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Alternative spatial growth and decay for constrained motion in an elastic cylinder. (English) Zbl 1074.74009
Summary: Alternative spatial growth and decay behavior is established for the motion of a (semi-infinite) cylinder composed of a nonhomogeneous anisotropic linear elastic material and subject to zero body force and zero lateral boundary conditions. The motion, induced by displacement prescribed on the base, is constrained to have the displacement and velocity at a given time proportional to the respective initial values. Neither initial data nor the asymptotic behavior at large axial distance are specified. A differential inequality is derived for certain time integrals of the cross-sectional energy flux, and integration leads to estimates that either exponentially grow or decay. Decay estimates are also obtained for the cross-sectional measures of strain energy, strain, displacement and its gradient, while explicit bounds in terms of the data are constructed for the amplitude in each decay estimate.

MSC:
74B05 Classical linear elasticity
74E10 Anisotropy in solid mechanics
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References:
[1] Flavin, J.N., Elasticity: Mathematical Methods and Applications pp 101– (1990)
[2] Chirita, S., Journal of Elasticity 42 pp 302– (1996) · Zbl 0891.73010 · doi:10.1007/BF00041790
[3] Bofill, F., Richerche di Matematica 46 pp 426– (1998)
[4] Payne, L.E., Journal of Mathematical Analysis and Applications 273 pp 75– (2002) · Zbl 1121.35331 · doi:10.1016/S0022-247X(02)00208-1
[5] Knops, R.J., Structured Media pp 144– (2001)
[6] Bramble, J.H., Contributions to Differential Equations 1 pp 94– (1963)
[7] Sigillito, V.G., Pitman Research Notes in Mathematics (1977)
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