66 results about "Modal superposition" patented technology

The invention provides a ship weld joint stress deduction and fatigue damage evaluation method and system, and the method comprises the steps: firstly building a finite element model of a container ship, calculating the inherent frequency of the finite element model and a corresponding vibration mode through employing a Lanczos algorithm, and forming a plurality of free vibration modes of the finite element model; the inherent frequency of each free vibration mode is compared with a preset frequency range, and the free vibration mode in the preset frequency range is reserved and serves as a basic mode; calculating a theoretical stress distribution field of the whole ship structure in each basic mode based on the vibration mode through a strain-displacement relation equation and a material constitutive equation, arranging a plurality of stress monitoring points and weld joint evaluation points, and performing inversion by adopting a mode superposition method to obtain stress values of the weld joint evaluation points; and finally, calculating a total fatigue damage value by adopting a rain flow counting method and combining a fatigue evaluation method, and evaluating whether the total fatigue damage value is reliable or not, thereby facilitating the realization of long-term fatigue life management of the welding seam area.

The invention relates to the field of mechanical engineering, in particular to a hydraulic-structure collaborative optimization design method for a shield pump, and aims to solve the problems of load distortion and structure matching imbalance caused by traditional staged optimization. The method comprises the following steps: constructing a fluid-solid bidirectional coupling simulation model, and extracting transient hydraulic loads under multiple working conditions; establishing a structure dynamic response agent model based on modal superposition and Gaussian process regression; key coupling parameters such as the impeller outlet width and the volute base circle diameter are recognized through a Sobol method; and the efficiency, the lift fluctuation rate, the stress and the vibration are taken as multiple targets, and a Pareto optimal solution is searched through an improved genetic algorithm. Manufacturing constraints are embedded in the optimization process, the single period is shorter than 48 hours, and fatigue life evaluation and knowledge base intelligent recommendation are supported. According to the method, closed-loop cooperation of hydraulic excitation and structural response is achieved, the vibration prediction error is lower than 10%, the optimization dimension is compressed to be within 5 dimensions, the efficiency is improved by 20 times or above, and the performance reliability and the design intelligence level of the shield pump are remarkably improved.

A bridge response reconstruction method based on main contribution mode superposition comprises the following steps: firstly, testing a bridge influence line, firstly obtaining a deflection influence line of a bridge, calculating a rigidity distribution function of the bridge through the deflection influence line, and then obtaining a vibration mode matrix of the bridge through a characteristic value method by combining a quality function obtained by a bridge design drawing. And analyzing the order of the main contribution mode by using the responded singular value spectrum, obtaining the vibration mode of the main contribution mode in combination with the vibration mode matrix, and substituting the measurement point vibration mode of the main contribution mode into a measurement point bridge response calculation formula based on mode superposition to obtain modal response. And substituting the vibration mode of the unmeasured area of the main contribution mode and the modal response into a bridge response calculation formula based on modal superposition, and reconstructing the response of the unmeasured area of the bridge. In the bridge unmeasured area response reconstruction theory, the error between the modal shape obtained by the finite element model and the actual modal shape is solved, and the precision of the modal response and the reconstruction response of the unmeasured area is improved.

The invention provides a temperature field reconstruction method and system based on digital twinning and application thereof, and the method comprises the steps: obtaining multi-moment temperature field data of target equipment, and carrying out the spatial dimension reduction processing, and obtaining K dominant modes; based on the multi-moment temperature field data and the K dominant modes, calculating modal coefficients of the temperature field at each moment in each dominant mode, and forming modal coefficient time sequences in one-to-one correspondence with the dominant modes; training a time sequence prediction model based on the modal coefficient time sequence and the operation condition physical parameters of the target equipment in time alignment with the modal coefficient time sequence, and predicting an initial modal coefficient at a future moment by using the time sequence prediction model; performing feedback correction on the initial modal coefficient based on a correction mechanism to obtain a corrected modal coefficient; and reconstructing the temperature field of the target equipment by using the corrected modal coefficient and the K dominant modals. According to the method, through a technical chain of space dimension reduction, working condition fusion, feedback correction and modal superposition, high calculation efficiency and high full-field reconstruction precision are both considered.

