Uncertainty Analysis Of Energy Finite Element Models Of Beam And Plate Structures

In engineering practice,vibration may lead to structural damage and failure.It may also reduce the service life of equipment.At the same time,the noise will affect people's health.In the high-end manufacturing industry,high-speed rail,ships and other transportation equipment mainly face the problem of medium-high frequency vibration.Finite element method and statistical energy analysis are commonly used in vibration analysis.But the two methods have some limitations in the efficiency of vibration analysis and the details of response in the medium-high frequency vibration analysis.The energy finite element method makes up for the deficiency of the above method in the medium-high frequency analysis.The energy flow model established by this method can be used to reflect the dynamic response of the structure.However,there are assumptions and simplification in the process of modeling,and material defects and manufacturing errors add the uncertain of model parameters.These problems will make it difficult for the energy finite element method to predict the real response.This paper is supported by the National Natural Science Foundation of China(No.51675306 and No.52075294),and systematically analyzes the uncertainty of energy finite element model.The probability density of structural parameters often depends on a large number of sample data.In the case of limited samples,interval analysis can be used as a method to obtain the response boundary.Therefore,it is necessary to analyze the interval of energy flow model to provide reference for obtaining the actual interval of response.Based on the energy flow model of beam and plate,corresponding interval analysis methods are proposed.On this basis,the excitation frequency,wave pattern and interval parameters are considered to explore the effect of response boundary of energy finite element model.The main research contents are as follows:Firstly,when the parameter interval is large,it is difficult for the traditional interval perturbation analysis to ensure the accuracy of the interval analysis of the energy flow model.In this paper,the iterative method based on evaluation index is proposed for the case of large parameter interval.The method uses the second-order Taylor expansion to establish the relationship between energy response and interval parameters.In order to improve the accuracy,the parameter sub interval is divided continuously,and the subinterval division evaluation index and error evaluation parameters are proposed.Compared with the results of Monte Carlo method and interval perturbation analysis,the reliability of the proposed method in accuracy is verified.Secondly,interval analysis is applied to the energy flow model of coupled structure.The energy flow model of one-dimensional coupled beam structure is more complex than that of single beam model.The efficiency of interval analysis will decrease.This paper presents an element merging method for the energy finite element model.The elements of each matrix in the energy flow model are treated by superposition,merging and other methods to obtain a simplified coupled beam energy flow model and interval analysis is carried out.On this basis,the effects of different wave types,relative radius of interval and excitation frequency on the response boundary are studied.Then,the interval analysis is extended to the energy flow model of two-dimensional coupled plate.Compared with the coupled beam,the coupled plate has more wave types.The energy finite element model of the coupled plate is simplified by the element merging method,and the elements of the energy density vector are concentrated on the coupling boundary of the coupled plate.In addition to exploring the relationship of the three wave patterns,excitation frequency and the response boundary,the influence of the uncertainty of coupling boundary connection on the response boundary is also explored.Finally,the energy flow model with non-uniform parameters is also used for interval analysis.Because the model contains different interval parameter units,it can not be directly used in interval analysis.In this paper,the transformation matrix is introduced to transform the energy flow model,so as to separate the uniform and non-uniform elements in the energy flow models of beam structure and plate structure.On this basis,the uncertainty analysis of the model is realized,and the influence of the two elements and the corresponding parameters on the response boundary is explored.