Abstract
A solution is given for the transverse oscillations, under elastic forces, of a cylindrical vessel containing an ideal two-layer liquid with elastic membranes at the free and inner surfaces of the stratified liquid. The following limiting cases for the elastic membrane are examined: it lies only at the free surface of a uniform and two-layer liquid; it separates a two-layer liquid; it exists at both the free and the inner surfaces of a two-layer liquid. The numerically calculated dependences of the first eigenfrequency on the tension of the membrane, liquid densities, and filling depth are analyzed.
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REFERENCES
Yu. N. Kononov and V. P. Shevchenko, “Free oscillations of a multilayer stratified liquid separated by elastic membranes, ” Teor. Prikl. Mekh., 29, 151–163 (1999).
Yu. N. Kononov, “Translational motion of a solid with a cavity that is partially filled with a stratified liquid, ” Visn. Donets. Un-tu. Ser. A, No. 1, 66–70 (1997).
N. N. Moiseev, “Small oscillations of an open vessel with liquid acted on by an elastic force, ” Ukr. Mat. Zhurn. 4, No. 2, 168–173 (1952).
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Kononov, Y.N. Transverse Oscillations of a Cylindrical Vessel with a Two-Layer Liquid Separated by an Elastic Membrane. Journal of Mathematical Sciences 103, 404–408 (2001). https://doi.org/10.1023/A:1011334900628
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DOI: https://doi.org/10.1023/A:1011334900628