Abstract
We consider unsteady triaxial tension–compression of a moving parallelepiped filled with a Newtonian viscous fluid and changing its linear dimensions (with a constant volume) during motion. The statement of the linearized problem is given in terms of three-dimensional perturbations imposed on the main process. To study this problem, we apply the method of integral relations based on the use of variational inequalities for estimating quadratic functionals. These estimates lead to sufficient integral criteria for stability with respect to the energy measure under small perturbations—to criteria for Lyapunov stability, asymptotic stability, and exponential stability. We derive a system of linear inequalities including two characteristic Reynolds numbers under which the initial three-dimensional picture of perturbations is a priori known to be exponentially stable.
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Funding
This work was supported by the Russian Foundation for Basic Research, projects nos. 18-29-10085mk and 19-01-00016a.
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Translated by V. Potapchouck
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Georgievskii, D.V. Stability of Unsteady Triaxial Tension–Compression of a Viscous Parallelepiped with Respect to the Energy Measure. Diff Equat 57, 630–635 (2021). https://doi.org/10.1134/S0012266121050074
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DOI: https://doi.org/10.1134/S0012266121050074