CN113139305A - Structural damping design method of composite propeller - Google Patents

Structural damping design method of composite propeller Download PDF

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CN113139305A
CN113139305A CN202010051879.8A CN202010051879A CN113139305A CN 113139305 A CN113139305 A CN 113139305A CN 202010051879 A CN202010051879 A CN 202010051879A CN 113139305 A CN113139305 A CN 113139305A
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damping
composite material
composite
modal
strain
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洪毅
贺博
刘文博
王荣国
赫晓东
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

The invention relates to a structural damping design method of a composite propeller. The method comprises the steps of predicting the numerical value of the full-band composite damping, and determining the material specific damping coefficient under each order of fixed frequency; establishing a finite element model of the propeller blade made of the composite material, and determining modal damping of the propeller made of the composite material; and determining the composite material propeller structure damping. The vibration calculation and evaluation of the composite material propeller can be well completed, and the design of the damping composite material propeller with an adjustable structure is realized; the method is simple and easy to implement, can greatly reduce the development cost of the composite material propeller, and meets the actual use requirement of the composite material propeller. The invention effectively controls the tail shaft vibration phenomenon induced by the composite propeller.

Description

Structural damping design method of composite propeller
Technical Field
The invention relates to the technical field of composite propeller structure damping design, in particular to a composite material propeller structure damping design method.
Background
As a power plant for underwater high-speed operation, the dynamic characteristics of composite propellers are an important issue that must be paid attention to during the research process. On one hand, the underwater wet modal characteristics (natural frequency, modal shape and the like) of the composite propeller blade need to be known, and a foundation is provided for the dynamic frequency modulation design and the water elasticity analysis of the composite propeller; on the other hand, in order to effectively control the vibration of the composite propeller, the structural damping (main structural dynamic performance parameters) of the composite propeller blade needs to be considered in the design process, so that the structural damping of the blade is increased as much as possible, the vibration excitation is reduced, and the radiation noise is reduced while the structural and functional requirements of the composite propeller are ensured, thereby realizing the design goal of structure/damping integration.
As known from relevant documents at home and abroad, the past researches on the dynamic characteristics of the composite material blade mostly surround the analysis of natural frequency and modal shape, and the setting of the damping parameters usually adopts empirical values. However, for the novel underwater composite material structure of the composite material propeller blade for the ship, no relevant test or actual measurement data provides a basis for the dynamic analysis of the composite material propeller blade. Therefore, the invention provides a numerical calculation and evaluation method of the structural damping of the composite propeller blade according to the structural characteristics of the composite propeller, so that the composite propeller blade with adjustable structural damping for the ship is designed according to the application requirements of different ships, and the composite propeller blade can meet the requirements of strength and hydrodynamic performance and effectively control the tail shaft vibration induced by the composite propeller blade.
Disclosure of Invention
The invention provides a structural damping design method of a composite propeller, aiming at realizing the regulation and control design of the structural damping of a composite propeller blade and effectively controlling the tail shaft vibration phenomenon induced by the composite propeller, and the invention provides the following technical scheme:
1. a structural damping design method of a composite propeller is characterized by comprising the following steps: the method comprises the following steps:
step 1: predicting the value of the full-band composite damping, and determining the material specific damping coefficient under each order of fixed frequency;
step 2: establishing a finite element model of the propeller blade made of the composite material, and determining modal damping of the propeller made of the composite material;
and step 3: determining the structural damping of the composite propeller, wherein the step 3 specifically comprises the following steps:
step 3.1: the damping matrix of the structure is represented by a function of a mass matrix and a stiffness matrix, the damping matrix is determined according to a mass ratio damping factor and a stiffness ratio damping factor, and the damping matrix is represented by the following formula:
C＝αM+βK (1)
wherein, alpha is a mass ratio damping factor, and beta is a stiffness ratio damping factor;
step 3.2: calculating the average damping coefficient according to the modal damping coefficients of the composite material blade under different modes
Figure BDA0002371463440000021
And acquiring corresponding frequency
Figure BDA0002371463440000022
The average modal damping is obtained by multiplying the frequency and damping coefficient of each order of modal by a weight of 0.7, 0.1, 0.1, 0.1, respectively, using a weighted average method to obtain an average modal damping of
Figure BDA0002371463440000023
The average modal damping obtained by the average calculation is
Figure BDA0002371463440000024
Step 3.3: determining a mass specific damping factor alpha and a stiffness specific damping factor beta according to the average modal damping and the corresponding frequency, and determining the mass specific damping factor alpha and the stiffness specific damping factor beta according to the following formulas:
Figure BDA0002371463440000025
Figure BDA0002371463440000026
wherein the content of the first and second substances,
Figure BDA0002371463440000027
and
Figure BDA0002371463440000028
average modal damping coefficients determined for the weighted average and the average calculation, respectively;
Figure BDA0002371463440000029
and
Figure BDA00023714634400000210
calculating a determined average modal frequency for the weighted average and the average;
and taking the mass ratio damping factor and the rigidity ratio damping factor as evaluation parameters of the structural damping of the propeller blade made of the composite material.
Preferably, the step 1 specifically comprises:
step 1.1: establishing a geometric model of the composite material laminated plate sample, and establishing a finite element model of the composite material unidirectional laminated plate by defining unit types and stacking directions and dividing grids;
modal analysis is carried out on the composite material by utilizing a finite element method based on modal strain energy, and the specific damping coefficient psi of the composite material under different frequencies is extractediWherein i ═ 1, … 5 denotes the different material directions of the composite;
step 1.2: according to the specific damping coefficients of the composite material under different frequencies, for the direction of the normal stress of the material, the specific damping coefficient two-dimensional interpolation function of the composite material in the direction of the material is constructed through the specific damping coefficient values under different frequencies, the specific damping coefficient interpolation functions of the composite material in the respective directions are constructed, and the numerical prediction of the specific damping coefficient of the full-band composite material is effectively realized.
Preferably, the step 2 specifically comprises:
step 2.1: the method comprises the following steps of utilizing a finite element method based on modal strain energy to complete modal analysis on the composite propeller blade, extracting strain energy under an arbitrary layer k in an arbitrary layer unit e of the composite propeller blade under a first-order natural frequency of the composite propeller blade, and representing the strain energy through the following formula:
Figure BDA0002371463440000031
wherein σ1And ε1Is the positive stress and strain of the k-th layer,
Figure BDA0002371463440000032
strain energy that is the positive stress and positive strain of the kth layer; sigma2And ε2Is the lateral stress and the lateral strain of the k-th layer,
Figure BDA0002371463440000033
strain energy which is the transverse stress and transverse strain of the kth layer; sigma5And ε5In-plane shear stress and shear strain of the k-th layer,
Figure BDA0002371463440000034
strain energy which is the in-plane shear stress and shear strain of the kth layer; sigma3And gamma3Is the (1,3) plane transverse shear stress and transverse shear strain,
Figure BDA0002371463440000035
the strain energy of the (1,3) plane transverse shear stress and transverse shear strain; sigma4And gamma4Is the transverse shear stress and the transverse shear strain in the (2,3) plane,
Figure BDA0002371463440000036
strain energy which is the transverse shear stress and the transverse shear strain in the (2,3) plane;
step 2.2: when each laminated unit e of the composite blade contains n layers, the calculated strain energy at any k-th layer determines the strain energy component of the unit e in each direction by the following formula:
Figure BDA0002371463440000037
wherein the content of the first and second substances,
Figure BDA0002371463440000038
and
Figure BDA0002371463440000039
in-plane strain energy in the material direction;
Figure BDA00023714634400000310
and
Figure BDA00023714634400000311
transverse shear strain energy in the material direction;
when a composite blade contains m units, then the total strain energy of the blade can be expressed as
Figure BDA00023714634400000312
Wherein U is the total strain energy of the blade;
determining the dissipation energy of the laminated unit e, and expressing the dissipation energy of the laminated unit e by the following formula:
Figure BDA00023714634400000313
wherein, Delta UeIn order to dissipate the energy of the laminated unit e,
Figure BDA00023714634400000314
the longitudinal specific damping coefficient of the kth layer of composite material;
Figure BDA00023714634400000315
is the transverse biresight coefficient;
Figure BDA00023714634400000316
is the in-plane shear Bidamping coefficient;
Figure BDA00023714634400000317
and
Figure BDA00023714634400000318
is the transverse shear specific damping coefficient;
determining a total dissipated energy of the composite propeller blade, the total dissipated energy of the composite propeller blade being represented by:
Figure BDA0002371463440000041
