中国物理B ›› 2012, Vol. 21 ›› Issue (5): 57202-057202.doi: 10.1088/1674-1056/21/5/057202

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

丁霞1,贾艳霞2,魏恩泊3   

  1. 1. College of Mathematics and Physics, Qingdao University of Science & Technology, Qingdao 266061, China;
    2. Hisense Trans-Tech Company Limited, Qingdao 266071, China;
    3. Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
  • 收稿日期:2011-10-08 修回日期:2012-04-27 出版日期:2012-04-01 发布日期:2012-04-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 40876094 and JQ10974106), the National High Technology Research and Development Program of China (Grant Nos. 2009AA09Z102 and 2008AA09A403), the Excellent Youth Fundation of Shandong Scientific Committee, China (Grant No. JQ201018), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AZ002).

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

Ding Xia(丁霞)a), Jia Yan-Xia(贾艳霞)b), and Wei En-Bo(魏恩泊)c)†   

  1. a. College of Mathematics and Physics, Qingdao University of Science & Technology, Qingdao 266061, China;
    b. Hisense Trans-Tech Company Limited, Qingdao 266071, China;
    c. Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
  • Received:2011-10-08 Revised:2012-04-27 Online:2012-04-01 Published:2012-04-01
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 40876094 and JQ10974106), the National High Technology Research and Development Program of China (Grant Nos. 2009AA09Z102 and 2008AA09A403), the Excellent Youth Fundation of Shandong Scientific Committee, China (Grant No. JQ201018), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AZ002).

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摘要： 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 Eapp = E0 (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function εi (r) = Ck rk (r ≤ a), where r is the radius of the cylindrical inclusion, and Ck, 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.

关键词: graded composite, effective nonlinear alternating-current and direct-current response, local electric field distribution

Abstract: 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 Eapp = E0 (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function εi(r) = Ck rk (r ≤ a), where r is the radius of the cylindrical inclusion, and Ck, 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.

Key words: graded composite, effective nonlinear alternating-current and direct-current response, local electric field distribution

中图分类号:  (Composite materials)

  • 72.80.Tm
42.79.Ry (Gradient-index (GRIN) devices) 72.20.Ht (High-field and nonlinear effects) 41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems)