Effective Nonlinear AC And DC Response To A Class Of Graded Spherical Composites

Non-uniform dielectric composites are formed of one or more gradient inclusionparticles that generally embedded in the uniform host. These composites can not only keepthe advantages of each component material, but also generate properties that the individualcomponent materials do not have. According to the practical application, these compositescan be designed based on proportion, size and form of each fraction, which have potentialin application of the engineering technology.In this paper, by using the perturbation expansion method, the potential distributionand the effective dielectric response of a class of composites are studied under the externalAC and DC electric fieldE0(1sin t). There, the composites are a class of nonlineargradient composites, in that the spherical particles, which dielectric profile satisfies theequation i (r) c rkk(r a, r is the radius of the spherical inclusion andc k, k,a areparameters), are embedded in the homogeneous host. In dilute limit, the approximationanalytic solutions of the potential distributions at all harmonics in the host and theinclusion region are derived, respectively. Meanwhile, the effective nonlinear dielectricresponse at all harmonics and the general effective nonlinear dielectric response are alsocalculated. Furthermore, comparison between effective nonlinear dielectric response at allharmonics and general effective nonlinear dielectric response is discussed. The maincontents are as follows:1. The research status and development process of the gradient composites aredescribed，and the main research content of this paper is given briefly.2. Using the perturbation method, the potential distribution of the nonlinear gradientcomposites with the constitutive relationD E E2E between the electricdisplacement and electric field is investigated under the action of an external AC and DCelectric field. In this gradient composite, the spherical inclusion particles are randomlyembedded in the host. The approximation analytic solutions of the potential distribution inthe host and the inclusion region are calculated, respectively.3. Based on the Landau’s method and the potentials obtained in the second part, thelinear dielectric response coefficient*n, the third-order nonlinear polarizabilitycoefficient*n at all harmonics frequency n and the general effective nonlinear response eand eof the graded composites are received. Moreover, the comparisonsbetween them are performed.4. The results of this thesis are summarized and discussed, and the outlook for furtherwork is pointed out.