The invention provides a large truss vibration control controlled mode selection method based on optical performance indexes, which comprises the following steps of: 1, establishing a finite element model of a large truss structure, and performing mode analysis on the large truss structure to obtain mode information of vibration of the large truss structure; 2, a linear system of the large truss structure is built through a modal superposition method; 3, calculating the dynamic response of the large truss structure under the required working condition, and obtaining the size of each order of modality under the required working condition; step 4, according to the position of the optical measurement point, establishing a calculation expression of the optical performance index under the physical coordinate, and performing quadratic form fitting; and 5, calculating the modal value of each order of modal to each optical index under the required working condition, and carrying out sorting and screening according to the modal value. According to the invention, the problem of effective mode loss caused by a traditional mode truncation method is solved.

The invention provides an assembly deviation prediction method considering surface macro and micro characteristics and assembly deformation. Comprising the steps of part surface macro-micro feature representation based on primary function modal superposition, non-ideal surface model construction considering an actual machining surface, and non-ideal surface contact state calculation based on a difference plane and point cloud registration method. And solving non-ideal surface contact deformation based on a conjugate gradient-fast Fourier algorithm and establishing an assembly deviation transfer model considering surface macro and micro characteristics and assembly deformation. According to the method, surface form and position errors generated by part machining errors and assembly deformation errors caused by loads in the assembly process are fully considered, the deviation domain model and the Minkowski summation method are combined to simulate transmission of the assembly deviation, the prediction precision of the product assembly deviation is effectively improved, and meanwhile the operation speed is remarkably increased; and real-time monitoring and timely deviation adjustment in the assembling process are achieved.

This invention belongs to the field of simulation correction technology and discloses a finite element simulation correction method and system for the vibration response of a structure excited by turbulent boundary layer. The method includes: obtaining a turbulent cross-spectral expression as input based on CFD calculations or a classical turbulent cross-spectral model; obtaining analytical results of the vibration displacement, velocity, or acceleration response based on the theoretical model of the vibration response of an elastic plate under turbulent boundary layer excitation using the modal superposition method; obtaining numerical results of the vibration displacement, velocity, or acceleration response based on the spatial discretization of the elastic plate and the numerical model of the plate vibration response under turbulent boundary layer excitation; subtracting the analytical results from the numerical results at the corresponding frequencies to obtain a correction amount for the finite element simulation results of the vibration response of the structure excited by turbulent boundary layer; and subtracting the correction amount from the finite element simulation results of the displacement, velocity, or acceleration response of the turbulent-excited structure to obtain the final correct structural response result.

The application discloses a kind of multi-point excited time domain load identification method, using modal superposition method to carry out the transient dynamics response analysis of engineering equipment structure, respectively on each excitation load degree of freedom, obtain the time history response of all expected response degrees of freedom;In frequency domain, construct the transmission relationship between the external excitation load degree of freedom and the expected response degree of freedom, respectively Fourier transform is carried out to all the applied external excitation load and the obtained dynamics response, then construct transfer function at each frequency point;According to the expected dynamics response, construct appropriate external excitation load, Fourier transform is carried out to all the expected dynamics response, according to the constructed transfer function, calculate the external excitation load at each frequency point in frequency domain;Finally, using inverse Fourier transform converts the external excitation load in frequency domain to time domain;The application can solve the ill-posed problem of time domain load identification, and also can provide important support for dynamics control under different dynamic load environment.

