Method for constructing vibration and wave displacement field of ship hull grillage structure based on dynamic stiffness method
Patent Information
- Application Number
- CN202611013114.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-08
- Publication Date
- 2026-08-21
AI Technical Summary
若缺少专门的位移场构建流程，则难以将动刚度法获得的边界自由度转化为可视化的模态振型、强迫响应场和波传播位移场
[0022]本发明的有益效果是：本发明提供的基于动刚度法的船体板架结构振动与波动位移场构建方法，首先获取目标板架结构在目标分析类型下的整体边界自由度向量，整体边界自由度向量由整体动刚度方程求解得到，然后基于目标板构件的编号和连接拓扑，从整体边界自由度向量中提取目标板构件对应的全局边界自由度子向量，接着根据目标板构件的空间方向，进一步将目标板构件对应的全局边界自由度子向量转换为局部边界自由度向量，最后根据目标板构件对应的局部边界自由度向量确定目标板构件对应的位移场，并将目标板构件对应的位移场映射至全局坐标系，构建目标板架结构对应的位移场，从而实现由目标板架结构在目标分析类型下的整体边界自由度向量到目标板架结构对应的位移场的构建，本发明突破了动刚度法仅以边界自由度表征结构响应的局限，实现了船体板架结构振动与波传播分析中由边界求解结果到板面连续位移场的解析构建，可获得板构件内部任意位置的位移响应及模态/波传播形态。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of dynamic response analysis technology, and in particular to a method for constructing vibration and wave displacement fields of ship hull plate structures based on the dynamic stiffness method. Background Technology
[0002] The construction of vibration and wave displacement fields for ships serves as a bridge between fundamental hull structural mechanics research and engineering noise reduction design, and is crucial for comprehensively improving the acoustic performance of ships. Existing methods generally employ dynamic stiffness analysis or finite element method for analyzing the dynamic response of hull plate structures. Dynamic stiffness analysis can solve for the natural frequencies, forced responses, and wave propagation characteristics of hull plate structures with fewer boundary degrees of freedom, making it suitable for semi-analytical dynamic modeling of hull plate structures. However, traditional dynamic stiffness analysis typically outputs only natural frequencies, response curves, transfer characteristics, or band structures, making it difficult to directly obtain the continuous displacement field at any location within the hull plate structure.
[0003] Displacement cloud in finite element method Figure 1 Generally, the displacements of discrete nodal components are obtained by interpolating element shape functions, and their accuracy depends on the mesh density and element order. Unlike finite element post-processing, the displacement field of plate members in the dynamic stiffness method can be represented by frequency-dependent analytical displacement functions. Without a dedicated displacement field construction process, it is difficult to convert the boundary degrees of freedom obtained by the dynamic stiffness method into visualized mode shapes, forced response fields, and wave propagation displacement fields.
[0004] Therefore, constructing the overall displacement field of vibration and wave of the hull plate structure based on the dynamic stiffness method, and improving the efficiency of dynamic response analysis of the hull plate structure, has become an urgent technical problem to be solved. Summary of the Invention
[0005] In view of this, it is necessary to provide a method for constructing the vibration and wave displacement field of a ship hull plate structure based on the dynamic stiffness method, so as to construct the overall displacement field of the plate structure on the basis of the dynamic stiffness method and improve the efficiency of dynamic response analysis of the plate structure.
[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for constructing the vibration and wave displacement field of a ship hull plate structure based on the dynamic stiffness method, comprising: Obtain the global boundary degree of freedom vector of the target plate frame structure under the target analysis type, which includes free vibration analysis, forced vibration analysis and wave propagation analysis; Based on the numbering and connection topology of the target plate components, extract the global boundary degree of freedom sub-vectors corresponding to the target plate components from the global boundary degree of freedom vectors. The target plate component is any plate component in the target plate frame structure. Based on the spatial orientation of the target plate component, the global boundary degree-of-freedom sub-vectors corresponding to the target plate component are converted into local boundary degree-of-freedom vectors; The displacement field corresponding to the target plate component is determined based on the local boundary degree of freedom vector of the target plate component, and the displacement field corresponding to the target plate component is mapped to the global coordinate system to construct the displacement field corresponding to the target plate frame structure.
