Research On Uncertain Acoustic Numerical Methods Based On The Evidence Theory And Finite Element Method

With the development of the numerical techniques and the computer performance, engineers can predict the acoustic performance by using the numerical computation methods. Based on the Helmholtz equation, the acoustic finite element method can effectively calculate the sound pressure response of the acoustic field problems and structural-acoustic problems under low frequency by discreting the acoustic field and establishing the finite element equations. Uncertainties associated with the environmental conditions, model stability, numerical simplification, manufacturing level, and anthropogenic causes, etc exist in acoustic problems. Generally, uncertainties can be categorized into two types, namely aleatory uncertainty and epistemic uncertainty. Recently, research on uncertain acoustic numerical methods mainly focus on the probability model and interval model, but rarely on the epistemic uncertainty model.In order to analyze the acoustic field and the structural-acoustic system with epistemic uncertain parameters, a systemic research work on the acoustic numerical computation methods based on the evidence theory is carried out in this thesis and an evidence theory-based finite element method (ETFEM) is proposed.The main research work and innovative achievements in this thesis are as follows(1) The formulation of the acoustic and structural-acoustic finite element method is induced based on the acoustic dynamic equation.(2) As a generalization of the above probability and non-probability uncertainty models, the evidence theory is employed to model the imprecision of uncertain parameters in acoustic fields and the structural-acoustic systems. Evidence theory can deal with the problem with limited or even conflicting information. A "risk prediction" and "conservatism prediction" of the system response can be obtained by the belief measures and plausibility measures.(3) Based on the theory of interval analysis and perturbation method, the basic formulation of ETFEM is induced, and the interval of expectation and variance is used to describe the distribution characteristics of evidence variables. Three numerical examples are given to demonstrate the effectiveness of the present method, which include a2D acoustic tube and a2D car acoustic cavity with epistemic uncertain parameters, and a2D car acoustic cavity with conflicting information.(4) The ETFEM method is extended to the structural-acoustic fields with...