Numerical Analysis Of Periodical Composite Structural-acoustic Problems With Multi-scale Mixed Aleatory And Epistemic Uncertainties

In order to achieve sustainable development,materials in engineering is required to be light and rigid.Composite materials can meet these requirements.Therefore,composite materials are widely used in engineering.However,when excitation is applied on thin,light and flexible composite structures,especially when the frequency of excitation is close to the natural frequency of the composite board or the cavity of the passenger compartment,severe vibrations will occur and noise will be transmitted to the passengers.Therefore,it is of great significance to analyze the vibration of the composite structural-acoustic system.Due to the harsh environment,the inevitable manufacturing errors and the influence of incomplete cognition,parameters in the system are always associated with the uncertainty in engineering practice.If these uncertainties involved in structuralacoustic system are ignored,the results of vibro-acoustic analysis will be unreliable.With the support of the National Natural Science Foundation of China and the Hunan Natural Science Foundation of China,intensive researches are done on periodical composites structural-acoustic system with mixed aleatory and epistemic uncertainties.And Evidence-theory-based Polynomial Expansion Method(EPEM),the Fuzzy and Random generalized Polynomial Chaos Method(FRg PCM)and Fuzzy and Random Moment-based Arbitrary Polynomial Chaos Method(FRMAPCM)are proposed.Numerical examples validate these proposed methods.The main research results of this paper are:(1)For the response analysis of the periodical composites structural-acoustic system with bounded random variables,interval variables and evidence variables,an Evidence-theory-based Polynomial Expansion Method(EPEM)is proposed.This method converts bounded random variables and interval variables into evidence variables,and then uses the orthogonal polynomial expansion method to approximate the response,thereby estimating the upper and lower bounds of the cumulative probability distribution function of the response.Using EPEM,the probability boundary of the response can be obtained efficiently.Numerical examples verify the accuracy of the proposed method,and the effectiveness of the method is verified by two engineering examples.(2)For the response analysis of periodical composites structural-acoustic system with mixed aleatory and epistemic uncertainties,the generalized polynomial chaos method is introduced into the hybrid fuzzy and random uncertain model and the fuzzy and random generalized polynomial chaos method(FRg PCM)is proposed.The method was used to approximate the response of the system.In FRg PCM,the optimal orthogonal polynomial of the random variable is selected according to its probability distribution,and the fuzzy variable selects the legendre polynomial as its polynomial basis.The research results show that FRg PCM can achieve high accuracy.(3)The traditional polynomial chaos method will produce a fitting error when processing random variables with only sampling data information acquired,and the error may increase sharply during the transmission process.In response to this problem,a moment-based arbitrary polynomial chaos method is introduced into the hybrid fuzzy and random model,and the Fuzzy and Random Moment-based Arbitrary Polynomial Chaos Method(FRMAPCM)is proposed.The proposed method is applied to predict the response of system.FRg PCM constructs the polynomial basis according to the probability distribution of random variables,while FRMAPCM directly constructs a polynomial basis using random moments calculated from random sampling data to avoid errors caused by fitting probability density functions.The research results show that when random variables are given in the form of randomly sampled data,the calculation accuracy of FRMAPCM for the uncertainty analysis of the system is significantly higher than that of FRgPCM.