The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.

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SUMMARYNumerical solution of the Rayleigh equation in non-linear vibration is studied in this paper. The di erential equation is integrated on a particular interval (0; T p2 ) with the initial value condition, u = A i and du=dt = 0 at the time t = 0. The value T p2 is determined from the condition such that the trajectory of motion on the phase plane is a unclosed path around the original point with the both starting and the end point on the positive real axis. The target function method is developed to obtain the particular value T p2 . The obtained A i+1 (= u(T p2 )) will be used in the initial value condition of the next round integration. A stable periodic motion is obtained after some rounds of integration. The solution technique is out of the small parameter assumption in the Rayleigh equation. Finally, numerical examples and results are given.

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