Numerical Analysis And Topology Optimization Of The Composite Structural-acoustic System Involving Multi-scale Hybrid Uncertain Parameters

Composite materials are widely used in automotive and aviation fields because of their light weight,high strength and high toughness.The thinwalled thin plate w ill coupling with the surrounding sound field under the external excitation condition,the noise produced by structural vibration will affect the riding comfort of vehicles,resulting in discomfort of passengers and damage to human health.Composite thin plates have good application prospects in structural-acoustic systems due to their excellent mechanical properties and designability.Numerical analysis and topology optimization of composite structural-acoustic System(CSAS)based on ccoustic properties are effective means to improve the NVH performance of vehicles.At present,the numerical analysis about CSAS is mainly based on the determined system parameters.However,in practical engineering applications,uncertaintie s widely exist in the CSAS due to the errors in manufacturing,assembling and measuring,external load uncertainty and complex environmental conditions.On the one hand,these uncertain parameters exist at the macro level,such as the physical parameters of the sound field medium and environmental disturbances.On the other hand,it also exists from the micro level,such as the composition of the microstructure material physical parameters and distribution morphology.Besides,due to the limited statistical Information,hybrid uncertain parameters may exist in CSAS simultaneously.The analysis results may be inaccurate if the influence of these hybrid uncertainties was ignored.In addition,the research on microstructure topology optimization(MTO)of CSAS with multi-scale hybrid uncertainty needs to be further developed.Therefore,it is important to investigate the numerical analysis and topology optimization of CSAS involving multi-scale hybrid uncertainty.In this paper,the numerical analysis and MTO of CSAS with multi-scale hybrid uncertain parameters were studied systematically w ith the support of the National Youth Natural Science Foundation of China(51905162)and the Natural Science Foundation of Hunan Province(2019JJ50062).Based on the homogenization theory and orthogonal polynomial expansion,the effects of hybrid bounded random and interval uncertain parameters on the effective elastic properties of periodic composites were s tudied.Based on Finite Element Method(FEM),analysis models of CSAS involving different types of multi-scale mixed uncertain parameters were established.Then two nu merical analysis methods for CSAS with multi-scale hybrid uncertainties are proposed.Based on the adaptive genetic algorithm,the MTO method of CSAS involving multi-scale hybrid uncertain parameters were given.This investigation was carried out and completed as following:(1)A homogenization-based hybrid uncertainty analysis method(HHU AM)was proposed to calculate the effective elastic tensor of periodic microstructure with hybrid bounded random and interval uncertain parameters.Based on the homogenization method and Gegenbauer series expansion method,the expression of HHUAM was derived.In HH UAM,the effective elastic tensor with hybrid bounded uncertain parameters was approximated by the Gegenbauer series expansion.By using the orthogonality property of Gegenbauer polynomials,the expectation and variance of effective elastic tensors with hybrid bounded uncertain parameters can be calculated.The influence of hybrid bounded uncertainty in microstructure on uniform macroscopic elastic properties of heterogeneous materials was also studied.(2)A numerical analysis method based on generalized polynomial chaos was proposed to predict the sound pressure response of CSAS in volving hybrid interval random uncertainties.Firstly,the generalized polynomial chaos expansion is used to deal with the random uncertainty in CSAS,then the polynomial coefficients in the polynomial chaos were processed into qu adratic polynomial functions with respect to the distribution parameters to deal with the epistemic uncertainty in CSAS,and the quadratic polynomial coefficients were solved by the double-layer sampling strategy.The accuracy and efficiency of the proposed method were verified by two engineering examples.The results showed that the proposed method could not only calculate the expectation and variance range of sound pressure amplitude of CSAS,but also conveniently solve the cumulative probability distribution boundary of sound pressure of amplitude of CSAS,which has good engineering practicability.(3)For the numerical analysis of CSAS with multi-scale different types of epistemic uncertainties,a modified interval Monte Carlo method(MIMCM)based on probability box representation w as proposed.The multiple epistemic uncertain parameters were transformed into unified probability box form,and then the Interval Monte Carlo Method(IMCM)under the probability box framework was used to calculate the cumulative probability distribution boundary of the sound pressure amplitude of CSAS.In order to improve the accuracy and efficiency of interval analysis in IMCM,a Gegenbauer polynomial surrogate model using sparse sampling technique was established.The results of numerical examples showed that MIMCM can accurately and efficiently predict the sound pressure response of CSAS with multi-scale multiple types of epistemic uncertainties,and the probability information contained in the sound pressure response can be used to risk and conservative reliability analysis.(4)A robust MTO model of CSAS with multi-scale hybrid interval random uncertain parameters was established.The objective function of this model is the weighted sum of the expected and standard deviation of the sound pressure amplitude of CSAS,where the design variable was the material distribution of microstructured cells.In order to improve the efficiency of numerical analysis of CSAS with multi-scale interval random uncertainties,combining orthogonal matching pursuit and adaptive sampling techniques,a numerical analysis method based on sparse decomposed polynomial chaos was proposed to efficiently obtain the sound pressure amplitude of CSAS.Combined with adaptive genetic algorithm,an MTO algorithm for CSAS with interval random uncertainties was proposed.Taking hexahedral box and automobile cabin as examples,the results showed that the robust MTO considering multi-scale hybrid interval random uncertainties could obtain lower sound pressure level than the deterministic MTO.The numerical analysis methods studied in this paper can not only be effectively applied to the prediction and topology optimization design of CSAS with multi-scale hybrid uncertain parameters,but also have the potential to be applied to other engineering models,which can be appied to reudce the structural vibration and noise,and has important research value.