Research On Vibration Harmonic Response Correction And Parallel Implementation Based On Modal Acceleration Method

Structural dynamics plays an increasingly important role in aerospace,development of various weapons and equipment,and seismic structural design.The finite element analysis of structural dynamics is a main technical means to study the seismic and vibration response of structures,and plays an important role in structural dynamics optimization design.In the finite element analysis of dynamics,the modal superposition method is an important link from modal analysis to other dynamic analysis.At present,the commercial finite element software is mostly based on this method in structural dynamic response calculation,especially in large-scale calculation.On the one hand,the modal superposition method usually takes the first few modes to analyze,which can reduce the calculation amount to a large extent.On the other hand,because the modal truncation process is adopted in the calculation,the influence of the higher-order mode is ignored,leading to its solution accuracy be affected.In recent years,with the continuous improvement of high-performance computer hardware technology and the continuous development of various advanced algorithms,large-scale complex numerical simulation has gradually become a reality.As an important method in structural dynamics analysis,how to improve the calculation accuracy of modal superposition method has become an important issue in the development of large-scale finite element analysis software.In response to this problem,this paper explores a variety of correction methods based on modal superposition.For the harmonic response analysis,this paper combines the modal acceleration method with the large-scale finite element calculation platform PANDA,and carries out theoretical analysis,algorithm design,parallel implementation and case study.The main work of this paper is as follows:(1)This paper investigates a variety of existing vibration response correction methods based on modal superposition method,and investigates and explores related correction methods and theories.Combining the relevant frontier research dynamics at home and abroad and the feasibility of large-scale parallel implementation of each correction method,the modal acceleration method is determined as the core algorithm for vibration response correction.(2)This paper combs the data structure of the large-scale finite element computing platform PANDA,the algorithms involved in the main analysis types of structural dynamics,and the parallel solution process.Based on the mastery of the PANDA platform,this paper studies the technical approach of using the modal acceleration method to modify the vibration response on the PANDA platform,and determines the harmonic response analysis as the main correction type to carry out related research work.(3)Based on the PANDA platform,this paper develops a harmonic response correction analysis algorithm based on modal acceleration method,and studies the interface between modal analysis and harmonic response correction analysis,and realizes the call of modal analysis results in harmonic response analysis.This paper studies the corresponding iterative technique,which avoids the matrix inversion caused by the problem of large quantities of large-scale parallel computing.Using hierarchical,modular and object-oriented programming ideas,this paper implements the harmonic response correction analysis module based on modal acceleration method on the PANDA platform.(4)A numerical example study on the correction effect of the modal acceleration method is carried out in the PANDA platform.Starting from the selection of different modal orders,this paper compares the computational accuracy of modal acceleration method and modal superposition method.The research shows that the modal acceleration method has a significant improvement in the calculation accuracy compared with the modal superposition method.Modal acceleration can achieve higher accuracy with fewer modalities.By comparing the calculation times of the two methods,to achieve the same calculation accuracy,the modal acceleration method requires less computation time.Finally,this paper carried out multi-core parallel computing research.The results show that for millions of degrees of freedom model,the parallel computing efficiency of 100 cores can reach more than 30%.The module has good parallel scalability.The modal acceleration method used in this paper makes up for the shortcomings of the traditional modal superposition method,reduces the computational resource consumption,improves the calculation accuracy,and plays a certain role in promoting the development of the existing dynamic system and PANDA software platform.