The embodiment of the invention provides a hydrogen fuel flow simulation CFD post-processing method, device, equipment and medium, and relates to the technical field of numerical simulation, and the method is realized through the following steps: executing hydrogen fuel flow CFD simulation based on an aero-engine, and generating unstructured grid data; converting the unstructured grid data into a plurality of simulation result files, sorting grid geometric information and numerical value distribution data in the simulation result files, generating a time snapshot matrix, calculating an adjoint matrix S through the time snapshot matrix, and then obtaining a mode corresponding to each feature vector of the hydrogen fuel flow field; and through a mode corresponding to each feature vector of the hydrogen fuel flow field, calculating to obtain a magnification gi and a mode coefficient amplitude ba, and carrying out dynamic reconstruction and prediction on the hydrogen fuel flow field through a mode superposition method. According to the scheme, the flow field state at any moment can be reconstructed and predicted through a modal superposition method, and the post-processing efficiency is improved.

The present invention provides a dense modal response reconstruction method based on a state transfer matrix, belonging to the field of structural response reconstruction, and comprising the following steps: S1, decomposing each order modal response, separating the initial phase from the initial amplitude in the response, and expressing each order modal response in matrix form; S2, constructing the state matrices of the measured point and the point to be reconstructed, respectively, and obtaining the modal mode ratio matrix of the measured point and the point to be reconstructed; S3, constructing the state transfer matrix between the point to be reconstructed and the measured point; S4, reconstructing the response of the point to be reconstructed according to the state transfer matrix. The dense modal response reconstruction method based on a state transfer matrix proposed by the present invention, based on the modal superposition method of linear systems, separates the initial phase from the initial matrix in the modal response, and reconstructs the response according to the state transfer matrix between the point to be reconstructed and the measured point. This method can handle the response reconstruction of structures with dense modal characteristics and ensure the accuracy of the response reconstruction.

The invention provides an underwater ribbed cylindrical shell sound radiation prediction method and system based on parametric modeling, and the method comprises the following steps: (1) constructing a parametric shell model, and determining geometric parameters, material parameters, rib parameters and fluid parameters; (2) establishing a vibration control equation on the basis of a Donnell-Mushtari shell theory; (3) solving a frequency domain vibration response by adopting a modal superposition method, and calculating a modal amplitude; (4) calculating a sound radiation field based on a Helmholtz integral equation, acquiring near-field sound pressure through numerical integration, and acquiring far-field sound pressure by adopting a modal expansion method; and (5) changing the shell thickness and the excitation amplitude ratio F2 / F1 by optimizing structural parameters and excitation configuration, and observing and analyzing the distribution condition of near-distance radiation noise and the amplitude change condition of a main peak of a long-distance radiation noise level frequency response curve. The calculation method is simple, the real-time analysis effect is good, and technical support can be provided for vibration radiation noise analysis and low-noise structure design of an underwater operation platform and a pipeline structure.

The invention provides a method for analyzing the damage of a hidden part of a track structure after train derailment caused by an earthquake, and relates to the field of dynamic response analysis of track structures. The method comprises the following steps: establishing a track substructure model, sequentially establishing track substructures such as a steel rail, a fastener system, a track plate, a filling layer and a base plate from top to bottom, and introducing cohesion unit simulation between structural layers, according to the earthquake load simulation, earthquake waves are transmitted to the structural non-supporting point freedom degree through the structural supporting point freedom degree, and then the whole vehicle system is influenced. According to the method, the accuracy and the calculation efficiency of dynamic response analysis of a track structure under the earthquake action are remarkably improved by introducing an improved nonlinear elastic theory and a multi-point non-Hertz contact model and combining a modal superposition method and a multi-scale analysis method in consideration of a vehicle-track complex collision contact behavior after derailment.