wherein, delta U is the total dissipation energy of the propeller blade made of the composite material;
step 2.3: determining the modal damping coefficient psi of the propeller blade of the composite material according to the total strain energy and the total dissipation energy of the propeller blade of the composite material, and determining the modal damping coefficient of the propeller blade of the composite material according to the following formula:
ψ＝ΔU/U (8)
determining a modal damping loss factor, representing the modal damping loss factor η by:
η＝ψ/2π (9)。
the invention has the following beneficial effects:
the vibration calculation and evaluation of the composite material propeller can be well completed, and the design of the damping composite material propeller with an adjustable structure is realized; the method is simple and easy to implement, can greatly reduce the development cost of the composite material propeller, and meets the actual use requirement of the composite material propeller.
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FIG. 1 is a flow chart of a structural damping design method for a composite propeller.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The first embodiment is as follows:
as shown in fig. 1, the invention provides a structural damping design method of a composite propeller, which comprises the following steps:
step 1: predicting the value of the full-band composite damping, and determining the material specific damping coefficient under each order of fixed frequency;
the step 1 specifically comprises the following steps:
step 1.1: establishing a geometric model of a composite material laminated plate sample, wherein the size is 200mm x 10mm x 2mm, and establishing a finite element model of the composite material unidirectional laminated plate by defining unit types and layering directions and dividing grids;
modal analysis is carried out on the composite material by utilizing a finite element method based on modal strain energy, and the specific damping coefficient psi of the composite material under different frequencies is extractediWherein i ═ 1, … 5 denotes the different material directions of the composite;
step 1.2: according to the specific damping coefficients of the composite material under different frequencies, for the direction of the normal stress of the material, the specific damping coefficient two-dimensional interpolation function of the composite material in the direction of the material is constructed through the specific damping coefficient values under different frequencies, the specific damping coefficient interpolation functions of the composite material in the respective directions are constructed, and the numerical prediction of the specific damping coefficient of the full-band composite material is effectively realized.
Step 2: establishing a finite element model of the propeller blade made of the composite material, and determining modal damping of the propeller made of the composite material;
the step 2 specifically comprises the following steps:
step 2.1: the method comprises the following steps of utilizing a finite element method based on modal strain energy to complete modal analysis on the composite propeller blade, extracting strain energy under an arbitrary layer k in an arbitrary layer unit e of the composite propeller blade under a first-order natural frequency of the composite propeller blade, and representing the strain energy through the following formula:
Figure BDA0002371463440000051
wherein σ1And ε1Is the positive stress and strain of the k-th layer,
Figure BDA0002371463440000052
strain energy that is the positive stress and positive strain of the kth layer; sigma2And ε2Is the lateral stress and the lateral strain of the k-th layer,
Figure BDA0002371463440000053
strain energy which is the transverse stress and transverse strain of the kth layer; sigma5And ε5In-plane shear stress and shear strain of the k-th layer,
Figure BDA0002371463440000054
strain energy which is the in-plane shear stress and shear strain of the kth layer; sigma3And gamma3Is the (1,3) plane transverse shear stress and transverse shear strain,
Figure BDA0002371463440000055
the strain energy of the (1,3) plane transverse shear stress and transverse shear strain; sigma4And gamma4Is the transverse shear stress and the transverse shear strain in the (2,3) plane,
