Advances in Mechanical Engineering by Alexander N. Evgrafov

Author:Alexander N. Evgrafov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The wavenumber intervals where the negative group velocity is observed are less then in the case of a dry shell (18), due to the adjoint mass of liquid in the first case.

The normalized energy fluxes in the liquid (W) and the shell (S) and the normalized rotating, longitudinal, bending and momentum components () of the energy flux in the shell (28) illustrate the wave processes in the shell-liquid system of the next figures. The energy fluxes of the waves from the left dispersion curve are represented for the frequencies less the bifurcation one alone. The letters “a”, “b”, “c” in the designations of these curves conform to the corresponding sections of the dispersion curves in Fig. 1a.

In Fig. 2b, curves 1, 2, 3 correspond to the energy fluxes , , . The energy flux in the shell is dominant. It is not equal to zero compared to the energy flux in the liquid, and has the opposite sign and the equal module when . The energy flux in the liquid remains positive and is equal to the module for the waves from both branches in the neighborhood of the bifurcation point.

Distribution of the energy flux to different components is shown in Fig. 3, where curves 1 and 2 correspond to the energy flux components and . The main role in the energy transmission belongs to the rotating and longitudinal components of an energy flux, with the first one dominating. Calculations show that the limiting values of the bending and momentum components and are equal to zero at the bifurcation point and are much less than the rotating and longitudinal components in its neighborhood.

Fig. 3The energy flux in the shell and its components (1), (2) for the bifurcating curves

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