The application discloses a structural seismic response calculation method based on a dynamic guidance support vector machine, which comprises the following steps: a finite element model is established to extract structural dynamic characteristics; in combination with the structural dynamic characteristics, a single degree of freedom system motion equation is used as a constraint condition to optimize an objective function, and parameter optimization of a prediction model is realized; an LS-SVM algorithm is adopted to input structural characteristics and ground motion, and to output response quantities such as displacement and velocity, so as to construct a PDLS-SVM model; a modal decomposition method is used to decouple a multi-degree of freedom system, and a dynamic equation and a modal superposition principle are used to construct a seismic response prediction model; and based on a linear interpolation recursive formula, the performance of the seismic response prediction model of the structure is verified, and performance evaluation indexes are obtained; the application uses structural dynamic equations and physical laws as a basis, and considers structural dynamic characteristics to construct a data-independent seismic prediction model, so that the shortcomings of traditional methods and machine learning methods are overcome, and the calculation efficiency and accuracy are improved.

The invention discloses a composite vibration response analysis method under the combined action of basic excitation and nodal force excitation, and the method comprises the steps: applying a basic vibration load spectrum to a basic load action position, and carrying out the dynamics calculation of an equipment structure under the basic vibration load spectrum based on a modal superposition method, obtaining a basic excitation response under the basic vibration load spectrum; applying the node force load spectrum to the node force load action node, and carrying out dynamics calculation under the node force load spectrum on the equipment structure based on a modal superposition method to obtain a node force excitation response of the equipment structure under the node force load spectrum; performing superposition calculation on the basic excitation response and the node force excitation response by using a composite response superposition method to obtain a composite vibration response of the equipment structure; reliable composite vibration response of the equipment is obtained through numerical analysis, the reliability of environmental adaptability analysis and evaluation of the airborne precision equipment is improved, and the research and development risk of the precision equipment is effectively reduced.

A rocket system level structure vibration simulation and verification method, comprising: constructing a rocket system level structure finite element model based on modal superposition method, carrying out harmonic response analysis, constructing excitation-response transfer function in frequency domain, and determining dynamic load transfer path and amplification effect; combining the power spectral density of the rocket vibration environment, implementing random vibration analysis, quantifying the system level structure strength safety margin by calculating the fatigue life; selecting weak components or typical components to carry out targeted vibration test, and verifying the reliability of the system level vibration simulation method in the above steps through test data. The method can effectively improve the vibration environment prediction accuracy and structure design reliability.

This invention relates to a data processing method and storage medium for ice-elastic plate compression tests in the field of ship structural mechanics. The method includes the following steps: performing a compression test by compressing an ice sample with an elastic plate; after the compression test, obtaining the test pressure value and strain gauge test values ​​of the ice sample under compression; selecting a preset order mode shape using the modal superposition method to obtain a fitted deflection function; determining the fitted strain value corresponding to each test point of the elastic plate based on the fitted deflection function; calculating the time coefficient by combining the strain gauge test values ​​and the fitted strain values ​​using the least squares method to obtain the fitted deflection distribution function of the elastic plate; and calculating the compression energy of the elastic plate and the ice sample based on the fitted deflection distribution function and the test pressure value. This method focuses on the deformation of the elastic plate to explore the interaction between ice and the structure from an energy perspective, considering the feedback influence of structural deformation on the action process, thus forming a universal method for predicting ice loads.

The invention discloses an FE-VFIFE hybrid calculation method for nonlinear dynamic analysis of a complex structure, which is suitable for the fields of seismic engineering, ocean engineering and the like which require real-time simulation and analysis of the complex structure, the FE and the VFIFE are combined, dimension reduction of each linear substructure is realized through a modal superposition method in a conventional finite element, and the nonlinear dynamic analysis of the complex structure is realized. The whole system is decoupled into a series of modal equations, and the calculation amount is reduced; vector type finite elements are used for calculating the internal force of the nonlinear part, the situation that a global stiffness matrix is repeatedly updated in the calculation process is avoided, meanwhile, a Chang method is adopted for unconditional stable integration, and mass and damping correction factors are introduced to improve the calculation precision, increase the integration step length and improve the calculation efficiency. The method can be efficiently applied to real-time hybrid simulation of the local nonlinear problem of a complex structure system, and powerful support is provided for performance evaluation and design optimization of the complex structure under the action of complex dynamic loads such as earthquakes and marine environments.

