Impact response spectrum optimization method and apparatus based on modal participation factor

Abstract

This invention provides a method and apparatus for optimizing impact response spectra based on modal participation factors. The method includes: establishing a three-dimensional solid model of a stern tube using three-dimensional modeling software, and setting material parameters for each component in the three-dimensional solid model according to the actual properties of the materials used in the stern tube; meshing the three-dimensional solid model using finite element method (FE) software, and selecting an appropriate mesh density based on the complexity of the three-dimensional solid model and the shape of key components; performing modal analysis on the three-dimensional solid model in the FE software to obtain modal analysis results, each modal analysis result including modal mass and modal participation factor, and filtering the modal analysis results using an optimization algorithm; calculating the modal velocity and acceleration based on the filtered modal analysis results, generating a velocity impact response spectrum based on the modal velocity, and generating an acceleration impact response spectrum based on the modal acceleration. This invention improves the accuracy of the impact response spectrum.

Description

Technical Field

[0001] This invention relates to the field of ship impact resistance performance analysis technology, and in particular to an impact response spectrum optimization method and apparatus based on modal participation factor. Background Technology

[0002] With the continuous development of ship propulsion technology, the stern tube, as a crucial component of the ship's power system, has become a key factor in ensuring the normal operation of the vessel, particularly in terms of its strength and impact resistance. Currently, the design and analysis of ship stern tubes largely employ traditional static methods and simplified dynamic models. However, these methods often struggle to accurately predict the dynamic response and strength changes of the stern tube when faced with complex impact loads, especially sudden underwater impacts, thus affecting the overall performance and safety of the ship.

[0003] To improve the impact resistance of ship stern tubes, scholars both domestically and internationally have conducted extensive research and proposed various impact response analysis methods. However, existing analysis methods mainly focus on the influence of low-frequency vibrations and are mostly based on conventional modal analysis, failing to fully consider the optimization effect of multimodal participation factors on high-frequency response. This results in the inability to obtain accurate stress distribution and impact response under actual impact conditions.

[0004] Therefore, developing a new shock response spectrum optimization method based on modal participation factors to more accurately predict the performance of ship stern tubes under complex shock loads has become an urgent research need. Summary of the Invention

[0005] This invention provides a method and apparatus for optimizing the impact response spectrum based on modal participation factors, which addresses the shortcomings of existing technologies in obtaining accurate stress distribution and impact response under actual impact conditions. By combining modal analysis and spectral analysis, a more accurate impact response spectrum can be generated.

[0006] This invention provides a method for optimizing the impulse response spectrum based on modal participation factors, comprising:

[0007] A three-dimensional solid model of the stern tube is created using 3D modeling software, and the material parameters of each component in the three-dimensional solid model are set according to the actual properties of the material used in the stern tube.

[0008] The three-dimensional solid model is meshed using finite element software, and an appropriate mesh density is selected based on the complexity of the three-dimensional solid model and the shape of the key components.

[0009] Modal analysis was performed on the three-dimensional solid model in finite element software to obtain various modal analysis results, including modal quality and modal participation factor. Optimization algorithms were used to filter the modal analysis results.

[0010] Based on the selected modal analysis results, calculate the modal velocity and modal acceleration. Generate the velocity impact response spectrum based on the modal velocity and the acceleration impact response spectrum based on the modal acceleration.

[0011] According to the impact response spectrum optimization method based on modal participation factor provided by the present invention, the modal analysis results also include modal frequencies and mode shapes.

[0012] According to the present invention, an impact response spectrum optimization method based on modal participation factors is provided, in which modal analysis is performed on the three-dimensional solid model in finite element software to obtain the modal analysis results, and an optimization algorithm is used to filter the modal analysis results, including:

[0013] Modal analysis is performed on the three-dimensional solid model in finite element software according to the set modal order to obtain the results of each modal analysis.

[0014] If the sum of modal masses in the modal analysis results is greater than a first preset proportion of the mass of the three-dimensional solid model, only modal analysis results with modal masses greater than a second preset proportion and modal participation factors greater than a third preset proportion are retained; otherwise, the modal order is reset.

