Research On The Uncertainty Analysis And The Application In Car Interior Noise Control Of Acoustic Metamaterials

Acoustic metamaterials(AMs)are man-made periodic composite materials,because of the extraordinary features,which have attracted much attention among the scholars at home and abroad in recent years.Traditional researches of AMs are usually based on deterministic parameters models.However,due to the effects of manufacturing,measurement and materials properties errors,the uncertain parameters in AMs are usually unavoidable in the practical engineering application.When these uncertain parameters coupled together,it may lead to the large deviation of the physical properties of AMs.In order to ensure the performance reliability of AMs,it is of great significance to predict the physical properties of uncertain AMs effectively.In order to deal with the uncertain AMs problems,the numerical analysis methods of the interval,random,interval and random hybrid uncertain AMs are formulated in this paper,which are used to predict the influence of these three types uncertain parameters on band structure,mode shapes and frequency response function of AMs.In addition,to solve the problem of peak noise response of the car driver’s right ear,a kind of AMs plate structure is proposed to reduce the noise in car.The main contents of this paper are shown as follows:(1)Based on the interval perturbation finite element method(IPFEM),the interval AMs analysis model is formulated,which can be applied to analyze the change ranges of the band structure frequencies,mode shape displacements and frequency responses of interval AMs.In IPFEM,according to the first-order perturbation technique,the band structure frequencies,mode shape displacements and frequency responses can be approximated as the linear functions of interval parameters,the deviation of these physical properties can be calculated when their perturbation radius are determined.(2)An analysis method of random AMs based on the transformed stochastic perturbation finite element method(TSPFEM)is formulated,which can be employed to calculate the probability density functions of band structure frequencies,mode shape displacements and frequency responses of AMs with random parameters.In this analysis method,the band structure frequencies,mode shape displacements and frequency responses are approximated as the linear functions of interval parameters by using the first-order perturbation technique,then the probability density functions of the these physical properties can be calculated by the change-of-variable method.(3)Combined with the interval and random hybrid perturbation finite element method(IRHPFEM),the numerical analysis method of the hybrid uncertain AMs is proposed.In this analysis method,the band structure frequencies,mode shape displacements and frequency responses are approximated as the linear functions of interval and random parameters by using the hybrid perturbation technique.Then,the expectations and variances of these physical properties can be calculated by the random interval moment method.Finally,the change ranges of the expectations and variances can be obtained by vertex method and Monte-Carlo method(MCM),respectively.(4)A kind of AMs plate structure is proposed and the effects of structure and material parameters on band gaps are studied.To solve the problem of peak noise response at the location of car driver’s right ear,the AMs plate structure with reasonable parameters is proposed and its uncertainty is analyzed to ensure the effectiveness of its application to reduce the car interior noise.