[0007] In one possible implementation, obtaining the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type includes: When the target analysis type is free vibration analysis, the global boundary degree of freedom vector is determined based on the singular value decomposition results of the global dynamic stiffness matrix of the target plate frame structure at the natural frequency. When the target analysis type is forced vibration analysis, the global boundary degree of freedom vector is determined based on the global dynamic stiffness equation after applying boundary conditions. When the target analysis type is wave propagation analysis, the global boundary degree of freedom vector is determined based on the Bloch periodic transformation matrix and the boundary degree of freedom vector in Bloch coordinates.
[0008] In one possible implementation, determining the global boundary degree-of-freedom vector based on the singular value decomposition result of the global dynamic stiffness matrix of the target plate frame structure at its natural frequency includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0009] in, Represents the global boundary degree of freedom vector. Representation matrix The Column vector, Indicates the first A singular value, Represents the natural frequency The overall dynamic stiffness matrix at the location, Describes a left singular matrix. Represents a singular value matrix. This represents a right singular matrix.
[0010] In one possible implementation, determining the global boundary degree-of-freedom vector based on the global dynamic stiffness equation after applying boundary conditions includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0011] in, Represents the global boundary degree of freedom vector. This represents the global dynamic stiffness matrix after applying boundary conditions. This represents the external stimulus vector.
[0012] In one possible implementation, determining the global boundary degree-of-freedom vector based on the Bloch periodic transformation matrix and the boundary degree-of-freedom vector in Bloch coordinates includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0013] in, Represents the global boundary degree of freedom vector. Represents the Bloch periodic transformation matrix. This represents the boundary degree of freedom vector in Bloch coordinates.
[0014] In one possible implementation, the step of converting the global boundary degree-of-freedom sub-vector corresponding to the target plate component into a local boundary degree-of-freedom vector based on the spatial orientation of the target plate component includes: The local boundary degree-of-freedom vector is determined based on the following formula:
[0015] in, This represents the local boundary degree of freedom vector corresponding to the target plate component. This represents the coordinate transformation matrix corresponding to the target plate component. This represents the global boundary degree of freedom sub-vector corresponding to the target plate component.
[0016] In one possible implementation, determining the displacement field corresponding to the target plate component based on the local boundary degree-of-freedom vector of the target plate component includes: Based on the correlation between the boundary degrees of freedom of plate members and the coefficients of analytical displacement functions in the dynamic stiffness method, the vector of analytical displacement function coefficients corresponding to the target plate member is determined. Based on the analytical displacement function coefficient vector and analytical displacement function matrix of the target plate component, the displacement field of the target plate component is determined.
[0017] In one possible implementation, the analytical displacement function coefficient vector corresponding to the target plate component is determined based on the following formula:
[0018] in, This represents the coefficient vector of the analytical displacement function corresponding to the target plate component. This represents the displacement matrix formed on the boundary by the analytical displacement function corresponding to the target plate component. This represents the local boundary degree of freedom vector corresponding to the target plate component.
[0019] In one possible implementation, the displacement field corresponding to the target plate component is determined based on the following formula:
[0020] in, This represents the displacement field corresponding to the target plate component. This represents the analytical displacement function matrix corresponding to the target plate component. This represents the vector of coefficients of the analytical displacement function corresponding to the target plate component.
[0021] In one possible implementation, the method further includes: After constructing the displacement field corresponding to the target plate frame structure, the displacement field of the target plate frame structure is constructed based on the finite element method, and the MAC and normalized L2 error between the displacement field corresponding to the target plate frame structure and the displacement field of the target plate frame structure constructed based on the finite element method are determined.