[0015] According to the present invention, an impulse response spectrum optimization method based on modal participation factors is provided, and each modal participation factor is extracted using the following formula:

[0016]

[0017] Among them, P a The participation factor for the a-th mode is... Let be the acceleration vector of the a-th mode. Let T be the system quality matrix, and T be the transpose operation.

[0018] According to the present invention, an impact response spectrum optimization method based on modal participation factors is provided, which calculates the modal velocity and modal acceleration based on the analysis results of each selected modality, including:

[0019] Calculate the basic acceleration of each mode based on the modal mass from the selected modal analysis results;

[0020] Calculate the modal accelerations in the given impact direction based on the modal base accelerations, and calculate the modal velocities in the given impact direction based on the modal base velocities.

[0021] According to the present invention, an impact response spectrum optimization method based on modal participation factors is provided, which calculates the base acceleration and base velocity of each modality based on the modal mass in the selected modal analysis results using the following formula:

[0022]

[0023]

[0024] Where A0 is the basic acceleration of each mode, V0 is the basic velocity of each mode, and m0 is the mass of each mode.

[0025] According to the impact response spectrum optimization method based on modal participation factors provided by the present invention, after generating velocity impact response spectra based on the velocities of each mode and acceleration impact response spectra based on the accelerations of each mode, the method further includes:

[0026] The impact resistance of the stern tube is evaluated based on the velocity impact response spectrum or the acceleration impact response spectrum.

[0027] If the stress or deformation of the stern tube exceeds the safety limit based on its impact resistance performance, the stern tube is improved. The improvement includes one or more of the following: increasing the material strength of key components, using higher strength alloy materials for key components, adjusting the geometry of the stern tube, and optimizing the modal participation factor.

[0028] The present invention also provides an impulse response spectrum optimization device based on modal participation factor, comprising:

[0029] The model building module is used to build a three-dimensional solid model of the stern tube using three-dimensional modeling software, and to set the material parameters of each component in the three-dimensional solid model according to the actual properties of the material used in the stern tube.

[0030] The mesh generation module is used to perform mesh generation on the three-dimensional solid model using finite element software, and selects an appropriate mesh density based on the complexity of the three-dimensional solid model and the shape of key components.

[0031] The analysis and optimization module is used to perform modal analysis on the three-dimensional solid model in finite element software to obtain modal analysis results, including modal quality and modal participation factor. The optimization algorithm is used to filter the modal analysis results.

[0032] The response spectrum generation module is used to calculate the velocity and acceleration of each modality based on the selected modal analysis results, generate the velocity-impact response spectrum based on the modal velocity, and generate the acceleration-impact response spectrum based on the modal acceleration.

[0033] The impact response spectrum optimization method and apparatus based on modal participation factors provided by this invention have significant technical advantages and beneficial effects compared with existing technologies. By combining modal analysis and optimization algorithms, this solution effectively solves the problems of insufficient accuracy and inability to accurately reflect high-frequency modal responses in traditional impact resistance performance analysis. Specifically, the technical effects of this invention are reflected in the following aspects:

[0034] 1. Compared to previous methods that only considered modal quality, this method adds consideration of the modal participation factor, improving the accuracy and reliability of the impact response spectrum.

[0035] Existing methods for calculating impact response spectra mostly rely on low-frequency modal responses. These methods tend to neglect the influence of mid- and high-frequency modes when dealing with complex impact conditions, leading to biased calculation results. This invention, however, optimizes the calculation of modal participation factors, comprehensively considering the contribution of mid- and high-frequency modes to the impact response, generating a more accurate impact response spectrum. This optimization process makes the stress and deformation predictions of equipment under impact loads more consistent with reality, significantly improving the accuracy and reliability of impact resistance performance analysis. With a precise response spectrum, the impact resistance of equipment can be more accurately assessed, thereby optimizing the design and ensuring the long-term reliability and safety of the equipment.

[0036] 2. Address the issue of insufficient accuracy in existing methods and improve their impact resistance.

