Purpose
The purpose of this paper is to provide a theoretical analysis of the fracture behavior of multiple axisymmetric interface cracks between a homogeneous isotropic layer and its functionally graded material (FGM) coating under torsional loading.
Design/methodology/approach
In this paper, the authors employ the distributed dislocation technique to the stress analysis, an FGM coating-substrate system under torsional loading with multiple axisymmetric cracks consist of annular and penny-shaped cracks. First, with the aid of the Hankel transform, the stress fields in the homogeneous layer and its FGM coating are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations which are employed to calculate the SIFs.
Findings
From the numerical results, the following key points were observed: first, for two types of the axisymmetric interface cracks, the SIFs decrease with growing in the values of the non-homogeneity. Second, the SIFs increase with increases in interface crack length. Third, the magnitude of the SIFs decreases with increases in the FGM coating thickness. Fourth, the interaction between cracks is an important factor affecting the SIFs of crack tips.
Originality/value
New analytical dislocation solution in an FGM coating-substrate system is developed.
A self-recurrent wavelet neural network (SRWNN) is used to control suppression of vibration of an Euler-Bernoulli beam under excitation of a moving mass traveling along a vibrating path. The proposed control structure uses one SRWNN as an identifier and one as a controller. The SRWNN identifier is trained to model the dynamic behavior of the process and provide the SRWNN controller with information about system sensitivity. The SRWNN controller uses the sensitivity information provided by the SRWNN identifier to update weights and produce a signal that controls beam vibration. The gradient descent method and adaptive learning rates (ALRs) are used to update all SRWNN weights. The ALRs are obtained using the discrete Lyapunov stability theorem which guarantees the convergence of the proposed control structure. The performance and robustness of the proposed controller are evaluated at different mass ratios of moving mass to beam and for dimensionless velocity of a moving mass. The simulations verify the effectiveness and robustness of the controller.
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