Vibration forecasting modeling method for ring rib cone-column combined shell

Abstract

The invention relates to a vibration forecasting modeling method for a ring rib cone-column combined shell, which comprises the following steps of: deducing a dynamic stiffness matrix of a conical shell from basic conical shell vibration response solution, degenerating the conical shell into a cylindrical shell and an annular plate by changing a cone vertex angle of the conical shell, and then, carrying out vibration forecasting modeling on the cylindrical shell and the annular plate by taking the conical shell, the annular plate and the cylindrical shell as basic substructures. The method comprises the following steps of: splicing a plurality of substructure shells by utilizing the conditions of displacement continuity and internal force balance on a splicing surface of the combined shell to form an overall dynamic stiffness matrix of the combined shell under a global coordinate system, and forecasting the inherent frequency and vibration response of the combined shell by utilizing the dynamic stiffness matrix.

Description

Technical Field

[0001] The invention relates to the technical field of vibration prediction modeling methods, in particular to a vibration prediction modeling method for a ring-ribbed cone-column combined shell. Background Art

[0002] Combined shells are typical components in the structures of submarines, aircraft, rockets and other equipment. Due to the internal equipment excitation and the influence of the external environment, long-term excessive vibration and noise can cause fatigue damage to the combined shell, which can lead to huge economic losses or disasters. Therefore, in order to avoid resonance between the natural frequency of the combined shell itself and the excitation frequency of the equipment, the vibration characteristics of the combined shell need to be predicted in the combined shell design stage for reference by relevant combined shell designers.

[0003] Common methods for calculating combined shells in the prior art include Anasys, Abaqus, etc., but their vibration and noise calculations require a lot of manual experience, and different combined shell models need to be remodeled, which is cumbersome, time-consuming, labor-intensive, and low in precision. The present invention is based on an accurate analytical calculation method, is easy to implement through programming, has the advantages of parametric modeling, simple modeling process, and high calculation efficiency. Summary of the invention

[0004] In view of the shortcomings in the above-mentioned existing production technology, the applicant provides a vibration prediction modeling method for a ring-ribbed cone-column combined shell, so that rapid vibration prediction of the combined shell structure can be achieved through programming, and the prediction evaluation results can provide a reference for the vibration and noise reduction design of the relevant combined shell structure.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A vibration prediction modeling method for ring-stiffened cone-cylinder composite shell.

[0007] Confirm the governing equations for vibration of conical shells:

[0008]

[0009] In the above formula, u c , v c and w c They are the axial, tangential and radial displacements of the conical shell, and each section includes four u c , v c , w c and Four displacement variables; N c , M c , T c and S c Four internal force variables;

[0010] in, and is the partial differential coefficient in the vibration control equation of the conical shell. The specific expression is as follows:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Where: μ is the Poisson's ratio of the cone shell material, ρ is the density of the material, h is the thickness of the cone shell, is the Laplace operator;

[0021] The dynamic model of the conical shell is based on the power series method and is solved using the power series superposition method in the literature. The displacement expressions of the conical shell in three directions can be written as:

[0022]

[0023] Among them: a m , b m , c m is the power series superposition coefficient, m is the power series superposition cutoff number, n is the circumferential mode number of the conical shell, x c is the displacement along the generatrix of the conical shell, θ is the circumferential angle, and by substituting equation (3) into the vibration equation (1) of the conical shell, the recursive relationship between the power series coefficients can be obtained as follows:

[0024]

[0025] When the power series m>0, the coefficients in formula (4) can be expressed by the eight coefficients a0, a1, b0, b1, c0, c1, c2, c3. Therefore, these eight coefficients are also called the displacement basis functions of the conical shell. By combining the above formulas, when the circumferential mode number n is specifically determined, the displacement function expression of the conical shell can be written as:

[0026]

[0027] The coefficient expression in the above formula is:

[0028]

[0029] Substituting equations (5) and (6) into equation (3), the final expression of the conical shell displacement is:

[0030]

[0031] According to the relationship between the intermediate internal force and displacement of the thin shell, the internal force expression on the conical shell section is:

[0032]

[0033] In the above formula:

[0034]

[0035] Substituting equation (7) into the relationship between displacement and internal force, the internal force can also be written as an expression of basis function, and the conical shell boundary x c =-L c and x c =L c The displacement at the two nodes of the conical shell can be regarded as the dynamic stiffness matrix expression at both ends of the 8×8 conical shell:

[0036]

[0037] In the above formula [D C ] is the dynamic stiffness matrix of the conical shell, which is the most basic unit in the combined shell prediction model;

[0038] During the splicing process of the composite shell, the displacement continuity and internal force balance on the splicing surfaces of the two substructure shells are required.