[0037] Traditional shock resistance analysis methods often fail to fully consider the impact of complex impact loads on the multimodal response of equipment, thus making accurate performance evaluation impossible under various impact conditions. The optimization method in this invention fully considers the combined response of low-frequency and high-frequency modes, enabling the calculation results to comprehensively reflect the actual impact performance of components such as the stern tube, thereby optimizing the design and improving the ship's shock resistance in complex environments. This improvement not only enhances the reliability of equipment under high-intensity impact environments such as underwater explosions and naval warfare but also effectively reduces navigation risks caused by equipment damage.

[0038] 3. Optimize the design process and reduce design and testing cycles.

[0039] By optimizing the calculation based on modal participation factors, more accurate shock resistance performance analysis can be performed during the design phase, reducing the reliance on numerous physical tests required in traditional methods. Traditional design methods often require multiple experiments to verify the shock response, while the method of this invention significantly shortens the design and testing cycle through numerical simulation and optimization analysis. By simulating different impact conditions, potential problems can be identified in advance and design optimizations can be performed, thereby improving design efficiency and reducing R&D costs.

[0040] 4. Improve computational efficiency and reduce computational costs.

[0041] Compared to traditional time-domain simulation methods or purely experimental methods, this invention optimizes modal analysis and the calculation of impact response spectra, providing not only high-precision analysis results but also significantly improving computational efficiency. Traditional methods require substantial computational resources, especially when the system is complex, resulting in very high computational and time costs. In contrast, this invention effectively reduces computation time and costs while maintaining accuracy.

[0042] 5. Improve the accuracy and applicability of impact-resistant designs.

[0043] The technical solution of this invention is not only applicable to military equipment such as ships, but can also be widely applied to the design and optimization of impact resistance performance for civilian vessels and other marine engineering equipment. Through the optimized impact response spectrum, impact conditions under various complex environments can be simulated more accurately, ensuring higher reliability of the design in practical applications. This technological innovation makes impact-resistant design not limited to specific fields, but has broad applicability, enabling its application to a wider range of engineering fields and meeting increasingly complex equipment design needs.

[0044] 6. Improve equipment lifespan and safety

[0045] By accurately assessing impact resistance, this invention effectively reduces potential safety hazards during the design process. Optimized design effectively prevents equipment damage due to insufficient impact resistance, thereby extending equipment lifespan and reducing maintenance frequency and costs. Furthermore, accurate impact response prediction provides safer operation, reducing the risk of safety accidents caused by equipment failure and enhancing overall equipment safety. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating the impact response spectrum optimization method based on modal participation factor provided by the present invention.

[0048] Figure 2 This is a schematic diagram of the stern tube model in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0049] Figure 3 This is a schematic diagram of the elastic support at the annular seat of the stern tube model in the impact response spectrum optimization method based on modal participation factor provided by the present invention.

[0050] Figure 4 This is a schematic diagram of the elastic support of the front bearing end face in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0051] Figure 5 This is a schematic diagram of the fixed support of the rear bearing end face in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0052] Figure 6 This is a schematic diagram of the calculation results of the 400th order modal participation factor in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0053] Figure 7 This is a schematic diagram of the impact spectrum response analysis process in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0054] Figure 8 This is a schematic diagram of the X-direction acceleration spectrum in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0055] Figure 9 This is a schematic diagram of the Y-direction acceleration spectrum in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0056] Figure 10 This is a schematic diagram of the Z-direction acceleration spectrum in the impact response spectrum optimization method based on modal participation factor provided by the present invention;

[0057] Figure 11 This is a schematic diagram of the structure of the impact response spectrum optimization device based on modal participation factor provided by the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0059] The following is combined with Figure 1 The present invention describes an impulse response spectrum optimization method based on modal participation factor, comprising:

[0060] Step 101: Use 3D modeling software to create a 3D solid model of the stern tube, and set the material parameters of each component in the 3D solid model according to the actual properties of the material used in the stern tube;

[0061] Step 102: Use finite element software to mesh the three-dimensional solid model, and select an appropriate mesh density based on the complexity of the three-dimensional solid model and the shape of the key components.

[0062] Step 103: Perform modal analysis on the three-dimensional solid model in finite element software to obtain modal analysis results. Each modal analysis result includes modal quality and modal participation factor. Use an optimization algorithm to filter the modal analysis results.

