Uncertain Numerical Analysis And Topology Optimization For The Structural-acoustic Coupled System

Thin-wall structures are widely applied in the airplane,ship,automobile,and so on.In these applications,structural vibrating is one of the main noise sources.The analysis and topology optimization of the structural-acoustic coupled system based on the acoustic performance have extremely important significance on reducing cabin noise and improving riding comfort.Traditional numerical analysis of the structural-acoustic coupled system usually assumes that parameters of the system are deterministic.However,due to the effects of manufacturing or assembling errors,aggressive environment factors and unpredictable external excitations,uncertainties widely exist in the structural-acoustic coupled system.In most cases,the uncertainties of these nondeterministic parameters are small.Unfortunately,these small uncertainties may result in a great deviation of the response of the structural-acoustic coupled system due to the coupling effects among nondeterministic parameters.Considering the diversity of the uncertainty existed in the structural-acoustic coupled system,as-well as the universality of composite materials in engineering practical application,it is demand to study the numerical analysis method for the uncertain structural-acoustic coupled system,especially for the uncertain composite structural-acoustic coupled system.Besides,the topology optimization for the structural-acoustic coupled.system is limited on the macro scale.The microstructural topology optimization for the structural-acoustic coupled system is still on its preliminary stage.Through the microstructural topology optimization for the unit cell of the macro composite structure,the overall macroscopic vibration and acoustic performance of the composite structure can be improved,which has great significance to control the noise of a closed structural-acoustic cavity.Therefore,the microstructural topology optimization of structural-acoustic coupled systems on the basis of acoustic performance is promising and demand.Supported by National Natural Science Foundation(No.11572121 and No.11402083),this dissertation mainly focus on the uncertain analysis and topology optimization of the structural-acoustic coupled system.The uncertain numerical analysis model of the structural-acoustic coupled system are constructed by using the nondeterministic theory and corresponding uncertain analysis methods are developed.Based on the homogenization theory,the influence of the microscopic uncertainty in material properties on a homogenized macroscopic elastic property of an inhomogeneous material are investigated.Then the multi-scale uncertain numerical analysis model of the structural-acoustic coupled system are constructed and the corresponding uncertain analysis method are developed.A microstructural topology optimization model of the structural-acoustic coupled system for improving the acoustic performance is constructed and the corresponding optimization algorithm is developed.Furthermore,with taking multi-scale uncertain parameters into consideration,a robust microstructural topology optimization model of the structural-acoustic coupled system is constructed and the corresponding optimization algorithm is proposed.The main research work and innovative achievements in this dissertation are:(1)An efficient interval Monte Carlo method based on the first-order matrix decomposition perturbation method(FMDPM)is developed for the response analysis of the structural-acoustic coupled system with p-box variables.In the interval Monte Carlo method based on FMDPM,a standard uniform random number between 0 and 1 is firstly generated.Then an interval can be obtained through the intersection of a line whose vertice coordinate value is equal to the random number and the lower and upper bound defining the p-box.Through the FMDPM,the variation range(max.and min.)of the frequency response can be c.alculated.After completing several times of repetitions of interval analysis,the lower and upper bounds of the cumulative distribution function of the frequency response can be assembled.Results of a numerical example show that.the lower and upper bounds of the cumulative distribution function of the frequency response can be calculated effectively by the proposed method.Besides,the conservative estimation and risky estimation of the desired design demand can be obtained by the proposed method.(2)A hybrid stochastic interval perturbation method(HSIPM)is proposed for the unified energy flow analysis in structural-acoustic coupled system under two hybrid uncertain models.The first type of hybrid uncertain model is the hybrid probability and interval model.The second type of hybrid uncertain model is the interval probability model.In the HSIPM,by temporarily neglecting the uncertainties of interval variables,the first-order stochastic perturbation method is adopted to calculate the expectation and variance of the energy vector.Afterwards,the interval of the expectation and variance of the energy vector can be obtained by the first-order interval perturbation method.Results of a numerical example show that the HSIPM can effectively predict the intervals of the expectation and standard variance of the energy of the structural-acoustic coupled systemunder two hybrid uncertain models.Furthermore,the HSIPM has the higher computational efficiency compared with the Monte Carlo method.