Figure BDA0002371463440000056
strain energy which is the transverse shear stress and the transverse shear strain in the (2,3) plane;
step 2.2: when each laminated unit e of the composite blade contains n layers, the calculated strain energy at any k-th layer determines the strain energy component of the unit e in each direction by the following formula:
Figure BDA0002371463440000057
wherein the content of the first and second substances,
Figure BDA0002371463440000058
and
Figure BDA0002371463440000059
in-plane strain energy in the material direction;
Figure BDA00023714634400000510
and
Figure BDA00023714634400000511
is made of woodTransverse shear strain energy in the material direction;
when a composite blade contains m units, then the total strain energy of the blade can be expressed as
Figure BDA00023714634400000512
Wherein U is the total strain energy of the blade;
determining the dissipation energy of the laminated unit e, and expressing the dissipation energy of the laminated unit e by the following formula:
Figure BDA0002371463440000061
wherein the content of the first and second substances,
Figure BDA0002371463440000062
the longitudinal specific damping coefficient of the kth layer of composite material;
Figure BDA0002371463440000063
is the transverse biresight coefficient;
Figure BDA0002371463440000064
is the in-plane shear Bidamping coefficient;
Figure BDA0002371463440000065
and
Figure BDA0002371463440000066
is the transverse shear specific damping coefficient;
determining a total dissipated energy of the composite propeller blade, the total dissipated energy of the composite propeller blade being represented by:
Figure BDA0002371463440000067
wherein, delta U is the total dissipation energy of the propeller blade made of the composite material;
step 2.3: determining the modal damping coefficient psi of the propeller blade of the composite material according to the total strain energy and the total dissipation energy of the propeller blade of the composite material, and determining the modal damping coefficient of the propeller blade of the composite material according to the following formula:
ψ＝ΔU/U (6)
determining a modal damping loss factor, representing the modal damping loss factor η by:
η＝ψ/2π (7)。
and step 3: and determining the composite material propeller structure damping.
The step 3 specifically comprises the following steps:
step 3.1: the damping matrix of the structure is represented by a function of a mass matrix and a stiffness matrix, the damping matrix is determined according to a mass ratio damping factor and a stiffness ratio damping factor, and the damping matrix is represented by the following formula:
C＝αM+βK (8)
wherein, alpha is a mass ratio damping factor, and beta is a stiffness ratio damping factor;
step 3.2: calculating the average damping coefficient according to the modal damping coefficients of the composite material blade under different modes
Figure BDA0002371463440000068
And acquiring corresponding frequency
Figure BDA0002371463440000069
The average modal damping is obtained by multiplying the frequency and damping coefficient of each order of modal by a weight of 0.7, 0.1, 0.1, 0.1, respectively, using a weighted average method to obtain an average modal damping of
Figure BDA00023714634400000610
The average modal damping obtained by the average calculation is
Figure BDA00023714634400000611
Step 3.3: determining a mass specific damping factor alpha and a stiffness specific damping factor beta according to the average modal damping and the corresponding frequency, and determining the mass specific damping factor alpha and the stiffness specific damping factor beta according to the following formulas:
Figure BDA0002371463440000071
Figure BDA0002371463440000072
wherein the content of the first and second substances,
Figure BDA0002371463440000073
and
Figure BDA0002371463440000074
average modal damping coefficients determined for the weighted average and the average calculation, respectively;
Figure BDA0002371463440000075
and
Figure BDA0002371463440000076
calculating a determined average modal frequency for the weighted average and the average;
and taking the mass ratio damping factor and the rigidity ratio damping factor as evaluation parameters of the structural damping of the propeller blade made of the composite material.