[0063] Step 104: Calculate the modal velocity and modal acceleration based on the selected modal analysis results, generate the velocity impact response spectrum based on the modal velocity, and generate the acceleration impact response spectrum based on the modal acceleration.

[0064] This technical solution primarily addresses the impact resistance performance analysis of ship stern tubes in complex impact environments, proposing an impact response spectrum optimization method based on modal participation factors. This method utilizes the optimization of modal participation factors to improve the accuracy of the impact response spectrum and optimize the impact resistance performance of key ship components under actual impact conditions. This solution, through finite element analysis (FEA) simulation calculations combined with modal analysis and impact response spectrum techniques, can provide more accurate stress analysis results and offer effective theoretical support for ship design and optimization.

[0065] For equipment modeling and material parameter setting, firstly, based on the actual engineering design, a three-dimensional solid model of the stern tube is created using CAD software (such as SolidWorks), such as... Figure 2 As shown in the diagram, the model should include all parts of the stern tube, including the front bearing hub, rear bearing hub, and intermediate nozzle. Special attention should be paid to key components related to impact loads during modeling, such as bearings and their contact surfaces, and support rings.

[0066] Next, the material parameters for each component are set according to the actual properties of the material (such as elastic modulus, Poisson's ratio, density, etc.). For the stern tube, high-strength materials such as alloy steel are usually selected.

[0067] For the establishment and meshing of the finite element model, finite element analysis software (such as ANSYS) is used to mesh the established 3D model. The accuracy of meshing directly affects the accuracy of the calculation results; therefore, an appropriate mesh density needs to be selected based on the complexity of the model and the shape of key components. Especially for rotating parts and stress surfaces, the mesh should be refined to ensure the accurate transfer of impact loads. (See model support details.) Figure 3 , Figure 4 and Figure 5 .

[0068] For modal analysis and modal participation factor (MOF) calculation, modal analysis was performed in finite element software to calculate the frequency, mode shape, and modal mass of each mode. By extracting the MOF, the contribution of different modes to the impact response was analyzed. The MOF reflects the degree of influence of different modes on the impact response; this calculation result will be used for subsequent impact response spectrum optimization.

[0069] Modal quality and modal participation factors are extracted from the modal analysis results. This approach expands upon previous methods that only considered effective modal quality by adding consideration for modal participation factors.

[0070] Based on the results of modal analysis, an optimization algorithm is used to adjust the effective modal mass, and then the dominant modes are selected to generate a high-precision impact response spectrum. Traditional impact response spectra are mostly based on low-frequency modal responses, while this scheme optimizes the modal participation factor and combines it with multimodal analysis (such as selecting all modes with modal masses greater than 1% of the total mass and combining them with modes whose modal participation factors account for the dominant order, and these dominant order modes also require that the sum of the effective modal masses used for calculation is at least greater than 80%), so that the impact response spectrum more accurately reflects the response of all modes under impact.

[0071] This embodiment addresses the shortcomings of traditional methods that only consider low-frequency modal responses by optimizing the impact response spectrum based on modal participation factors (MOFs). By using MOFs to comprehensively consider the influence of all modes on the impact response, and combining spectral analysis methods, it generates an accurate impact response spectrum by precisely calculating MOFs and optimizing their role in the calculation. Unlike traditional methods, this approach comprehensively considers the impact response of all modes, making the predicted impact loading more consistent with actual working conditions, thus significantly improving the accuracy of the impact response spectrum. This allows for a more accurate assessment of the impact resistance performance of equipment such as ship stern tubes. This innovation not only optimizes the impact resistance design process and improves design efficiency but also significantly enhances the safety and reliability of ships and other marine equipment in complex impact environments. The application of this technology can effectively reduce design costs, shorten the development cycle, and provide a more reliable design basis for various marine engineering equipment.

[0072] Based on the above embodiments, the modal analysis results in this embodiment also include modal frequencies and mode shapes.

[0073] Based on the above embodiments, this embodiment performs modal analysis on the three-dimensional solid model in finite element software to obtain various modal analysis results, and uses an optimization algorithm to filter the modal analysis results, including:

[0074] Modal analysis is performed on the three-dimensional solid model in finite element software according to the set modal order to obtain the results of each modal analysis.

