Hybrid Uncertain Analysis for Exterior Acoustic Field Prediction with Interval Random Parameters

For exterior acoustic field problems that lack sufficient information to construct precise probability distributions, an interval random model is introduced to deal with the uncertain parameters. In the interval random model, the probability variables are employed to treat the uncertain parameters, whereas some distribution parameters of random variables are modeled as interval variables instead of precise values. Based on the interval random model, the interval random finite element equation for exterior acoustic fields is established and a hybrid uncertain analysis method is presented to solve the exterior acoustic field problem with interval random variables. In the presented method, by temporarily neglecting the uncertainties of interval variables, a first-order stochastic perturbation method is adopted to calculate the expectation and the variance of the response vector. According to the monotonicity of the expectation and variance of the response vector with respect to the interval variables, the lower and upper bounds of the expectation and variance of the response vector can be calculated by the vertex method. In addition, in order to ensure accuracy of the proposed method, the subinterval technique is introduced and investigated. The numerical example of a square flexible shell model is presented to demonstrate the effectiveness of the proposed method.</jats:p

Squeal reduction of a disc brake system with fuzzy uncertainties

Automotive brake squeal has become one of the major concerns in the automotive industry. The researches on suppressing brake squeal are of great practical significances. However, most of the existing researches have not taken into account the parameters uncertainties, although it is well known that uncertain factors widely exist in the brake systems. To reduce disc brake squeal more effectively, a practical approach for the stability analysis and improvement of an automotive disc brake system with fuzzy uncertainties is proposed. In the proposed approach, the uncertainties associated with friction coefficient, material properties and loading properties are taken into consideration, and the uncertain parameters of the brake system are represented by fuzzy numbers. The brake system stability is investigated by performing complex eigenvalue analysis (CEA), and response surface methodology (RSM) is employed to approximate the implicit relationship between the dominant unstable mode and system parameters. Then, the stability analysis model of the brake is constructed based on RSM, CEA and fuzzy analysis. As a numerical example, the stability analysis of a commercial disc brake system with fuzzy uncertainties is carried out, and the influences of different uncertain parameters on system stability are investigated. The analysis results show that the stability of the fuzzy brake can be improved effectively by increasing the specific modulus of back plate. The proposed approach can be considered as a potential method for squeal reduction of automotive disc brake systems under fuzzy case