moment in the 1-direction.

[0069] According to the stiffness matrix of the carbon nanotube-reinforced composite single-ply in the principal coordinate system, the stress expressions in three directions of the k-th layer of carbon nanotube-reinforced composite single-ply are

[0070]

[0071] In the formula, are respectively the stresses of the k-th layer of carbon nanotube-reinforced composite single-ply in the carbon nanotube-reinforced composite laminate in the 1-direction, 2-direction, and shear direction in the principal coordinate system.

[0072] According to the stress transformation matrix and strain transformation matrix between the principal coordinate system and the fiber coordinate system of the carbon nanotube-reinforced composite single-ply, the stresses and strains of the k-th layer of carbon nanotube-reinforced composite single-ply in the fiber coordinate system are obtained, and the expressions of the stresses and strains are

[0073]

[0074]

[0075] In the formula, are respectively the stresses of the k-th layer of carbon nanotube-reinforced composite single-ply in the carbon nanotube-reinforced composite laminate in the fiber direction, perpendicular to the fiber direction, and shear direction in the fiber coordinate system, are respectively the strains of the k-th layer of carbon nanotube-reinforced composite single-ply in the carbon nanotube-reinforced composite laminate in the fiber direction, perpendicular to the fiber direction, and shear direction in the fiber coordinate system.

[0076] Step 4), the specific damping capacity of the carbon nanotube reinforced composite monolayer in the fiber direction, perpendicular to the fiber direction, and shear direction is used to characterize the energy dissipation of the carbon nanotube reinforced composite monolayer. Combining the specific damping capacity in the three directions with the stress and strain of each monolayer of the carbon nanotube reinforced composite, the dissipated energy and strain energy of the carbon nanotube reinforced composite monolayer per unit width are obtained. The expressions for the dissipated energy and strain energy are respectively

[0077]

[0078] where ΔU k and U k are respectively the dissipated energy and strain energy of the k-th layer of the carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate per unit width. ψ x and ψ y are respectively the specific damping capacity of the carbon nanotube reinforced composite monolayer in the fiber direction and perpendicular to the fiber direction. ψ xy is the specific damping capacity of the carbon nanotube reinforced composite monolayer in the shear direction. L and h are respectively the length and thickness of the carbon nanotube reinforced composite laminate.

[0079] By summing up the dissipated energy and strain energy of each carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate, the damping of the carbon nanotube reinforced composite laminate in one vibration period is obtained as

[0080]

[0081] where ξ and K are respectively the damping and the total number of plies of the carbon nanotube reinforced composite laminate.

[0082] Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms used herein (including technical terms and scientific terms) have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as such here.

[0083] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A damping prediction method for a carbon nanotube reinforced composite laminate, characterized in that, The steps are as follows: Step 1), establish the fiber coordinate system and the principal coordinate system of the carbon nanotube reinforced composite monolayer plate, and obtain the stiffness matrix of the carbon nanotube reinforced composite monolayer plate in the principal coordinate system according to the stress-strain relationship of the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system; Step 2), obtain the bending stiffness matrix of the carbon nanotube reinforced composite laminate according to the stiffness matrix of the carbon nanotube reinforced composite monolayer plate in the principal coordinate system; Step 3), according to the force condition of the carbon nanotube reinforced composite laminate, combine the bending stiffness matrix of the carbon nanotube reinforced composite laminate to obtain the stress and strain of each monolayer plate of the carbon nanotube reinforced composite laminate in the principal coordinate system, and convert them into the stress and strain in the fiber coordinate system according to the stress-strain relationship of the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system; Step 4), according to the stress and strain of each monolayer plate of the carbon nanotube reinforced composite, combine the specific damping capacities in three directions of the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system to obtain the dissipated energy and strain energy in each carbon nanotube reinforced composite monolayer plate, and sum up each layer to obtain the dissipated energy and strain energy of the carbon nanotube reinforced composite laminate, and further obtain the damping of the carbon nanotube reinforced composite laminate.