[0075] If the sum of modal masses in the modal analysis results is greater than a first preset proportion of the mass of the three-dimensional solid model, only modal analysis results and corresponding modal participation factors with modal masses greater than a second preset proportion and modal participation factors greater than a third preset proportion are retained; otherwise, the modal order is reset.

[0076] The calculated results for the modal mass and effective modal mass of order 400 are as follows: Figure 6 As shown, the modal analysis results are shown in Table 1 (only a portion is shown due to the high order).

[0077] After the calculation is completed, it is also necessary to ensure that the sum of the effective modal masses (the ratio of modal mass to the total model mass) is greater than 80% to guarantee that the simulation accuracy is within the allowable error range in engineering. In Table 1, the total modal mass is 13.06t, and the total model mass is 13.165t, with a mass ratio of approximately 99%, which meets the requirements.

[0078] Table 1

[0079]

[0080] In addition, such as Figure 7As shown, a multi-index weighted scoring method can be used to screen modal components by comprehensively considering modal quality, modal frequency, and mode shape from the modal analysis results. The specific modal screening steps are as follows:

[0081] Modal quality basic screening: According to GJB1060.1-91, the cumulative modal quality of the screened modes must be greater than 80% of the total system quality. Modal quality is screened using the following formula:

[0082] Modal mass percentage:

[0083] Cumulative Modal Quality Validation:

[0084] in, The mass percentage of the a-th mode ( (This mode is retained) For the a-th modal mass, Let be the total mass of the system, and k be the modal order after screening.

[0085] Frequency response screening: The modal frequencies must cover the key frequency bands of the impact spectrum, and resonance and coverage of the excitation frequency bands must be avoided. At that time, retain that frequency point. Then determine when At this time, the frequency points in this group are relatively concentrated, and the mode groups within this dense frequency band need to be given special attention. The specific formula is as follows:

[0086] Frequency similarity:

[0087] Frequency density:

[0088] in, Let be the relative frequency deviation (dimensionless) at the a-th frequency point. The structural modal frequencies to be screened. The dominant frequency of the shock spectrum is the frequency value corresponding to the peak value of the shock spectrum curve. This is a frequency density coefficient, dimensionless, reflecting the degree of concentration of a set of frequency points. The average frequency (used to identify key mode groups within a frequency set).

[0089] Mode shape feature screening: The mode shape must make a significant contribution to key parts of the stern tube (such as the front / rear bearing hubs and support rings). The main screening factor is the mode shape participation factor. This indicates that the modal contributes significantly to the overall vibration response of the structure and should be considered a core analysis object. Simultaneously, the modal strain energy accounts for... The strain energy contribution of this mode is significant and must be retained; it cannot be ignored in modal analysis or vibration response calculation.

[0090] Modal participation factor:

[0091] Modal strain energy ratio:

[0092] in, For mode shape vectors, For the quality matrix, Here is the structural stiffness matrix. Let b be the total strain energy of all n-order modes, and b be the traversal index, representing all modes from 1 to n (the total range).

[0093] Finally, the modal significance coefficients are calculated by combining the above three methods. The modal analysis results at that time are retained, and the formula is as follows:

[0094] Multi-indicator weighted scoring formula:

[0095] Among them, the aggravation coefficient (Modal quality) (Frequency similarity) (Modal participation).

[0096] Based on the above embodiments, this embodiment extracts the modal participation factors using the following formula:

[0097]

[0098] Among them, P a The participation factor for the a-th mode is actually a constant. Let be the acceleration vector of the a-th mode (a 1×n row vector, where n is the number of degrees of freedom of the system). The system mass matrix (an n×n square matrix, where n is the number of system degrees of freedom) describes the mass magnitude corresponding to each degree of freedom of the system, as well as the mass coupling relationship between different degrees of freedom; T is the transpose operation.

[0099] Modal participation factor It is calculated through the relationship between modal displacement and mass matrix, and represents the degree of contribution of that mode to the system's impact response. In other words, the larger the participation factor, the more important the contribution of that mode to the system's dynamic response under impact.

