Natural Frequency Calculation Of Random Structures Using Recursive Stochastic Finite Element Method And Padé Approximation

In the scientific research work and practical engineering practice,the randomness of the structure can not always be avoided,whether it is the uncertainty of the structural material parameters of the structure or the uncertainty of the external load of the structure,and it is necessary to consider the content.These uncertainties have an unpredictable effect on the structure.In order to quantify these uncertainties,many experts and scholars have proposed solutions from different perspectives.This paper focuses on the RSFEM method,which shows the advantages of RSFEM method to other methods.It also points out that RSFEM method maybe exit some errors when deal with structures with large coefficient of variation,this problem is solved in the following chapters.Combining Padé approximation with RSFEM,the examples show that the calculation results are good.In this paper,we can solve the problem of random structure frequency calculation.Here are the contents of this article and some innovative points to sum up:(1)In recent years,the new ideas of emerging methods in the field of random structures have been comprehensively collated and summarized.While introducing these methods,the article also introduces the origin,development,application scope and follow-up direction of each method.(2)In this paper,the recursive stochastic finite element method is briefly introduced in the introduction,and the method is introduced in detail in the second chapter.After the theoretical analysis,the paper gives a detailed example of random structure.The RSFEM method and the Monte-Carlo method are used to contrast and analyze the results.The results are compared with the obtained results,and the accuracy and validity of the RSFEM method are described.(3)When the nonlinearity of the random structure is very strong and the parameter variability is large(generally larger than 0.3),the RSFEM method will gradually increase the error of the random structure frequency.In this case,it is difficult to solve the natural frequency of the random structure by RSFEM to achieve the requirements,the need to start on the basis of the fourth step on the method to a certain degree of improvement in order to achieve the purpose of expanding the scope of RSFEM law.(4)In this paper,we propose a new method to improve the recursive stochastic finite element method by combining the Padé approximation,so that the recursive stochastic finite element method combined with Padé approximation can reduce the frequency statistic error when calculating the random structure frequency of higher order.(5)In the range of random variables,there are some problems of "singularity" in the form of Padé approximation.According to the reference,the paper uses a combination of Padé approximation to solve the problem.The new method of construction is better than the original method,and the error is in a very small range,which proves the effectiveness of the new method.