(3)An interval homogenization-based method(IHM)is proposed for the estimation of the effective elastic tensor for microscopic material properties with interval uncertainty.The IHM is based on the homogenization analysis and the first-order Taylor series.In the sub-interval homogenization-based method(Sub-IHM),by substituting the interval into several sub-intervals,the intervals of effective elastic tensor are calculated by IHM and the interval union arithmetic.Results of numerical examples show that the accuracy of IHM is very good when the input interval uncertainty level is small,and the Sub-IHM can guarantee the accuracy for estimating the effective elastic tensor when the input interval uncertainty level is large.Besides,a small deviation in the material property parameters is likely to result in very large deviations of the effective elastic tensor.Furthermore,it can be found out that the D12H is the most affected by the interval uncertainty in microscopic material properties,followed by D11H and D22H,and D66H is the least affected.(4)A homogenization-based interval finite element method(HIFEM)is developed for the response analysis of structural-acoustic coupled system involving periodical composites and multi-scale uncertain-but-bounded parameters.The HIFEM is derived by integrating the homogenization-based finite element method with the first-order Taylor expansion interval analysis method.Results of numerical examples show that the HIFEM can effectively predict the frequency response of the periodical composite structural-acoustic system with multi-scale uncertain-but-bounded ranges when the input interval uncertainty level is small.The accuracy of the HIFEM for predicting the frequency response of the periodical composite structural-acoustic system with multi-scale uncertain-but-bounded parameters can be ensured through introducing the subinterval technique into the HIFEM.(5)A microstructural topology optimization model for the structural-acoustic coupled system is constructed.The discrete design variables are used in the microstructural topology optimization,and the constitutive matrix is interpolated by the power-law scheme at the micro scale.The equivalent macro material properties of the microstructure are computed through the homogenization method.The design objective is to minimize the sound pressure level(SPL)in an interior acoustic medium.The bi-directional evolutionary structural optimization(BESO)method is extended to solve the structural-acoustic coupled optimization problem to find the optimal material distribution of the microstructure.Results of numerical examples show that the resonance frequency of optimum design has a shifting compared with original design.Besides,the sound pressure at the reference point of the optimum design is smaller than that of the original design at the target frequency.(6)A robust microstructural topology optimization model for the structural-acoustic coupled system with multi-scale random parameters is constructed.A homogenization-based stochastic finite element method(HSFEM)is first developed for quantifying the behavior of the structural-acoustic system with multi-scale random parameters.The exploit of the HSFEM transforms the problem of microstructural topology optimization with multi-scale random parameters to an augmented deterministic microstructural topology optimization problem.The discrete design variables are used in the microstructural topology optimization,and the constitutive matrix is interpolated by the power-law scheme at the micro scale.The optimization objective function is to minimize the summation of the expectation and standard variance of the sound pressure amplitudes through weighting coefficient.Based on BESO,a robust microstructural topology optimization algorithm for the structural-acoustic coupled system with multi-scale random parameters is developed.Results of an umerical example show that the multi-scale random uncertainties involved in microstructural topology optimization have an effect on the microstructural topology design.Moreover,the robust optimum design considering the multi-scale random uncertainty usually can achieve better performance than the deterministic optimum design.This dissertation conducted a systematical research for the uncertain analysis and topology optimization of the structural-acoustic coupled system.Two uncertain analysis methods named as HSIPM and efficient interval Monte Carlo method based on FMDPM are developed for the response analysis of the structural-acoustic coupled system with uncertain parameters;A nondeterministic numerical analysis method named as IHM is proposed for estimating the effective elastic properties of periodic microstructures with interval parameters;Two uncertain numerical analysis methods named as HIFEM and HSFEM are proposed for the response analysis of the periodic composite structural-acoustic coupled system with multi-scale uncertain parameters;A deterministic microstructural topology optimization methodology and a robust one are proposed for the periodic composite structural-acoustic coupled system with deterministic parameters and multi-scale random parameters,respectively.The results of numerical examples verified the effectiveness of the proposed methods.This indicates that the proposed methods in this dissertation have a good engineering application in predicting and reducing the noise of a closed structural-acoustic cavity.