[0100] The calculated result of the X-direction modal participation factor of order 400 is as follows: Figure 7 As shown in Table 2, the modal analysis results are presented (only a portion is shown due to the high order). The Y and Z directions are also calculated using the same formulas.

[0101] Table 2

[0102]

[0103] Based on the above embodiments, this embodiment calculates the modal velocity and modal acceleration according to the selected modal analysis results, including:

[0104] Calculate the basic acceleration of each mode based on the modal mass from the selected modal analysis results;

[0105] Calculate the modal acceleration in the given impact direction based on the modal base acceleration, and calculate the modal velocity in the given impact direction based on the modal base velocity.

[0106] An acceleration impact response spectrum is generated based on the acceleration of each mode. The impact response spectrum includes the velocity impact response spectrum and the acceleration impact response spectrum. The velocity and acceleration of each order and direction can be obtained as needed. In this embodiment, the acceleration impact spectrum is calculated.

[0107] Based on the above embodiments, this embodiment calculates the basic acceleration of each modality according to the modal mass using the following formula:

[0108]

[0109]

[0110] Where A0 is the basic acceleration of each mode, V0 is the basic velocity of each mode, and m0 is the mass of each mode.

[0111] The shafting system is installed at the hull and outer plating, and the design values ​​used for surface ships are calculated using the formulas described above. First, the calculation... and Then take and The smaller value in the equation represents the impact design acceleration of the system in a given impact direction during dynamic analysis. The angular frequency is used. Design values ​​for surface ships are generally calculated in three directions, as shown in Table 3. The final acceleration impact spectrum is... Figure 8 , Figure 9 and Figure 10 .

[0112] Table 3

[0113]

[0114] Based on the above embodiments, this embodiment, after generating the velocity impact response spectrum based on each modal velocity and the acceleration impact response spectrum based on each modal acceleration, further includes:

[0115] The impact resistance of the stern tube is evaluated based on the velocity impact response spectrum or acceleration impact response spectrum.

[0116] If the stress or deformation of the stern tube exceeds the safety limit based on its impact resistance performance, the stern tube is improved. The improvement includes increasing the material strength of key components, using higher strength alloy materials for key components, adjusting the geometry of the stern tube (such as increasing wall thickness, optimizing the support structure, etc.), and optimizing the impact spectrum involving modal order and participation factor (by changing the design to reduce sensitive parts of the impact response).

[0117] This embodiment provides a precise and efficient method for evaluating the shock resistance performance of ship stern tubes based on the optimization of the shock response spectrum using modal participation factors. This method enables more accurate prediction of the dynamic response of critical ship components in complex marine environments, improving design reliability and safety. This technology is not only applicable to military vessels but can also be widely used in the shock resistance performance analysis and optimization of civilian ships and other marine engineering equipment.

[0118] The following describes the shock response spectrum optimization device based on modal participation factor provided by the present invention. The shock response spectrum optimization device based on modal participation factor described below and the shock response spectrum optimization method based on modal participation factor described above can be referred to in correspondence.

[0119] like Figure 11 As shown, the present invention provides an impulse response spectrum optimization device based on modal participation factor, comprising:

[0120] The model building module 1101 is used to build a three-dimensional solid model of the stern tube using three-dimensional modeling software, and to set the material parameters of each component in the three-dimensional solid model according to the actual properties of the material used in the stern tube.

[0121] The mesh generation module 1102 is used to perform mesh generation on the three-dimensional solid model using finite element software, and selects an appropriate mesh density according to the complexity of the three-dimensional solid model and the shape of key components;

[0122] The analysis and optimization module 1103 is used to perform modal analysis on the three-dimensional solid model in finite element software to obtain modal analysis results. Each modal analysis result includes modal quality and modal participation factor. The optimization algorithm is used to filter the modal analysis results.

