A numerical-analytic solution is constructed for the problem of magnetoelasticity for a hollow cylinder immersed in a liquid and loaded from inside by an impulse-type axisymmetric mechanical pressure. Nonconducting and compressible internal and external media have different densities and elastic moduli, with their motion described by wave equations. The hollow cylinder is assumed to be an ideal conductor, and its motion is described by a linearized system of equations of magnetoelasticity; on internal and external boundaries, the conditions of conjugation hold. The problem is solved by the method of integral Laplace transforms in the time domain, and the inverse transforms are found by numerical inversion. The solutions obtained for the bounded problem are compared with solutions for a simplified unbounded problem.
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Selezov, I.T., Tkachenko, V.A. Propagation of unsteady waves in a hollow magnetoelastic cylinder in contact with liquid media. J Math Sci 56, 2784–2787 (1991). https://doi.org/10.1007/BF01097454
- Wave Equation
- Liquid Medium
- Elastic Modulo
- Hollow Cylinder
- External Medium