Effective nonlinear AC response to graded cylindrical composites

The perturbation method is used to study the effective nonlinear response of graded cylindrical composites with power-law gradient inclusions under a sinusoidal alternating current (AC) external field of finite frequency ω. In dilute limit, the local potentials and the formulae of effective nonlinear AC responses are derived at the fundamental frequency and the third harmonics. Furthermore, the general effective nonlinear responses are given and compared with the effective nonlinear AC responses of fundamental frequency and the third harmonics, and the relationships between the nonlinear effective AC response and the general effective nonlinear response are also determined.