非线性柱形涂层复合介质有效的直流-交流电响应

利用摄动展开方法, 研究了由圆柱形带涂层杂质随机嵌入基质所形成的非线性复合介质在外加 的带有不同频率和振幅的混合电场E₀ + E₁ sinωt+E₃ sin3ωt作用下有效的直流-交流电响应, 分别推导了复合介质在杂质核、涂层及基质区域的电势分布, 并在低杂质浓度下给出了复合介质有效的非线性响应及它们之间的关系. 关键词： 非线性柱形涂层复合介质 有效的非线性响应 外加交直流电场     

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_app = E₀ (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_i (r) = C_k r^k (r ≤ a), where r is the radius of the cylindrical inclusion, and C_k, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.     

梯度圆柱颗粒复合介质的有效非线性响应

应用非线性微分有效偶极近似方法,导出了关于非线性梯度圆柱颗粒的等效线性介电常数和三阶非线性极化率的微分式,研究了稀释极限下,圆柱形梯度颗粒无规置入线性介质中组成的复合介质的有效线性介电常数和三阶非线性极化率.作为应用,数值计算了具有幂指数梯度分布的介电常数的颗粒复合介质的有效非线性响应,及梯度金属电介质颗粒复合介质的表面plasmon共振效应.     

Effective response of nonlinear cylindrical coated composites under external AC and DC electric field

This paper uses the perturbation method to study effective response of nonlinear cylindrical coated composites. Under the external AC and DC electric field E_a(1 + sinωt), the local potentials of composites at all harmonic frequencies are induced. An effective nonlinear response to composite is given for the cylindrical coated inclusions in the dilute limit.     

共焦椭圆柱等值坐标电容器的电容

利用共焦椭圆柱坐标给出共焦椭圆柱电容器电容的一般表示,求解椭圆柱形电容器和双曲柱形电容器的电容,丰富了此类电容器电容值计算的结果.     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

Effective Dielectric Response of Composites with Graded Material

The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E₀. For the cylindrical inclusion with gradient dielectric function, ε_i(r)=b+cr, randomly embedded in a host with dielectric constant ε_m, we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D=εE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media are given.     

Effective Anisotropic Dielectric Properties of Crystal Composites

Transformation fieM method （TFM） is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropie dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.     

Effective AC response of nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, {{\bm E}}_a = {{\bm E}}_1 \sin (\omega t) + {{\bm E}}_3 \sin (3\omega t), is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

Dielectric responses of graded composites having generalized gradation profiles

Under an external uniform electric field, the dielectric response of graded cylindrical composites having generalized dielectric profile inclusions is investigated. The generalized dielectric profile of graded cylindrical inclusion is expressed in the form, $\varepsilon _i (r)=c(b+ r)^k\e^{\beta r}$ where $r$ is the radial variable of the cylindrical inclusions and $c$, $b$, $k$ and $\beta $ are parameters. The local potential solution of generalized dielectric profile graded composites is derived by means of the power series method and the effective dielectric response is predicted in the dilute limit. Moreover, from the result of generalized profile, the analytical solutions of local potentials and the effective responses of graded composites having three cases of dielectric profiles, i.e., the exponential profile $\varepsilon_\i (r)=c\e^{\beta r}$, the general power law profile $\varepsilon_\i (r)=c(b+r)^k$ and the profile $\varepsilon_\i (r)=cr^k\e^{\beta r}$, are sorted out, respectively. In the dilute limit, our exact results are used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded cylindrical composites, and it is shown that the DEDA is in excellent agreement with the exact result.     

金属/电介质颗粒复合介质的非线性交流响应

推广T矩阵法来研究二组分颗粒复合介质的非线性交流响应，解析推导出基频、三次及五次谐波频率下的有效线性介电常数及三阶和五阶非线性极化率的解析表达式.当组分颗粒的介电常数为实数时，表达式同以前微扰理论完全一致.进一步数值计算了金属-电介质复合介质的有效非线性交流响应，数值结果表明，体系的三阶、五阶非线性极化率在表面等离子共振频率附近有明显增强，而且，随着体积分数提高，共振峰增强且伴随着共振频率红移现象.还进一步讨论了维度效应对体系非线性交流响应的影响. 关键词： T矩阵方法 复合介质 非线性交流响应     

Effective response in nonlinear spherical coated composites under external AC and DC electric field