[0022] The beneficial effects of this invention are as follows: The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method provided by this invention first obtains the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type. The global boundary degree-of-freedom vector is obtained by solving the global dynamic stiffness equation. Then, based on the numbering and connection topology of the target plate components, the global boundary degree-of-freedom sub-vectors corresponding to the target plate components are extracted from the global boundary degree-of-freedom vector. Next, according to the spatial orientation of the target plate components, the global boundary degree-of-freedom sub-vectors corresponding to the target plate components are further converted into local boundary degree-of-freedom vectors. Finally, based on the target plate components... The corresponding local boundary degree-of-freedom vector determines the displacement field of the target plate component, and the displacement field of the target plate component is mapped to the global coordinate system to construct the displacement field of the target plate frame structure. This invention breaks through the limitation of the dynamic stiffness method, which only uses the boundary degree-of-freedom to characterize the structural response, and realizes the analytical construction of the continuous displacement field of the plate surface from the boundary solution results in the vibration and wave propagation analysis of the hull plate frame structure. It can obtain the displacement response and modal / wave propagation morphology at any position inside the plate component. Attached Figure Description
[0023] Figure 1 A schematic flowchart of an embodiment of the method for constructing vibration and wave displacement fields of ship hull plate frame structures based on dynamic stiffness method provided by the present invention; Figure 2 A schematic diagram of an embodiment of the coordinate transformation of a plate component provided by the present invention; Figure 3A schematic diagram of an embodiment of the displacement field construction results of a unidirectional stiffened plate frame structure provided by the present invention; Figure 4 A schematic diagram of an embodiment of the displacement field construction results of the orthogonal sandwich panel frame structure provided by the present invention; Figure 5 This is a schematic diagram of an embodiment of the overall displacement field splicing and error evaluation of the plate frame structure provided by the present invention. Detailed Implementation
[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0025] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.
[0026] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.
[0027] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0028] This invention provides a method for constructing vibration and wave displacement fields of a ship hull plate structure based on the dynamic stiffness method, which will be described below.
[0029] Figure 1 This is a schematic flowchart of an embodiment of the method for constructing vibration and wave displacement fields of ship hull plate frame structures based on the dynamic stiffness method provided by the present invention, as shown below. Figure 1 As shown, the method for constructing the vibration and wave displacement field of a ship hull plate structure based on the dynamic stiffness method includes: S101. Obtain the global boundary degree of freedom vector of the target plate frame structure under the target analysis type. The target analysis type includes free vibration analysis, forced vibration analysis and wave propagation analysis.
[0030] It should be noted that the method for constructing vibration and wave displacement fields of ship hull plate structures based on the dynamic stiffness method provided by this invention can be applied to the dynamic response analysis of ship plate structures, especially the displacement field analysis of ship plate structures.
[0031] When constructing the vibration and wave displacement fields of a ship's hull plate structure based on the dynamic stiffness method, the displacement field construction device (such as a desktop or portable computer) can first obtain the global boundary degree-of-freedom vectors of the target plate structure on the ship under the target analysis type, providing a data foundation for the subsequent construction of the plate structure displacement field. Target analysis types can specifically include free vibration analysis, forced vibration analysis, and wave propagation analysis.
[0032] S102. Based on the numbering and connection topology of the target plate components, extract the global boundary degree of freedom sub-vectors corresponding to the target plate components from the global boundary degree of freedom vectors. The target plate components are any plate components in the target plate frame structure.
[0033] It should be noted that after obtaining the global boundary degree of freedom vector of the target plate frame structure under the target analysis type, the global boundary degree of freedom sub-vector of the target plate component can be extracted from the global boundary degree of freedom vector according to the number and connection topology of the target plate component (any plate component in the target plate frame structure).
[0034] S103. Based on the spatial orientation of the target plate component, convert the global boundary degree-of-freedom sub-vectors corresponding to the target plate component into local boundary degree-of-freedom vectors.
[0035] It should be noted that after determining the global boundary degree-of-freedom sub-vectors corresponding to the target plate component, the global boundary degree-of-freedom sub-vectors corresponding to the target plate component can be further converted into local boundary degree-of-freedom vectors based on the spatial orientation of the target plate component.
[0036] S104. Determine the displacement field corresponding to the target plate component based on the local boundary degree of freedom vector corresponding to the target plate component, and map the displacement field corresponding to the target plate component to the global coordinate system to construct the displacement field corresponding to the target plate frame structure.
[0037] It should be noted that: Finally, the displacement field corresponding to the target plate component can be determined based on the local boundary degree-of-freedom vector of the target plate component, and then mapped to the global coordinate system to construct the displacement field corresponding to the target plate frame structure. This achieves the construction of the displacement field corresponding to the target plate frame structure from the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type. Constructing the displacement field of the target plate frame structure using the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type obtained by the stiffness method does not require resolving the global dynamic stiffness equation, resulting in less additional computational overhead and improving the efficiency of dynamic response analysis of plate frame structures.