[0123] The response spectrum generation module 1104 is used to calculate the velocity and acceleration of each modality based on the selected modal analysis results, generate the velocity impact response spectrum based on the modal velocity, and generate the acceleration impact response spectrum based on the modal acceleration.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the impulse response spectrum based on modal participation factors, characterized in that, include: A three-dimensional solid model of the stern tube is created using 3D modeling software, and the material parameters of each component in the three-dimensional solid model are set according to the actual properties of the material used in the stern tube. The three-dimensional solid model is meshed using finite element software, and an appropriate mesh density is selected based on the complexity of the three-dimensional solid model and the shape of the key components. Modal analysis was performed on the three-dimensional solid model in finite element software to obtain modal analysis results, including modal quality and modal participation factor. Optimization algorithms were used to filter the modal analysis results. Based on the selected modal analysis results, calculate the modal velocity and modal acceleration, generate the velocity impact response spectrum based on the modal velocity, and generate the acceleration impact response spectrum based on the modal acceleration. The participation factors for each modality are extracted using the following formula: ； Among them, P a The participation factor for the a-th mode is... Let be the acceleration vector of the a-th mode. Let T be the system quality matrix, and T be the transpose operation. Modal analysis was performed on the three-dimensional solid model using finite element software to obtain various modal analysis results. Optimization algorithms were then used to filter the modal analysis results, including: Modal analysis is performed on the three-dimensional solid model in finite element software according to the set modal order to obtain the results of each modal analysis. If the sum of modal masses in the modal analysis results is greater than a first preset proportion of the mass of the three-dimensional solid model, only modal analysis results with modal masses greater than a second preset proportion and modal participation factors greater than a third preset proportion are retained; otherwise, the modal order is reset. Based on the selected modal analysis results, calculate the modal velocity and modal acceleration for each mode, including: Calculate the foundation acceleration and foundation velocity of each mode based on the modal mass from the selected modal analysis results; Calculate the modal acceleration in the given impact direction based on the modal base acceleration, and calculate the modal velocity in the given impact direction based on the modal base velocity; The foundation acceleration and velocity of each mode are calculated using the following formulas based on the modal masses from the selected modal analysis results: ； ； Where A0 is the basic acceleration of each mode, V0 is the basic velocity of each mode, and m0 is the mass of each mode.

2. The method for optimizing the impulse response spectrum based on modal participation factors according to claim 1, characterized in that, The results of each modal analysis also include modal frequencies and mode shapes.

3. The method for optimizing the impulse response spectrum based on modal participation factors according to claim 1, characterized in that, After generating the velocity impact response spectrum based on the velocities of each mode and the acceleration impact response spectrum based on the accelerations of each mode, the process also includes: The impact resistance of the stern tube is evaluated based on the velocity impact response spectrum or the acceleration impact response spectrum. If the stress or deformation of the stern tube exceeds the safety limit based on its impact resistance performance, the stern tube is improved. The improvement includes one or more of the following: increasing the material strength of key components, using higher strength alloy materials for key components, adjusting the geometry of the stern tube, and optimizing the modal participation factor.

4. A device for optimizing the impulse response spectrum based on modal participation factors, characterized in that, The impulse response spectrum optimization method based on modal participation factor as described in any one of claims 1-3 includes: The model building module is used to build a three-dimensional solid model of the stern tube using three-dimensional modeling software, and to set the material parameters of each component in the three-dimensional solid model according to the actual properties of the material used in the stern tube. The mesh generation module is used to perform mesh generation on the three-dimensional solid model using finite element software, and selects an appropriate mesh density based on the complexity of the three-dimensional solid model and the shape of key components. The analysis and optimization module is used to perform modal analysis on the three-dimensional solid model in finite element software to obtain modal analysis results, including modal quality and modal participation factor. The optimization algorithm is used to filter the modal analysis results. The response spectrum generation module is used to calculate the velocity and acceleration of each modality based on the selected modal analysis results, generate the velocity impact response spectrum based on the modal velocity, and generate the acceleration impact response spectrum based on the modal acceleration. The participation factors for each modality are extracted using the following formula: ； Among them, P a The participation factor for the a-th mode is... Let be the acceleration vector of the a-th mode. Let T be the system quality matrix, and T be the transpose operation.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the shock response spectrum optimization method based on modal participation factor as described in any one of claims 1 to 3.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the impulse response spectrum optimization method based on modal participation factors as described in any one of claims 1 to 3.

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