2. The damping prediction method of the carbon nanotube reinforced composite laminate according to claim 1, characterized in that, The detailed steps of the said Step 1) are as follows: Step 1.1), take the fiber direction of the carbon nanotube reinforced composite monolayer plate as the x-axis, the direction perpendicular to the fiber as the y-axis, and the plate thickness direction as the z-axis to establish the fiber coordinate system (x, y, z) of the carbon nanotube reinforced composite monolayer plate; Step 1.2), take the length direction of the carbon nanotube reinforced composite monolayer plate as the 1-axis, the width direction as the 2-axis, and the plate thickness direction as the 3-axis to establish the principal coordinate system (1, 2, 3) of the carbon nanotube reinforced composite monolayer plate; Step 1.3), make each carbon nanotube reinforced composite monolayer plate in a plane stress state, that is, there is no stress in the thickness direction (z direction) of the carbon nanotube reinforced composite monolayer plate, and all stress components only exist in the (x, y) plane; according to the plane stress state assumption, obtain the stress-strain relationship in the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system as follows: Where, σ xx , σ yy , σ xy are the stresses of the carbon nanotube reinforced composite monolayer plate in the x-direction, y-direction, and shear direction in the (x, y) plane, respectively, ε xx , ε yy , ε xy are the strains of the carbon nanotube reinforced composite monolayer plate in the x-direction, y-direction, and shear direction in the (x, y) plane, respectively, Q xx and Q yy are the stiffnesses of the carbon nanotube reinforced composite monolayer plate in the x and y directions, respectively, Q xy is the coupling stiffness of the carbon nanotube reinforced composite monolayer plate in the (x, y) direction, and Q ss is the shear stiffness of the carbon nanotube reinforced composite monolayer plate; Step 1.4), according to the elastic modulus and shear modulus of the carbon nanotube reinforced composite monolayer plate, obtain the components of the stiffness matrix of the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system as follows: Where, E x and E y are the elastic moduli of the carbon nanotube reinforced composite laminate in the x and y directions respectively, G xy and v xy are the shear modulus and Poisson's ratio of the carbon nanotube reinforced composite laminate respectively; Step 1.5), according to the stress transformation matrix and strain transformation matrix between the fiber coordinate system and the principal coordinate system of the carbon nanotube reinforced composite monolayer plate, convert the stiffness matrix of the carbon nanotube reinforced composite monolayer plate in the fiber coordinate system into the stiffness matrix in the principal coordinate system, and the expression of the stiffness matrix in the principal coordinate system is where Q 11 and Q 22 are the stiffnesses of the nanotube-reinforced composite laminate in the 1 and 2 directions in the principal coordinate system, respectively, Q 66 is the shear stiffness of the nanotube-reinforced composite laminate in the principal coordinate system, Q 12 is the coupling stiffness of the nanotube-reinforced composite laminate in the (1, 2) direction in the principal coordinate system, Q 16 is the coupling stiffness between the 1 direction and the shear direction of the nanotube-reinforced composite laminate in the principal coordinate system, Q 26 is the coupling stiffness between the 2 direction and the shear direction of the nanotube-reinforced composite laminate in the principal coordinate system; [T] σ is the stress transformation matrix of the nanotube-reinforced composite laminate between the principal coordinate system and the fiber coordinate system, θ is the angle between the length direction and the fiber direction of the carbon nanotube-reinforced composite laminate, positive in the counterclockwise direction; [T] ε is the strain transformation matrix of the nanotube-reinforced composite laminate between the principal coordinate system and the fiber coordinate system, 3. The damping prediction method of the carbon nanotube reinforced composite laminate according to claim 2, characterized in that, The components of the bending stiffness matrix of the carbon nanotube reinforced composite laminate obtained according to the stiffness matrix of the carbon nanotube reinforced composite monolayer plate in the principal coordinate system in the said Step 2) are as follows: In the formula, D ij is the bending stiffness matrix component of the carbon nanotube reinforced composite laminate. 1, 2, and 6 respectively represent the length direction, width direction, and in-plane shear direction of the carbon nanotube reinforced composite monolayer in the principal coordinate system. K is the total number of monolayers of the carbon nanotube reinforced composite laminate. (Q ij ) k is the stiffness matrix component of the k-th layer of carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the principal coordinate system. z k , z k-1 respectively represent the distances from the upper and lower surfaces of the k-th layer of carbon nanotube reinforced composite monolayer to the middle surface of the carbon nanotube reinforced composite laminate.

4. The damping prediction method of the carbon nanotube reinforced composite laminate according to claim 3, characterized in that The detailed steps of the said Step 3) are as follows: Step 3.1), when there is only an in-plane bending moment M in the 1-direction of the principal coordinate system for the in-plane bending moment of the carbon nanotube reinforced composite laminate, the strains of the k-th layer of carbon nanotube reinforced composite single ply in the principal coordinate system within the carbon nanotube reinforced composite laminate are obtained according to the bending stiffness matrix of the laminate: In the formula, are the strains of the k-th carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the 1-direction, 2-direction, and shear direction in the principal coordinate system, respectively. M is the in-plane moment in the 1-direction. Step 3.2), the stresses in the three directions of the k-th layer of carbon nanotube reinforced composite single ply in the principal coordinate system are obtained according to the stiffness matrix of the carbon nanotube reinforced composite single ply in the principal coordinate system: In the formula, are the stresses of the k-th carbon nanotube reinforced composite monolayer in the carbon nanotube reinforced composite laminate in the 1-direction, 2-direction, and shear direction in the principal coordinate system, respectively. Step 3.3), the stresses and strains of the k-th layer of carbon nanotube reinforced composite single ply in the fiber coordinate system are obtained according to the stress transformation matrix and strain transformation matrix between the principal coordinate system and the fiber coordinate system of the carbon nanotube reinforced composite single ply: wherein, are the stresses in the fiber direction, perpendicular to the fiber direction, and shear direction of the k-th carbon nanotube reinforced composite ply in the carbon nanotube reinforced composite laminate in the fiber coordinate system, respectively, are the strains in the fiber direction, perpendicular to the fiber direction, and shear direction of the k-th carbon nanotube reinforced composite ply in the carbon nanotube reinforced composite laminate in the fiber coordinate system, respectively.

5. The damping prediction method of the carbon nanotube reinforced composite laminate according to claim 4, characterized in that The detailed steps of the said Step 4) are as follows: Step 4.1), the specific damping capacity of the carbon nanotube reinforced composite single ply in the fiber direction, perpendicular to the fiber direction, and shear direction is used to characterize the energy dissipation of the single ply. The dissipated energy and strain energy of the carbon nanotube reinforced composite single ply per unit width are obtained according to the specific damping capacity in the three directions as follows: where ΔU k and U k are the dissipated energy and strain energy of the k-th ply in the carbon nanotube reinforced composite per unit width laminate, respectively, and ψ x and ψ y are the specific damping capacities of the carbon nanotube reinforced composite ply along the fiber direction and perpendicular to the fiber direction, respectively, ψ xy is the specific damping capacity of the carbon nanotube reinforced composite ply in the shear direction, and L and h are the length and thickness of the carbon nanotube reinforced composite laminate, respectively; Step 4.2), the dissipated energy and strain energy of each carbon nanotube reinforced composite single ply within the carbon nanotube reinforced composite laminate are summed up to obtain the damping of the carbon nanotube reinforced composite laminate within one vibration period as where ξ and K are respectively the damping of the carbon nanotube reinforced composite laminate and the total number of plies.

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