A Study On Random Vibration Analysis Method And Engineering Applications

In the engineering field,the external environment of the structures and the load acting on the structures are very complex.And taking into account the manufacturing,processing and other factors of the structures cannot be achieved in full control,these also resulted in the structures with the randomness of physical parameters.Therefore,in the structure analysis and design process,structural parameters and the load cannot simply be treated as deterministic variables.The theory of randomness should be used to deal with the problem of the structural vibration,so to be able to calculate the real results of the structural analysis.Random vibration theory and methods developed in recent years are advanced thinking and an important means which dealing with such problems.But at home and abroad in the engineering field,random vibration theory and methods are still relatively little practical application,because there is a certain lack of random vibration analysis of existing methods in computational accuracy and efficiency,so the random vibration theory and methods need further research and development.For this problem,this article combines with the existing random vibration analysis methods and takes a variety of new ideas for targeted development and improvement.The main contents are as follows:(1)The integral term of general solution of state equation in precise time step integration method is analyzed by a compound integration of Cotes,and an improved precise time step integration method is given.The method inherits the advantages of traditional precise integration method with high accuracy,and overcomes the disadvantages of the matrix inverse,linear load assumptions.It can get a good result by multiple compounds computing at each large time step,and a succinct explicit expression of random dynamic response is deduced.Combining with the theory of random vibration,the method can deal effectively with time domain analysis of random vibration,and can deal effectively with frequency domain analysis of random vibration by constructing the virtual incentive.The effectiveness of this method is demonstrated by numerical results,and the rapidity and validity of this method is proved by analysis of the results.(2)Considering the large amount of calculation and long time of mathematical model of the large complex engineering structure analysis,structural model reduce to a lower order.Using dynamic condensation iteration method and the Lanczos vector superposition method,structural model reduce order in physical space and modal space.Combining with improved precise time step integration method,two kinds of fast random vibration analysis methods are proposed,which inherits the advantages of this method.By numerical examples,two methods can rapidly and accurately analyze the random vibration of large and complex structures.(3)When the physical parameters and geometric parameters of the structure are random,the structural dynamic differential equation will contain random parameters.Structural response is the function of random parameters,which is difficult to get the explicit expression.Random parameters and random excitations are independent of each other,so the influence of random parameters and random excitations to structure are calculated respectively.Latin Hypercube Sampling is used to deal with the random parameters,and the improved model order reduction method is derived based on the theory of Neumann series,which can quickly reduce order for the corresponding dynamic equations of each sample values.Compound random vibration of stochastic structure can be effectively analyzed by fast random vibration analysis methods.This study shows that the methods can rapidly and accurately analyze the compound random vibration problems of engineering structures.(4)The widely used solar panels in aerospace field are the main advanced energy sources of spacecraft.It features large size,soft stiffness and small damping,and Random vibration under random excitation will last for a long time.The vibration will severely influence the photoelectric efficiency of solar panels and the performance of spacecraft,so it is necessary to analyze Random vibration of solar panels.Using the methods in paper to calculate stochastic dynamic response of solar panels,this study shows that the methods are efficient and accurate,and the methods can provide effective reference for random vibration analysis of actual engineering structures.