Abstract
An analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.
Highlights
An analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied
When the circular cavity defect exists near the boundary, the anti-plane dynamic problems will be more complex than that of the elastic materials
Z hang[3,4] studied the scattering of SH waves by cylindrical inclusions and semi-cylindrical holes in the semi-space of bi-phase media by using Green’s function method and complex function method, and obtained the steady-state solution of the problem and analyzed the anti-plane dynamics of waves caused by interface cracks in bi-phase piezoelectric media
Summary
Since we need to truncate finite terms to solve the infinite algebraic equations, the selection of truncated terms will affect the final calculation results. Because there is no displacement field inside the circular cavity, the radial stress at the boundary of the circular cavity should be 0. The accuracy of the analysis method can be tested by the residual dimensionless stress at the boundary of the circular cavity. The results show that when the maximum residual stress is less than 5%, the accuracy of the calculated results can be guaranteed. The calculation result diagrams of dynamic stress concentration factor (DSCF) and magnetic field intensity concentration factor (MFICF) around the circular cavity are presented, which vary with the dimensionless wave number kR , dimensionless piezomagnetic parameters , material geometrical parameters, incident angle α0 and the geometric position of the circular cavity h R.
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