[0038] In summary, the method for constructing vibration and wave displacement fields of a ship hull plate structure based on the dynamic stiffness method provided in this embodiment of the invention first obtains the global boundary degree-of-freedom vector of the target plate structure under the target analysis type. The global boundary degree-of-freedom vector is obtained by solving the global dynamic stiffness equation. Then, based on the numbering and connection topology of the target plate components, the global boundary degree-of-freedom sub-vectors corresponding to the target plate components are extracted from the global boundary degree-of-freedom vector. Next, according to the spatial orientation of the target plate components, the global boundary degree-of-freedom sub-vectors corresponding to the target plate components are further converted into local boundary degree-of-freedom vectors. Finally, based on the spatial orientation of the target plate components... The displacement field corresponding to the target plate component is determined by the corresponding local boundary degree-of-freedom vector, and the displacement field corresponding to the target plate component is mapped to the global coordinate system to construct the displacement field corresponding to the target plate frame structure. This invention breaks through the limitation of the dynamic stiffness method, which only uses the boundary degree-of-freedom to characterize the structural response, and realizes the analytical construction of the continuous displacement field of the plate surface from the boundary solution results in the vibration and wave propagation analysis of the hull plate frame structure. It can obtain the displacement response and modal / wave propagation morphology at any position inside the plate component.
[0039] In some embodiments of the present invention, obtaining the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type includes: When the target analysis type is free vibration analysis, the global boundary degree of freedom vector is determined based on the singular value decomposition results of the global dynamic stiffness matrix of the target plate frame structure at the natural frequency. When the target analysis type is forced vibration analysis, the global boundary degree of freedom vector is determined based on the global dynamic stiffness equation after applying boundary conditions. When the target analysis type is wave propagation analysis, the global boundary degree of freedom vector is determined based on the Bloch periodic transformation matrix and the boundary degree of freedom vector in Bloch coordinates.
[0040] It should be noted that when obtaining the global boundary degree-of-freedom vector of the target plate frame structure under the target analysis type, if the target analysis type is free vibration analysis, the global boundary degree-of-freedom vector can be determined based on the singular value decomposition results of the global dynamic stiffness matrix of the target plate frame structure at the natural frequency; if the target analysis type is forced vibration analysis, the global boundary degree-of-freedom vector can be determined based on the global dynamic stiffness equation after applying boundary conditions; if the target analysis type is wave propagation analysis, the global boundary degree-of-freedom vector can be determined based on the Bloch periodic transformation matrix and the boundary degree-of-freedom vector in Bloch coordinates.
[0041] In some embodiments of the present invention, determining the global boundary degree-of-freedom vector based on the singular value decomposition result of the global dynamic stiffness matrix of the target plate frame structure at its natural frequency includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0042] in, Represents the global boundary degree of freedom vector. Representation matrix The Column vector, Indicates the first A singular value, Represents the natural frequency The overall dynamic stiffness matrix at the location, Describes a left singular matrix. Represents a singular value matrix. This represents a right singular matrix.
[0043] It should be noted that when the target analysis type is free vibration analysis, the global boundary degree of freedom vector can be determined according to the above formula.
[0044] In some embodiments of the present invention, determining the global boundary degree-of-freedom vector based on the global dynamic stiffness equation after applying boundary conditions includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0045] in, Represents the global boundary degree of freedom vector. This represents the global dynamic stiffness matrix after applying boundary conditions. This represents the external stimulus vector.
[0046] It should be noted that when the target analysis type is forced vibration analysis, the global boundary degree of freedom vector can be determined according to the above formula.
[0047] In some embodiments of the present invention, determining the global boundary degree-of-freedom vector based on the Bloch periodic transformation matrix and the boundary degree-of-freedom vector in Bloch coordinates includes: The global boundary degree-of-freedom vector is determined based on the following formula:
[0048] in, Represents the global boundary degree of freedom vector. Represents the Bloch periodic transformation matrix. This represents the boundary degree of freedom vector in Bloch coordinates.
[0049] It should be noted that when the target analysis type is wave propagation analysis, the overall boundary degree of freedom vector can be determined according to the above formula.