The second embodiment is as follows:
numerical prediction of full-band composite material specific damping coefficient
In order to predict the structural damping of the composite propeller, it is first necessary to predict the full-band specific damping coefficient of the composite material in each direction. The positive stress sigma can be calculated and obtained by constructing the composite material unidirectional laminated plate1Stress σ in the direction and transverse direction2Directional (1,2) in-plane shear stress σ5Directional (1,3) plane transverse shear stress sigma3Directional (2,3) plane transverse shear stress, σ4The specific damping coefficient of the composite material in the direction. The specific implementation method comprises the following steps:
firstly, establishing a geometric model of a composite material laminated plate sample according to the sample size specified by the composite material damping test standard GB/T18258-2000, wherein the size is 200mm by 10mm by 2mm, and establishing a finite element model of the composite material unidirectional laminated plate by defining unit types and stacking directions and dividing grids;
then, modal analysis is carried out on the composite material unidirectional laminated plate sample by using a finite element method based on modal strain energy, and the specific damping coefficient psi of the composite material under different frequencies and different directions is extractedi(i ═ 1, … 5), where i ═ 1, … 5, indicates the different material directions of the composite;
then, for the material positive stress σ1The direction, the two-dimensional interpolation function of the specific damping coefficient of the composite material in the material direction is constructed through the specific damping coefficient values under different frequencies, and the rest four material directions are analogized in sequence, so that the two-dimensional interpolation function of the specific damping coefficient of the composite material in the respective directions can be constructed, and the numerical prediction of the specific damping coefficient of the full-band composite material is effectively realized;
composite blade modal damping
Establishing a finite element model of the propeller blade made of the composite material, wherein the model is composed of a plurality of laminating units, and each laminating unit comprises a plurality of layers;
and carrying out modal analysis on the propeller blade made of the composite material by using a finite element method based on modal strain energy. Under the first-order natural frequency of the composite material blade, the strain energy under the random layering k in the random layering unit e of the composite material blade is extracted by combining the calculation formula (1)
Figure BDA0002371463440000081
Figure BDA0002371463440000082
Figure BDA0002371463440000083
Figure BDA0002371463440000084
Figure BDA0002371463440000085
In the formula, σ1，ε1Is the positive stress and strain of the kth layer; sigma2，ε2Is the lateral stress and the lateral strain of the k-th layer; sigma5，ε5In-plane shear stress and shear strain for the kth layer; sigma3，γ3The (1,3) plane transverse shear stress and transverse shear strain; sigma4，γ4Is the transverse shear stress and transverse shear strain in the (2,3) plane.
When each laminated unit e of the composite blade contains n layers, the strain energy at any k-th layer calculated according to the above formula (1) can be expressed as the strain energy components of the unit e in each direction:
Figure BDA0002371463440000086
in the formula
Figure BDA0002371463440000087
Is the in-plane strain energy associated with the material direction;
Figure BDA0002371463440000088
is the transverse shear strain energy associated with the material direction.
When a composite blade contains m units, then the total strain energy of the blade can be expressed as
Figure BDA0002371463440000089
Correspondingly, the dissipation energy of the laminated unit e can be expressed as
Figure BDA00023714634400000810
In the formula, Δ UeIn order to dissipate the energy of the laminated unit e,
Figure BDA00023714634400000811
the longitudinal specific damping coefficient of the kth layer of composite material;
Figure BDA00023714634400000812
is the transverse biresight coefficient;
Figure BDA00023714634400000813
is the in-plane shear Bidamping coefficient;
Figure BDA00023714634400000814
the transverse shear specific damping coefficient.
The specific damping coefficient can be obtained by calculating by using the two-dimensional interpolation function constructed in the step A: and calculating the obtained natural frequency of each order according to the modal analysis of the composite material blade, and calculating the material specific damping coefficient of each order in each direction under the natural frequency of each order by using the two-dimensional interpolation functions.
Further, the total dissipation energy of a composite propeller blade can be expressed as:
Figure BDA0002371463440000091
by utilizing the acquired total strain energy and total dissipation energy of the composite propeller blade, the modal damping coefficient psi of the composite propeller blade can be obtained by the following calculation:
ψ＝ΔU/U (6)
further, the modal damping loss factor is expressed as:
η＝ψ/2π (7)
for different modal frequencies, the stress and the strain of each layer of the composite propeller blade in each direction are different, so that the modal damping coefficient psi and the modal loss factor eta corresponding to each order of modal frequency are different.
