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About dynamic stability of deformable elements of vibration systems

Petr Velmisov, Andrey Ankilov
The dynamics and stability of the elastic elements of vibration devices, modeled by a channel containing elastic elements, are investigated. Inside the channel flows a stream of stirred liquid. The model of the device with two elastic elements is considered. The solution of the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable,
is given. The solution of the original problem is reduced to the study of a coupled system of partial differential equations for the deformations of elements, which makes it possible to study their dynamics. On the basis of the constructed functional for this system, the sufficient conditions of stability are obtained. The conditions impose restrictions on the parameters of the mechanical system. Based on the Galerkin method, the numerical
experiments for specific examples of mechanical systems were carried out, confirming the reliability of the investigations. A special case of the model of device with one elastic element is considered. Based on this case, a comparison with the model of the vibration device considered earlier is made.
CYBERNETICS AND PHYSICS, Vol. 8, No. 3. 2019, 175-184. https://doi.org/10.35470/2226-4116-2019-8-3-175-184
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