The invention discloses a structure nonlinear dynamic response incremental modal overlay analysis method and system, and belongs to the field of aerospace structure dynamics calculation. The method comprises the steps of constructing a finite element model and obtaining an initial matrix; dispersing the time-varying temperature field into a plurality of time increment intervals, updating material parameters in each interval, and calculating an instantaneous matrix; carrying out eigenvalue analysis and converting the kinetic equation into a modal coordinate system; solving a modal response increment by adopting a numerical integration method and converting the modal response increment to a physical coordinate system for superposition; and circularly executing until a full-time-history response is output. According to the method, the problem of rigidity nonlinearity caused by the temperature is solved through incremental linearization and modal order reduction, high calculation precision and high efficiency are achieved, and the method is suitable for dynamic design and analysis of aerospace structures in the high-temperature variable-temperature environment.

The present application relates to a kind of wave environment under suspended tunnel dynamic response frequency domain calculation method, belong to the field of tunnel structure.Based on classical dynamics theory, the elastic foundation beam simplification of pipe body with discrete anchor is carried out, the motion control equation of suspended tunnel is established using Hamilton principle, the wave force on suspended tunnel pipe body is calculated by potential flow theory and combined with boundary element numerical calculation method, finally the dynamic response of suspended tunnel is obtained by solving wave-solid coupling equation using modal superposition method.Based on potential flow theory, the accuracy and efficiency of the solution can be focused on simultaneously, it is suitable for large-scale structure, and the combination of elastic foundation beam model makes the calculation of wave-solid coupling not consume too much computing resources, comprehensive multi-parameter multi-condition analysis is carried out on the structure, the coupling effect of pipe body horizontal displacement and torsional displacement is considered, compared with the previous method, the calculation of the situation that pipe body appears larger horizontal displacement or torsional displacement will be more accurate.

The invention provides a reduced-order galloping analysis method based on intelligent mode selection, and belongs to the technical field of electric power operation and maintenance, and the method comprises the steps: building a digital model of a power transmission conductor, and representing the geometric configuration of the conductor; performing finite element modal analysis on the digital model to obtain a multi-order vibration modal vector of the conductor; implementing intelligent modal screening; quantifying key point displacement characteristics for each order of modal; constructing a modal feature vector, inputting the modal feature vector into the trained convolutional neural network for modal classification and dominant evaluation, and screening out a dominant modal set; performing mode superposition by using modes in the dominant mode set, and describing vertical vibration displacement and out-of-plane vibration displacement of the wire; and constructing a reduced-order kinetic energy and potential energy expression based on the dominant mode set, and obtaining a dimensionality-reduced kinetic model for solving. The method has the advantages that only key modals are reserved through the intelligent screening technology, the dimensionality of a kinetic equation is reduced, simulation analysis is converted into rapid completion from traditional long-time calculation, and the analysis period is shortened.

The invention discloses a curve track-bridge coupling system support stiffness identification method based on a vehicle scanning method, which belongs to the field of engineering structure monitoring, and comprises the following steps: establishing a curve double-beam system mechanical model with moving elastic mass, deducing a control equation, and solving by adopting a modal superposition method and Laplacian transformation to obtain the support stiffness of a curve track-bridge coupling system. Coupled system frequencies are extracted from contact points or vehicle responses, in particular track moduli are efficiently identified using fourth frequency components of first order modalities. The method has the advantages of being high in operation maneuverability, high in cost-benefit ratio and outstanding in implementation efficiency, and is suitable for health monitoring of the curve track-bridge coupling system.