[0039] Its further technical solution is:

[0040] During the splicing process of the conical shell and the cylindrical shell, the three substructure shells of the conical shell, the cylindrical shell and the annular plate can be regarded as two-port structures. Each port edge corresponds to 4 displacement variables and 4 internal force variables. Because the conical shell and the cylindrical shell share one edge, it is necessary to superimpose and splice the dynamic stiffness matrices of the two substructure shells on this edge.

[0041] The structural form of the combined shell is a combined shell with ribs.

[0042] A circular plate ribbed structure or an L-shaped ribbed structure is adopted.

[0043] In the structural form of the combined shell, the dynamic stiffness matrix of the conical shell is used as the basis for variable assembly, and eight structures are obtained by degenerating by changing the cone top angles of the two conical shells and the thickness of the conical shells.

[0044] According to the substructure theory, the combined shell is divided into five substructure shells, namely:

[0045] Outer cylindrical shell;

[0046] A circular ring plate connecting the two cylindrical shells;

[0047] Inner cylindrical shell;

[0048] Conical shell in composite shell;

[0049] The rib part in the ribbed cylindrical shell;

[0050] Starting from the most basic conical shell foundation, through formula (10), the dynamic stiffness matrices of the five substructure shells are obtained, namely D1, D2, D3, D4, and D5. Then, using the boundary conditions at the connection points of the five substructure shells, they are assembled into a complex shell structure.

[0051] The beneficial effects of the present invention are as follows:

[0052] The present invention is a combined shell vibration prediction method based on the spectral element method within the frequency domain. Starting from the solution of the basic cone shell vibration response, the dynamic stiffness matrix of the cone shell is derived. By changing the cone top angle of the cone shell, the cone shell is degenerated into a cylindrical shell and an annular plate. Then, with the cone shell, the annular plate and the cylindrical shell as three basic substructures, multiple substructure shells are spliced ​​by utilizing the displacement continuity and internal force balance conditions on the splicing surface of the combined shell to form an overall dynamic stiffness matrix of the combined shell in the global coordinate system. The dynamic stiffness matrix is ​​utilized to predict the natural frequency and vibration response of the combined shell.

[0053] Through the present invention, rapid vibration prediction of the combined shell structure can be realized through programming, and the prediction evaluation result can provide a reference for the vibration reduction and noise reduction design of the related combined shell structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the force and displacement of the truncated cone shell of the present invention.

[0055] Figure 2 This is a schematic diagram of the present invention when the dynamic stiffness matrices of two substructure shells are superimposed and spliced.

[0056] Figure 3 It is a schematic structural diagram of the external rib of the present invention.

[0057] Figure 4 It is a partial view of the outer rib of the present invention.

[0058] Figure 5 It is a schematic diagram of the structure of the inner rib of the present invention.

[0059] Figure 6 It is a partial view of the inner rib of the present invention.

[0060] Figure 7 It is a schematic diagram of the double-layer ribbed cylindrical shell structure (complex combined shell structure) of the present invention.

[0061] Figure 8 This is a physical picture of the combined shell test model of the present invention.

[0062] Fig. 9 It is a structural schematic diagram of the combined shell test model of the present invention.

[0063] Fig.10 This is a comparison chart (1) of the method used in the present invention and the test results.

[0064] Fig.11 This is a comparison chart (2) of the method used in the present invention and the test results.

[0065] Fig.12 This is a comparison chart of the calculation of the complex combined shell of the present invention using this method and finite element software.

