Nonlinear axisymmetric waves in compressible hyperelastic rods: Long finite amplitude waves. (English) Zbl 0788.73025
The paper presents the propagation of nonlinear axisymmetric wave in compressible hyperelastic circular cylindrical rods made of homogeneous isotropic materials and subjected to axial-radial deformations. For the compressible Mooney-Rivlin material, the equations of motion are obtained using the Hamilton’s principle. The equations of motion are written in non-dimensional form. On the basis of the equation valid asymptotically for axial and radial displacements, the second-order solitary wave solutions are obtained.
Reviewer: V.Marinca (Timişoara)
MSC:
| 74J10 | Bulk waves in solid mechanics |
| 74B20 | Nonlinear elasticity |
| 74J20 | Wave scattering in solid mechanics |
Keywords:
homogeneous isotropic materials; axial-radial deformations; Mooney-Rivlin material; Hamilton’s principle; second-order solitary waveReferences:
| [1] | Wright, T.: Nonlinear waves in rods. In: Proceedings of the IUTAM Symposium on Finite Elasticity (Carlson, D. E., Shields, R. T., eds.). The Hague: Martinus Nijhoff 1982. |
| [2] | Wright, T.: Nonlinear waves in rods: results for incompressible elastic materials. Stud. Appl. Math.72, 149-160 (1985). · Zbl 0558.73020 |
| [3] | Coleman, B. D., Newman, D. C.: On waves in slender elastic rods. Arch. Rat. Mech. Anal.109, 39-61 (1990). · Zbl 0716.73013 · doi:10.1007/BF00377978 |
| [4] | Nariboli, G. A.: Nonlinear longitudinal dispersive waves in elastic rods. J. Math. Phys. Sci.4, 64-73 (1970). · Zbl 0222.73032 |
| [5] | Ostrovskii, L. A., Sutin, A. M.: Nonlinear elastic waves in rods. PMM J. Appl. Math. Mech.41, 543-549 (1977). · Zbl 0392.73030 · doi:10.1016/0021-8928(77)90046-6 |
| [6] | Soerensen, M. P., Christiansen, P. L., Lomdahl, P. S.: Solitary waves on nonlinear rods I. J. Acoust. Soc. Am.78, 871-879 (1984). · Zbl 0564.73035 · doi:10.1121/1.391312 |
| [7] | Soerensen, M. P., Christiansen, P. L., Lomdahl, P. S., Skovgaard, O.: Solitary waves on nonlinear rods II. J. Acoust. Soc. Am.81, 1718-1722 (1987). · doi:10.1121/1.394786 |
| [8] | Clarkson, P. A., LeVeque, R. J., Saxton, R.: Solitary-wave interaction in elastic rods. Stud. Appl. Math.75, 95-122 (1986). · Zbl 0606.73028 |
| [9] | Jeffrey, A., Kawahara, T.: Asymptotic methods in nonlinear wave theory. London: Pitman 1982. · Zbl 0473.35002 |
| [10] | Ciarlet, P. G.: Mathematical elasticity. New York: North-Holland 1987. · Zbl 0612.73060 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