The present invention belongs to the technical field of railway engineering, and provides an efficient prediction method for the fatigue life of the elastic clip of high-speed railway fasteners, including: based on the natural frequencies obtained from the prestressed modal analysis of the solid element finite element model, the linear constraint stiffness of the elastic clip beam element model is optimized by using the particle swarm algorithm, and the static equivalent stress of the elastic clip beam element model, as well as the natural frequencies, vibration modes and modal equivalent stresses of different frequency orders in the prestressed modal analysis are derived, and the dynamic equation of the elastic clip in the installed state is established based on the modal superposition method; applying the vehicle-track spatial coupling dynamic model, generating the three-dimensional dynamic responses of the rail and the track slab corresponding to the contact position of the elastic clip, and using this as the excitation input into the elastic clip dynamic model, calculating the dynamic responses such as the vibration acceleration and equivalent dynamic stress of the elastic clip; based on the fatigue cumulative damage theory, calculating the fatigue life at different positions of the elastic clip, and judging the dangerous area and the most dangerous point where the elastic clip is prone to high-frequency fatigue fracture.

The present application relates to a kind of mechanical structure response reconstruction method and system based on optimal modal response estimation, belong to structural response reconstruction field, method includes according to free vibration modal response form construction response estimation signal;Residual between response estimation signal and real measurement signal is calculated;According to the spectral characteristics of residual signal, optimization objective function is constructed;Optimization function is solved using gradient descent algorithm, and the modal response of each order estimated is obtained;According to modal transfer ratio equation, structural response reconstruction is completed.The method of the present application is based on the modal superposition method of linear system as theoretical basis, by constructing response estimation signal and optimizing the spectral characteristics of residual signal, the optimal modal response estimation signal is obtained, and finally the response reconstruction is carried out through modal transfer ratio equation, this method can realize the response reconstruction of structure with dense modal characteristics based on single sensor data and ensure the accuracy of response reconstruction.

The invention discloses a multi-batch three-dimensional sensor optimization layout method in a modal test, which is used for extracting candidate sensor positions from a finite element model and solving the optimization problem by simultaneously considering a reference sensor and a mobile sensor. Firstly, a modal addition method is carried out on candidate sensor positions extracted from a finite element model, a reference sensor candidate set is selected, then an improved three-dimensional independence criterion and a minimum variance criterion of structural response estimation errors are combined, and three-dimensional sensor optimization layout is achieved by optimizing a batch with the worst objective function result. According to the method, the modal test precision of a large-scale structure or a complex structure can be effectively improved.

This invention relates to a time-domain calculation method for the dynamic response of suspended tunnels under multi-load coupling, belonging to the field of dynamic response analysis of suspended tunnels. Addressing the problems of poor versatility and difficulty in handling multi-load coupling and structural variations caused by inconsistent governing equations in traditional methods, this invention proposes establishing a unified equation of motion for the tunnel body. This equation is decomposed into a system of generalized coordinate ordinary differential equations using the modal superposition method. An implicit Newmark-β method is employed for solving the equations, and a sub-loop iteration mechanism is embedded to achieve dynamic coupling between loads and tunnel motion. By independently modeling anchor cable constraint reactions and using a modular environmental load interface, the method is compatible with complex terrain and various load coupling effects. This invention improves the versatility and computational efficiency of dynamic response analysis of suspended tunnels, solves the accuracy and stability challenges under multi-load interaction, and provides a reliable basis for engineering design.

A kind of cell flow field structure optimization method based on the vibration characteristics of proton exchange membrane fuel cell and its cell, method steps include: S1, establishing the three-dimensional finite element model of cell;S2, determine the vibration mode and inherent frequency of fuel cell;S3, load acceleration power spectrum density of random vibration load, obtain the structural response characteristics of fuel cell assembly under three-axis random vibration excitation;S4, each flow field structure pre-optimization scheme design is carried out, and the flow field structure geometric model is established;S5, obtain maximum stress and stress distribution coefficient;S6, obtain final optimization scheme;Cell has the flow field structure obtained by any optimization method described above;The present application improves the width ratio of flow channel and ridge by establishing three-dimensional finite element model and modal superposition method for modal analysis, significantly reduces the stress concentration and deformation of assembly under dynamic load environment, and improves the stability of fuel cell;Through simulation and optimization design, reduce stress distribution coefficient, make the stress distribution of fuel cell more uniform, significantly improve the performance and life of cell.