[0066] Fig.13 This is a comparative analysis diagram of the complex combined shell of the present invention using this method and finite element software calculation.

[0067] Fig.14 The present invention changes the angles of the two cone apexes and the thickness of the cone shells, degenerating into eight typical structural diagrams. DETAILED DESCRIPTION

[0068] The specific implementation of the present invention will be described below in conjunction with the accompanying drawings.

[0069] like Figure 1-Figure 13 As shown, a vibration prediction modeling method for a ring-ribbed cone-column combined shell of the present embodiment, cone-column, cone-cone, cone-column-sphere and other combined shells are typical structural components in aviation and underwater vehicles. Long-term vibration will cause fatigue damage of the structure. Therefore, it is necessary to establish a dynamic model of this combined shell to carry out dynamic characteristics analysis.

[0070] The invention is based on the vibration control equation of the conical shell, where the vibration control equation of the conical shell is:

[0071]

[0072] In the above formula, u c , v c and w cThey are the axial, tangential and radial displacements of the conical shell respectively. The force and displacement of the truncated conical shell are shown as follows Figure 1 As shown in the figure, each section includes four u c , v c , w c and Four displacement variables; N c , M c , T c and S c Four internal force variables.

[0073] In formula (1) and is the partial differential coefficient in the vibration control equation of the conical shell. The specific expression is as follows:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] In the above formula, μ is the Poisson's ratio of the conical shell material, ρ is the density of the material, and h is the thickness of the conical shell. is the Laplace operator. The dynamic model of the conical shell is based on the power series method and is solved using the power series superposition method in the literature. The displacement expressions of the conical shell in three directions can be written as:

[0084]

[0085] where a m , b m , c m is the power series superposition coefficient, m is the power series superposition cutoff number, n is the circumferential mode number of the conical shell, x c is the displacement along the generatrix of the conical shell, and θ is the circumferential angle. Substituting equation (3) into the vibration equation (1) of the conical shell, the recursive relationship between the power series coefficients can be obtained as follows:

[0086]

[0087] The specific expression of the recursive coefficient in the above formula can be found in the literature [Caresta]. According to the above recursive relationship, when the power series m>0, the coefficients in formula (4) can be expressed by the eight coefficients a0, a1, b0, b1, c0, c1, c2, c3, so these eight coefficients are also called the displacement basis functions of the conical shell. Combining the above formulas, when the circumferential mode number n is specifically determined, the displacement function expression of the conical shell can be written as:

[0088]

[0089] The coefficient expression in the above formula is:

[0090]

[0091] Substituting equations (5) and (6) into equation (3), the final expression of the conical shell displacement is:

[0092]

[0093] According to the relationship between the intermediate internal force and displacement of the thin shell, the internal force expression on the conical shell section is:

[0094]

[0095] In the above formula:

[0096]

[0097] Substituting equation (7) into the relationship between displacement and internal force, the internal force can also be written as an expression of basis function. c =-L c and x c =L c The displacement at the two nodes of the conical shell is considered as the displacement at the two nodes of the conical shell. The dynamic stiffness matrix expression of the two ends of the 8×8 conical shell can be obtained as follows:

[0098]

[0099] In the above formula [D C ] is the dynamic stiffness matrix of the conical shell, which is the most basic unit in the combined shell prediction model of the present invention. During the splicing process of the combined shell, the displacement continuity and internal force balance on the splicing surface of the two substructure shells are required. Figure 2The typical conical shell and cylindrical shell splicing process shown in FIG. 1 can be regarded as a two-port structure. The three substructure shells of the conical shell, cylindrical shell and annular plate in the present invention can be regarded as two-port structures. Each port side corresponds to 4 displacement variables and 4 internal force variables. Because the conical shell and the cylindrical shell share one side, it is necessary to superimpose the dynamic stiffness matrices of the two substructure shells on this side. Figure 2 as shown in .