[0050] In some embodiments of the present invention, the step of converting the global boundary degree-of-freedom sub-vector corresponding to the target plate component into a local boundary degree-of-freedom vector based on the spatial orientation of the target plate component includes: The local boundary degree-of-freedom vector is determined based on the following formula:
[0051] in, This represents the local boundary degree of freedom vector corresponding to the target plate component. This represents the coordinate transformation matrix corresponding to the target plate component. This represents the global boundary degree of freedom sub-vector corresponding to the target plate component.
[0052] It should be noted that when converting the global boundary degree-of-freedom sub-vectors corresponding to the target plate component into local boundary degree-of-freedom vectors, the local boundary degree-of-freedom vectors can be determined according to the above formula.
[0053] In some embodiments of the present invention, determining the displacement field corresponding to the target plate component based on the local boundary degree-of-freedom vector corresponding to the target plate component includes: Based on the correlation between the boundary degrees of freedom of plate members and the coefficients of analytical displacement functions in the dynamic stiffness method, the vector of analytical displacement function coefficients corresponding to the target plate member is determined. Based on the analytical displacement function coefficient vector and analytical displacement function matrix of the target plate component, the displacement field of the target plate component is determined.
[0054] It should be noted that when determining the displacement field of the target plate component based on the local boundary degree of freedom vector of the target plate component, the analytical displacement function coefficient vector of the target plate component can be determined first based on the correlation between the boundary degree of freedom of the plate component and the analytical displacement function coefficients in the dynamic stiffness method. Then, the displacement field of the target plate component can be determined based on the analytical displacement function coefficient vector and the analytical displacement function matrix of the target plate component.
[0055] In some embodiments of the present invention, the analytical displacement function coefficient vector corresponding to the target plate component is determined based on the following formula:
[0056] in, This represents the coefficient vector of the analytical displacement function corresponding to the target plate component. This represents the displacement matrix formed on the boundary by the analytical displacement function corresponding to the target plate component. This represents the local boundary degree of freedom vector corresponding to the target plate component.
[0057] It should be noted that the coefficient vector of the analytical displacement function corresponding to the target plate component can be determined according to the above formula.
[0058] In some embodiments of the present invention, the displacement field corresponding to the target plate component is determined based on the following formula:
[0059] in, This represents the displacement field corresponding to the target plate component. This represents the analytical displacement function matrix corresponding to the target plate component. This represents the vector of coefficients of the analytical displacement function corresponding to the target plate component.
[0060] It should be noted that the displacement field corresponding to the target plate component can be determined according to the above formula.
[0061] In some embodiments of the present invention, the method further includes: After constructing the displacement field corresponding to the target plate frame structure, the displacement field of the target plate frame structure is constructed based on the finite element method, and the MAC and normalized L2 error between the displacement field corresponding to the target plate frame structure and the displacement field of the target plate frame structure constructed based on the finite element method are determined.
[0062] It should be noted that the validity of the displacement field corresponding to the target plate frame structure determined in this invention can be determined by identifying the MAC and normalized L2 error between the displacement field corresponding to the target plate frame structure and the displacement field of the target plate frame structure constructed based on the finite element method. For example, the MAC and normalized L2 error between the displacement field corresponding to the target plate frame structure and the displacement field of the target plate frame structure constructed based on the finite element method can be determined by the following formula:
[0063]
[0064] in, The displacement field vector constructed in this invention, This is the displacement field vector for finite element comparison.
[0065] The following specific embodiments illustrate the process of constructing the vibration and wave displacement field of a ship hull plate structure based on the dynamic stiffness method provided by the present invention. The specific process of constructing the vibration and wave displacement field of a ship hull plate structure based on the dynamic stiffness method includes the following steps: 1. Obtain the global boundary degree of freedom vector of the plate frame structure under the target analysis type. The target analysis types include free vibration analysis, forced vibration analysis, and wave propagation analysis.
[0066] When the target analysis type is free vibration analysis, at the natural frequency Regarding the overall dynamic stiffness matrix Perform singular value decomposition:
[0067] Take the right singular vector corresponding to the minimum singular value as the global boundary degree of freedom vector:
[0068] In the formula, For the i-th singular value, For matrix The k-th column vector.
[0069] When the target analysis type is forced vibration analysis, the frequency domain response is obtained by applying the global dynamic stiffness equation after applying boundary conditions:
[0070] In the formula, The overall dynamic stiffness matrix after applying boundary constraints. This is the external excitation vector.