The present invention discloses a method for analytically calculating the vibration and noise of an outer-rotor axial-flux hub motor, belonging to the technical field of motor vibration and noise calculation, and comprising the following steps: S1: Establish an air-gap magnetic field model and calculate the electromagnetic force; S2: Calculate the modal parameters and vibration modes of the end cover; S3: Calculate the vibration response of the end cover; S4: Obtain the overall sound power level of the flux motor; S5: Verify the results. Based on the modal superposition method, the present invention can calculate the vibration response of any point on the end cover surface and quickly predict the electromagnetic vibration and noise in the entire speed range, providing a theoretical basis for the optimal design of the axial-flux motor vibration and noise, and is worthy of being popularized and used.

The invention discloses a simple harmonic vibration analysis method based on a modal superposition method, and the method comprises the steps: carrying out the modal analysis of a three-dimensional model of equipment, and obtaining a solution of the modal space of the equipment; a periodic load is obtained, the previous solution of the modal space is selected as the solution of the displacement response of the system in the physical space, the system motion equation under the simple harmonic vibration after coordinate transformation is solved, and a frequency response curve of the equipment structure is obtained; whether the maximum deformation value of the equipment structure under the action of the corresponding periodic load is smaller than an allowable value or not is analyzed by combining the frequency response curve of the equipment structure, and if yes, it is verified that the equipment design meets the requirement; otherwise, verifying that the equipment design does not meet the design requirement, performing reinforcement design on the part with weak structural strength, and repeating the steps until the equipment design meets the requirement. The method ensures that the use of the equipment is not influenced when the equipment is subjected to specified periodic load, and is used for improving the product design efficiency and shortening the equipment design period.

This invention discloses a hybrid FE-VFIFE calculation method for nonlinear dynamic analysis of complex structures, applicable to fields such as earthquake engineering and marine engineering that require real-time simulation and analysis of complex structures. This method combines FE and VFIFE, using the modal superposition method in conventional finite element methods to reduce the dimensionality of each linear substructure, decoupling the entire system into a series of modal equations and reducing computational load. Vector finite element methods are used to calculate the nonlinear internal forces, avoiding repeated updates to the global stiffness matrix during calculation. The Chang method is employed for unconditional stability integration, and mass and damping correction factors are introduced to improve computational accuracy, increase the integration step size, and enhance computational efficiency. This invention can be efficiently applied to real-time hybrid simulation of local nonlinear problems in complex structural systems, providing strong support for performance evaluation and design optimization of complex structures under complex dynamic loads such as earthquakes and marine environments.

This disclosure relates to a method and system for predicting the surface roughness of side milling based on multi-mode superposition, including: acquiring multi-mode parameters of the cutting tool and machining parameters; determining an ideal tool tip trajectory based on the machining parameters; establishing a tool vibration response model under periodic cutting force excitation based on the principle of modal superposition and the multi-mode parameters, and calculating the vibration amplitude distribution at different heights along the tool axis; extracting the time-domain vibration response at the tool tip height as a vibration disturbance term, superimposing it onto the ideal tool tip trajectory to construct the tool tip motion trajectory; constructing a surface morphology model based on the tool tip motion trajectory to obtain the theoretical distribution law of surface roughness with the tool axial height; constructing a neural network prediction model based on the multi-mode parameters, machining parameters, and theoretical distribution law, training the model using a loss function based on the tool vibration response model, and obtaining the surface roughness prediction result of the tool. This disclosure can improve the accuracy and reliability of roughness prediction.