[0100] The side ② at the bottom of the conical shell overlaps the side ③ at the top of the cylindrical shell, so the displacement continuity and internal force continuity conditions of the side ② of the conical shell and the side ③ of the cylindrical shell need to be met. The dynamic stiffness matrix of the conical shell is written as a two-port structure, and the dynamic stiffness matrix of the conical shell and the cylindrical shell in the above figure can be written as:

[0101]

[0102] In the above formula, D ij is a 4×4 matrix. Since edges ② and ③ overlap, U2=U3=U * 、F2=F3=F * ,U * is the displacement matrix on the merged splicing edge, F * is the force matrix on the merged splicing edge. The two equations in the above formula (11) are written together as follows:

[0103]

[0104] The splicing of other multiple substructure shells is similar.

[0105] (1) When the truncation angle is not 0°, it is a conical shell structure;

[0106] (2) When the cone apex angle of the conical shell is 0 degrees, the dynamic model of the conical shell can be degenerated into the dynamic model of the cylindrical shell. (3) When the cone apex angle of the conical shell is 90 degrees, the dynamic model of the conical shell can be degenerated into the dynamic model of the annular plate.

[0107] The structural forms of the combined shells in the present invention can be obtained by varying the dynamic stiffness matrix of the conical shells. The present invention mainly uses the cone-conical combined shell structure. By changing the cone top angles of the two conical shells and the thickness of the conical shells, the combined shells can be degenerated into 8 typical structures. Fig.14 .

[0108] In the present invention, the annular plate is used as a ribbed component and is spliced ​​with a conical shell, a cylindrical shell or a combined shell thereof. Figure 3-Figure 7 shown.

[0109] Among them, the complex double-layer combined shell structure first divides the above combined shell into 5 substructure shells according to the substructure theory:

[0110] ① is the outer cylindrical shell;

[0111] ② is the annular plate connecting the two cylindrical shells;

[0112] ③ is the inner cylindrical shell;

[0113] ④ is the conical shell in the combined shell;

[0114] ⑤ is the rib part in the ribbed cylindrical shell.

[0115] Although there are five different shell structures, starting from the most basic conical shell foundation, we can obtain the dynamic stiffness matrices of the five substructure shells as D1, D2, D3, D4, and D5 by using formula (10). Then, by using the boundary conditions at the connection of the five substructure shells, they can be assembled into a complex shell structure.

[0116] In addition to the common circular plate ribbed structure, it can also be expanded to an L-shaped ribbed structure.

[0117] It should be noted that the above-mentioned conical shell dynamic stiffness matrix is ​​derived in its local coordinate system. For example, when splicing multiple combined shell structures, each substructure conical shell structure needs to be converted to the global coordinate system for splicing.

[0118] The combined shell vibration prediction method in the patent of this invention was used to compare with the classical finite element and experimental results, which further proved the correctness of the combined shell calculation method in the present invention.

[0119] The calculation method described in the present invention has the advantages of high calculation effect, fast convergence, easy programming, and parametric law analysis. Compared with traditional commercial finite element software, it does not require repeated modeling and meshing, and only requires the input of a few parameters to achieve parametric modeling. In traditional finite element calculations, it is necessary to divide the combined shell into grids. The size of the grid determines the accuracy of the calculation frequency range. The smaller the grid, the higher the calculation accuracy. However, this requires a lot of time and computing resources. The calculation method proposed in the patent of the present invention has a displacement shape function that strictly satisfies the control equation. An entire conical shell structure only needs to be divided into a whole, and the calculation frequency range can reach the high frequency range.

[0120] The present invention is based on the dynamic stiffness matrix of a conical shell. By changing the cone vertex angle of the conical shell, the conical shell is degenerated into an annular plate or a cylindrical shell, and it is no longer necessary to derive the vibration control equation of the annular plate or the cylindrical shell again, which greatly reduces the number of parameters for modeling and calculation, and reduces the theoretical derivation process of the cylindrical shell and the annular plate. Then, the equilibrium and continuity conditions at the connection section of the combined shell are used to splice the overall dynamic stiffness matrix of the combined shell, which can include a total of 8 combined shell structure forms.

[0121] The structural form of the simulated rib plus rib of the present invention can be applied to the outer rib form, the inner rib form and the double-layer shell structure of the combined shell structure.

