Dynamic responses of a crack in a layered graded magnetoelectroelastic sensor subjected to harmonic waves

The mechanical model is established for the dynamic fracture problem of a layered graded magnetoelectroelastic sensor subjected to harmonic waves. Fourier integral transform is employed to derive the system of Cauchy singular integral equations, numerical solutions of which are obtained by the Lobatto–Chebyshev collocation method put forth by Erdogan and Gupta. The energy release rate (ERR) is chosen as the fracture parameter. Parametric studies on ERRs yield some guidelines for engineering applications: (1) to avoid the peak value of ERR, the wave number of applied loading should be as large as possible; (2) smaller values for non-homogeneity parameters and larger thickness for the sensitive coating can be chosen to enhance the anti-fracture ability of the sensor; (3) cracks in the lower-half region of the guiding layer are more dangerous than those in the upper half, and the monitoring for the former should be specially strengthened.