Composite material paddle structure damping
From the dynamic equilibrium equation of the composite propeller blade, the damping matrix of the structure can be regarded as a function of the mass matrix and the stiffness matrix, and is expressed as follows:
C＝αM+βK (8)
wherein alpha is a mass specific damping factor;
beta is the stiffness birthdamping factor.
Thus, for a composite propeller blade, once the mass/stiffness specific damping factor is determined, the structural damping is determined.
Firstly, the modal damping coefficients of the composite material blade under different modes (i is 1,2,3 and 4) calculated in the step B are utilized to calculate the average damping coefficient
Figure BDA0002371463440000092
And obtaining the corresponding frequency
Figure BDA0002371463440000093
Considering that the first order modes have a dominant influence in resonance, one of the average modal damping is obtained by multiplying the frequency and damping coefficient of each order mode by the weight 0.7, 0.1, 0.1, 0.1, respectively, and then using a weighted average method, i.e.
Figure BDA0002371463440000094
While the other average modal damping is obtained by a direct average calculation, i.e.
Figure BDA0002371463440000095
And substituting the average modal damping and the corresponding frequency into a formula (9) to obtain a mass ratio damping factor alpha and a stiffness ratio damping factor beta, and taking the mass ratio damping factor and the stiffness ratio damping factor as evaluation parameters of the structural damping of the propeller blade made of the composite material.
Figure BDA0002371463440000101
Figure BDA0002371463440000102
In the formula (I), the compound is shown in the specification,
Figure BDA0002371463440000103
is the average modal damping coefficient;
Figure BDA0002371463440000104
is the average modal frequency.
The above description is only a preferred embodiment of the structural damping design method for the composite propeller, and the protection scope of the structural damping design method for the composite propeller is not limited to the above embodiments, and all technical solutions belonging to the idea belong to the protection scope of the present invention. It should be noted that modifications and variations which do not depart from the gist of the invention will be those skilled in the art to which the invention pertains and which are intended to be within the scope of the invention.

Claims (3)

1. A structural damping design method of a composite propeller is characterized by comprising the following steps: the method comprises the following steps:
step 1: predicting the value of the full-band composite damping, and determining the material specific damping coefficient under each order of fixed frequency;
step 2: establishing a finite element model of the propeller blade made of the composite material, and determining modal damping of the propeller made of the composite material;
and step 3: determining the structural damping of the composite propeller, wherein the step 3 specifically comprises the following steps:
step 3.1: the damping matrix of the structure is represented by a function of a mass matrix and a stiffness matrix, the damping matrix is determined according to a mass ratio damping factor and a stiffness ratio damping factor, and the damping matrix is represented by the following formula:
C＝αM+βK (1)
wherein, alpha is a mass ratio damping factor, and beta is a stiffness ratio damping factor;
step 3.2: calculating the average damping coefficient according to the modal damping coefficients of the composite material blade under different modes
Figure FDA0002371463430000011
And acquiring corresponding frequency
Figure FDA0002371463430000012
The average modal damping is obtained by multiplying the frequency and damping coefficient of each order of modal by a weight of 0.7, 0.1, 0.1, 0.1, respectively, using a weighted average method to obtain an average modal damping of
Figure FDA0002371463430000013
The average modal damping obtained by the average calculation is
Figure FDA0002371463430000014
Step 3.3: determining a mass specific damping factor alpha and a stiffness specific damping factor beta according to the average modal damping and the corresponding frequency, and determining the mass specific damping factor alpha and the stiffness specific damping factor beta according to the following formulas:
Figure FDA0002371463430000015
Figure FDA0002371463430000016
wherein the content of the first and second substances,
Figure FDA0002371463430000017
and
Figure FDA0002371463430000018
average modal damping coefficients determined for the weighted average and the average calculation, respectively;
Figure FDA0002371463430000019
and
Figure FDA00023714634300000110
calculating a determined average modal frequency for the weighted average and the average;
and taking the mass ratio damping factor and the rigidity ratio damping factor as evaluation parameters of the structural damping of the propeller blade made of the composite material.