[0122] The above description is an explanation of the present invention, not a limitation of the present invention. The scope of the present invention is defined in the claims. Any form of modification may be made within the scope of protection of the present invention.

Claims

1. A vibration prediction modeling method for a ring-stiffened cone-column composite shell, characterized in that: Confirm the governing equations for vibration of conical shells: In the above formula, u c , v c and w c They are the axial, tangential and radial displacements of the conical shell, and each section includes four u c , v c , w c and Four displacement variables; N c , M c , T c and S c Four internal force variables; in, and is the partial differential coefficient in the vibration control equation of the conical shell. The specific expression is as follows: Where: μ is the Poisson's ratio of the cone shell material, ρ is the density of the material, h is the thickness of the cone shell, is the Laplace operator; The dynamic model of the conical shell is based on the power series method and is solved using the power series superposition method in the literature. The displacement expressions of the conical shell in three directions can be written as: Among them: a m , b m , c m is the power series superposition coefficient, m is the power series superposition cutoff number, n is the circumferential mode number of the conical shell, x c is the displacement along the generatrix of the conical shell, θ is the circumferential angle, and by substituting equation (3) into the vibration equation (1) of the conical shell, the recursive relationship between the power series coefficients can be obtained as follows: When the power series m>0, the coefficients in formula (4) can be expressed by the eight coefficients a0, a1, b0, b1, c0, c1, c2, c3. Therefore, these eight coefficients are also called the displacement basis functions of the conical shell. By combining the above formulas, when the circumferential mode number n is specifically determined, the displacement function expression of the conical shell can be written as: The coefficient expression in the above formula is: Substituting equations (5) and (6) into equation (3), the final expression of the conical shell displacement is: According to the relationship between the intermediate internal force and displacement of the thin shell, the internal force expression on the conical shell section is: In the above formula: Substituting equation (7) into the relationship between displacement and internal force, the internal force can also be written as an expression of basis function, and the conical shell boundary x c =-L c and x c =L c The displacement at the two nodes of the conical shell can be regarded as the dynamic stiffness matrix expression at both ends of the 8×8 conical shell: In the above formula [D C ] is the dynamic stiffness matrix of the conical shell, which is the most basic unit in the combined shell prediction model; During the splicing process of the composite shell, the displacement continuity and internal force balance on the splicing surfaces of the two substructure shells are required.

2. The vibration prediction modeling method of a ring-stiffened cone-column composite shell according to claim 1, characterized in that: During the splicing process of the conical shell and the cylindrical shell, the three substructure shells of the conical shell, the cylindrical shell and the annular plate can be regarded as two-port structures. Each port edge corresponds to 4 displacement variables and 4 internal force variables. Because the conical shell and the cylindrical shell share one edge, it is necessary to superimpose and splice the dynamic stiffness matrices of the two substructure shells on this edge.

3. The vibration prediction modeling method of a ring-stiffened cone-column composite shell according to claim 1, characterized in that: The structural form of the combined shell is a combined shell with ribs.

4. The vibration prediction modeling method of a ring-stiffened cone-column composite shell according to claim 3, characterized in that: A circular plate ribbed structure or an L-shaped ribbed structure is adopted.

5. The vibration prediction modeling method of a ring-stiffened cone-column composite shell according to claim 1, characterized in that: In the structural form of the combined shell, the dynamic stiffness matrix of the conical shell is used as the basis for variable assembly, and eight structures are obtained by degenerating by changing the cone top angles of the two conical shells and the thickness of the conical shells.

6. The vibration prediction modeling method of a ring-stiffened cone-column composite shell according to claim 5, characterized in that: According to the substructure theory, the combined shell is divided into five substructure shells, namely: Outer cylindrical shell; A circular ring plate connecting the two cylindrical shells; Inner cylindrical shell; Conical shell in composite shell; The rib part in the ribbed cylindrical shell; Starting from the most basic conical shell foundation, through formula (10), the dynamic stiffness matrices of the five substructure shells are obtained, namely D1, D2, D3, D4, and D5. Then, using the boundary conditions at the connection points of the five substructure shells, they are assembled into a complex shell structure.

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