By using the perturbation method, effective nonlinear direct current (DC) and alternating current (AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of external electric field E_a =E₀ +E₁ sin ωt+E₃ sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

具有各向异性的梯度颗粒复合材料的有效介电响应

本文研究了具有梯度壳层椭球颗粒复合体系的有效介电响应，在稀释条件下用准静态近似方法, 推导了颗粒壳层具有任意介电梯度形式的椭球颗粒复合体系的有效介电常数和部分共振条件的一般表达式。并以壳层的介电常数为主轴的幂函数形式为例，得出了通过调节壳层的介电梯度形式、颗粒的结构和形状,可以提高该体系的有效介电常数和实现部分共振的结论。     

Numerical simulation of nonlinear magnetic-mechanical-electric coupling effect in laminated magnetoelectric composites

Considering the significant nonlinear magnetoelectric (ME) characteristics in laminated ME composites, we build a numerical model of magnetic-mechanical-electric coupling effect based on the nonlinear magnetostrictive constitutive relation. The change of the ME field coefficients with bias magnetic field predicted by this model shows good agreement with the experimental result, both qualitatively and quantitatively. Furthermore, this paper considers and predicts the magnetoelectric conversion charateristics of laminated ME composites, calculates and analyzes the influence of the thickness ratio of magnetostrictive layer, the geometrical size of laminated composites, the saturation magnetization, and the types of piezoelectric materials on the ME conversion coefficient of ME laminated composites. We believe that this research provides a theoretical basis for the production of magnetoelectric devices with good magnetoelectric conversion characteristics.     

Analysis of transient responses in a laminated piezoelectric cylindrical shell

A hybrid numerical method is proposed for analysis of transient responses in a multilayered piezoelectric cylindrical shell.In the present method,the associated equations of the displacement field and the electro-potential field are developed using an analytical-numerical method.The piezoelectric cylindrical shell is discretized into layered annular elements along the wall thickness direction.The governing equations are determined by Hamilton's Principle considering the coupling between the elastic and elec...     

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method,effective nonlinear direct current(DC) and alternating current(AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field E a = E 0 + E 1 sin ωt + E 3 sin 3ωt with different amplitudes and frequencies.The local potentials of composites at all harmonics are given in the inclusion particles and the host regions.All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Z-scan analysis of high-order nonlinear refraction effect induced by using elliptic Gaussian beam

The irradiance of an elliptic Gaussian beam that is high enough to excite high-order nonlinear refraction effect is used to calculate the normalized on-axis transmittance function in the z-scan technique by introducing complex beam parameters which make the calculation simpler. The transmittance formula is applied to the first-, first two-, and first three-order nonlinearities. Numerical evaluation shows that the symmetry no longer holds when using an elliptic Gaussian beam instead of a circular Gaussian beam. A distortion is observed in the central part of the curve, which decreases as ellipticity increases. Moreover, the variation of the normalized peak-valley difference decreases as ellipticity decreases.     

Effective AC Response of Nonlinear Spherical Coated Composites

Under alternating current electric field, effective response of granular nonlinear composites with spherical coated inclusions is investigated in the dilute limit by using the perturbation approach. For an external sinusoidal applied field with finite frequency ω, the local fields and potentials of composites in general consist of components at all harmonics for cubic nonlinear constitutive relationships. We derive the local potentials of spherical coated composites at harmonics. Moreover, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.     

Current-voltage characteristics of lead zirconate titanate/nickel bilayered hollow cylindrical magnetoelectric composites

Current--voltage measurements obtained from lead zirconate titanate/nickel bilayered hollow cylindrical magnetoelectric composite showed that a sinusoidal current applied to the copper coil wrapped around the hollow cylinder circumference induces voltage across the lead zirconate titanate layer thickness. The current--voltage coefficient and the maximum induced voltage in lead zirconate titanate at 1~kHz and resonance (60.1~kHz) frequencies increased linearly with the number of the coil turns and the applied current. The resonance frequency corresponds to the electromechanical resonance frequency. The current--voltage coefficient can be significantly improved by optimizing the magnetoelectric structure geometry and/or increasing the number of coil turns. Hollow cylindrical lead zirconate titanate/nickel structures can be potentially used as current sensors.     

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE xα|E|2E. Under the external AC and DC electric field Eapp = Eα(1 sinwt), the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute limit.