[0071] When the target analysis type is wave propagation analysis, the complete boundary degrees of freedom of the unit cell are recovered from the reduced degrees of freedom according to the Bloch periodic transformation relationship:
[0072] In the formula, This is the Bloch periodic transformation matrix. The boundary degree of freedom vector in Bloch coordinates.
[0073] 2. Based on the plate component numbers and connection topology, from the global boundary degree of freedom vector Extract the global boundary degree-of-freedom subvector corresponding to the i-th plate component .
[0074] 3. Combining Figure 2 Let's look at how, based on the spatial orientation of the i-th plate component, we can use the coordinate transformation matrix... Convert global boundary degrees of freedom to local boundary degrees of freedom:
[0075] In the formula, Let be the boundary degree of freedom vector of the i-th plate component in the local coordinate system.
[0076] 4. Based on the relationship between the boundary degrees of freedom and the coefficients of the analytical displacement function of a plate member in the dynamic stiffness method, solve for the analytical coefficient vector of the i-th plate member:
[0077] In the formula, Let be the coefficient vector of the analytical displacement function of the i-th plate member. This is the displacement matrix formed on the boundary by the analytical displacement function of the plate member.
[0078] 5. Convert the analytical coefficient vector Substituting the analytical displacement function of the plate member, a continuous displacement field is constructed at any point (x, y) inside the plate member:
[0079] In the formula, , This is the frequency-dependent analytical displacement function matrix.
[0080] 6. Map the local displacement fields of each plate component back to the global coordinate system, and splice them together according to the connection topology of the plate frame structure to form the overall displacement field. For the connection boundary, the displacement continuity relationship consistent with the dynamic stiffness matrix assembly is adopted to ensure the continuity of the displacement fields of adjacent plate components.
[0081] 7. Output displacement fields corresponding to different analysis types. For free vibration analysis, output the mode shapes and total displacement fields of the characteristic modes; for forced vibration analysis, output the forced vibration response field at the specified frequency; for wave propagation analysis, output the Bloch eigenfield displacement field. Combined with... Figure 3 The following are the results of constructing different types of displacement fields for a unidirectional stiffened plate frame structure. Combined with... Figure 4 The results show the construction of different types of displacement fields for orthogonal sandwich panel frame structures.
[0082] 8. Evaluate the representativeness error of the construction results. (Combined with...) Figure 5 By comparing the normalized displacement field constructed in this invention with the finite element displacement field, the modal confidence criterion (MAC) and the normalized L2 error can be calculated:
[0083]
[0084] In the formula, The displacement field vector constructed in this invention, This is the displacement field vector for finite element comparison.
[0085] This invention transforms the boundary degrees of freedom obtained by the dynamic stiffness method into a continuous displacement field within the plate frame structure, facilitating intuitive observation of structural deformation. Utilizing analytical displacement functions to construct the displacement field avoids the disadvantage of semi-analytical modeling by ordinary nodal interpolation methods. Unified construction of free vibration modes, forced vibration response fields, and wave propagation displacement fields is beneficial for explaining modal deformation, vibration localization, wave propagation modes, and bandgap formation mechanisms in plate frame structures. Displacement field construction is performed after the frequency or response solutions are obtained, eliminating the need to resolve the global dynamic stiffness equation and minimizing additional computational overhead.
[0086] The above provides a detailed description of the method for constructing vibration and wave displacement fields of ship hull plate structure based on dynamic stiffness method provided by the present invention. Specific examples are used in this paper to illustrate the principle and implementation of the present invention. The above description of the embodiments is only for the purpose of helping to understand the method and core idea of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method, characterized in that, include: Obtain the global boundary degree of freedom vector of the target plate frame structure under the target analysis type, which includes free vibration analysis, forced vibration analysis and wave propagation analysis; Based on the numbering and connection topology of the target plate components, extract the global boundary degree of freedom sub-vectors corresponding to the target plate components from the global boundary degree of freedom vectors. The target plate component is any plate component in the target plate frame structure. Based on the spatial orientation of the target plate component, the global boundary degree-of-freedom sub-vectors corresponding to the target plate component are converted into local boundary degree-of-freedom vectors; The displacement field corresponding to the target plate component is determined based on the local boundary degree of freedom vector of the target plate component, and the displacement field corresponding to the target plate component is mapped to the global coordinate system to construct the displacement field corresponding to the target plate frame structure.
2. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 1, characterized in that, The process of obtaining the overall boundary degree-of-freedom vector of the target plate frame structure under the target analysis type includes: When the target analysis type is free vibration analysis, the global boundary degree of freedom vector is determined based on the singular value decomposition results of the global dynamic stiffness matrix of the target plate frame structure at the natural frequency. When the target analysis type is forced vibration analysis, the global boundary degree of freedom vector is determined based on the global dynamic stiffness equation after applying boundary conditions. When the target analysis type is wave propagation analysis, the global boundary degree of freedom vector is determined based on the Bloch periodic transformation matrix and the boundary degree of freedom vector in Bloch coordinates.
3. The method for constructing vibration and wave displacement fields of ship hull plate frame structures based on the dynamic stiffness method according to claim 2, characterized in that, The determination of the global boundary degree-of-freedom vector based on the singular value decomposition results of the global dynamic stiffness matrix of the target plate frame structure at its natural frequency includes: The global boundary degree-of-freedom vector is determined based on the following formula: in, Represents the global boundary degree of freedom vector. Representation matrix The Column vector, Indicates the first A singular value, Represents the natural frequency The overall dynamic stiffness matrix at the location, Describes a left singular matrix. Represents a singular value matrix. This represents a right singular matrix.
4. The method for constructing vibration and wave displacement fields of ship hull plate frame structures based on the dynamic stiffness method according to claim 2, characterized in that, The determination of the global boundary degree-of-freedom vector based on the global dynamic stiffness equation after applying boundary conditions includes: The global boundary degree-of-freedom vector is determined based on the following formula: in, Represents the global boundary degree of freedom vector. This represents the global dynamic stiffness matrix after applying boundary conditions. This represents the external stimulus vector.
5. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 2, characterized in that, The determination of the global boundary degree-of-freedom vector based on the Bloch periodic transformation matrix and the boundary degree-of-freedom vector in Bloch coordinates includes: The global boundary degree-of-freedom vector is determined based on the following formula: in, Represents the global boundary degree of freedom vector. Represents the Bloch periodic transformation matrix. This represents the boundary degree of freedom vector in Bloch coordinates.
6. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 1, characterized in that, The step of converting the global boundary degree-of-freedom sub-vectors corresponding to the target plate component into local boundary degree-of-freedom vectors based on the spatial orientation of the target plate component includes: The local boundary degree-of-freedom vector is determined based on the following formula: in, This represents the local boundary degree of freedom vector corresponding to the target plate component. This represents the coordinate transformation matrix corresponding to the target plate component. This represents the global boundary degree of freedom sub-vector corresponding to the target plate component.
7. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 1, characterized in that, The determination of the displacement field corresponding to the target plate component based on the local boundary degree-of-freedom vector of the target plate component includes: Based on the correlation between the boundary degrees of freedom of plate members and the coefficients of analytical displacement functions in the dynamic stiffness method, the vector of analytical displacement function coefficients corresponding to the target plate member is determined. Based on the analytical displacement function coefficient vector and analytical displacement function matrix of the target plate component, the displacement field of the target plate component is determined.
8. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 7, characterized in that, The analytical displacement function coefficient vector corresponding to the target plate component is determined based on the following formula: in, This represents the vector of coefficients of the analytical displacement function corresponding to the target plate component. This represents the displacement matrix formed on the boundary by the analytical displacement function corresponding to the target plate component. This represents the local boundary degree of freedom vector corresponding to the target plate component.
9. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 7, characterized in that, The displacement field corresponding to the target plate component is determined based on the following formula: in, This represents the displacement field corresponding to the target plate component. This represents the analytical displacement function matrix corresponding to the target plate component. This represents the vector of coefficients of the analytical displacement function corresponding to the target plate component.
10. The method for constructing vibration and wave displacement fields of a ship hull plate frame structure based on the dynamic stiffness method according to claim 1, characterized in that, The method further includes: After constructing the displacement field corresponding to the target plate frame structure, the displacement field of the target plate frame structure is constructed based on the finite element method, and the MAC and normalized L2 error between the displacement field corresponding to the target plate frame structure and the displacement field of the target plate frame structure constructed based on the finite element method are determined.