2. The method of claim 1, wherein the method comprises the steps of: the step 1 specifically comprises the following steps:
step 1.1: establishing a geometric model of the composite material laminated plate sample, and establishing a finite element model of the composite material unidirectional laminated plate by defining unit types and stacking directions and dividing grids;
modal analysis is carried out on the composite material by utilizing a finite element method based on modal strain energy, and the specific damping coefficient psi of the composite material under different frequencies is extractediWherein i ═ 1, … 5 denotes the different material directions of the composite;
step 1.2: according to the specific damping coefficients of the composite material under different frequencies, for the direction of the normal stress of the material, the specific damping coefficient two-dimensional interpolation function of the composite material in the direction of the material is constructed through the specific damping coefficient values under different frequencies, the specific damping coefficient interpolation functions of the composite material in the respective directions are constructed, and the numerical prediction of the specific damping coefficient of the full-band composite material is effectively realized.
3. The method of claim 1, wherein the method comprises the steps of: the step 2 specifically comprises the following steps:
step 2.1: the method comprises the following steps of utilizing a finite element method based on modal strain energy to complete modal analysis on the composite propeller blade, extracting strain energy under an arbitrary layer k in an arbitrary layer unit e of the composite propeller blade under a first-order natural frequency of the composite propeller blade, and representing the strain energy through the following formula:
Figure FDA0002371463430000021
wherein σ1And ε1Is the positive stress and strain of the k-th layer,
Figure FDA0002371463430000022
strain energy that is the positive stress and positive strain of the kth layer; sigma2And ε2Is the lateral stress and the lateral strain of the k-th layer,
Figure FDA0002371463430000023
strain energy which is the transverse stress and transverse strain of the kth layer; sigma5And ε5In-plane shear stress and shear strain of the k-th layer,
Figure FDA0002371463430000024
strain energy which is the in-plane shear stress and shear strain of the kth layer; sigma3And gamma3Is the (1,3) plane transverse shear stress and transverse shear strain,
Figure FDA0002371463430000025
the strain energy of the (1,3) plane transverse shear stress and transverse shear strain; sigma4And gamma4Is the transverse shear stress and the transverse shear strain in the (2,3) plane,
Figure FDA0002371463430000026
strain energy which is the transverse shear stress and the transverse shear strain in the (2,3) plane;
step 2.2: when each laminated unit e of the composite blade contains n layers, the calculated strain energy at any k-th layer determines the strain energy component of the unit e in each direction by the following formula:
Figure FDA0002371463430000027
wherein the content of the first and second substances,
Figure FDA0002371463430000028
and
Figure FDA0002371463430000029
in-plane strain energy in the material direction;
Figure FDA00023714634300000210
and
Figure FDA00023714634300000211
transverse shear strain energy in the material direction;
when a composite blade contains m units, then the total strain energy of the blade can be expressed as
Figure FDA00023714634300000212
Wherein U is the total strain energy of the blade;
determining the dissipation energy of the laminated unit e, and expressing the dissipation energy of the laminated unit e by the following formula:
Figure FDA0002371463430000031
wherein, Delta UeIn order to dissipate the energy of the laminated unit e,
Figure FDA0002371463430000032
the longitudinal specific damping coefficient of the kth layer of composite material;
Figure FDA0002371463430000033
is the transverse biresight coefficient;
Figure FDA0002371463430000034
is the in-plane shear Bidamping coefficient;
Figure FDA0002371463430000035
and
Figure FDA0002371463430000036
is the transverse shear specific damping coefficient;
determining a total dissipated energy of the composite propeller blade, the total dissipated energy of the composite propeller blade being represented by:
Figure FDA0002371463430000037
wherein, delta U is the total dissipation energy of the propeller blade made of the composite material;
step 2.3: determining the modal damping coefficient psi of the propeller blade of the composite material according to the total strain energy and the total dissipation energy of the propeller blade of the composite material, and determining the modal damping coefficient of the propeller blade of the composite material according to the following formula:
ψ＝ΔU/U (8)
determining a modal damping loss factor, representing the modal damping loss factor η by:
η＝ψ/2π (9)。
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