Dynamic response of a cylindrical cavity to SH wave in inhomogeneous continuum with modulus varying two-dimensionally. (English) Zbl 1490.74037
Summary: Due to the inhomogeneity of shear modulus, the constitutive form of the medium becomes more complicated, which increases the difficulty of solving the analytical solution. In this paper, a new form of shear modulus is derived. Meanwhile, the wave number in the medium is also variable. By using the method of complex function and conformal transformation, the problem of dynamic stress concentration around a cylindrical cavity in an infinite inhomogeneous medium is solved. Combined with an auxiliary displacement function and a pair of new mapping functions, in the solving process, the analytical expressions of displacement field and stress field are given. The validity of this method is verified by comparing with the published results. Through numerical results, the distribution of dynamic stress concentration factor around a cylindrical cavity is analyzed under different inhomogeneous parameters and reference wave numbers.
MSC:
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74J10 | Bulk waves in solid mechanics |
| 74S70 | Complex-variable methods applied to problems in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
Keywords:
variable wave number; cylindrical cavity; shear modulus; inhomogeneous medium; dynamic stress concentration factor; conformal mapping; analytic solutionReferences:
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