I.O.Lukovsky, M.A.Chernova A nonlinear modal theory for drop oscillations |
Acoustic bulletin, Vol. 14 ¹ 3, (2011) |
| The general nonlinear modal equations describing the motions of a liquid drop at zero-gravity condition are derived on the base of the Lukovsky-Miles variational method. Using these equations and the nonlinear algebra for the Legendre polynomials transformations, the third-order asymptotic nonlinear modal theory for axisymmetric oscillations of the drop is developed. In the above theory, the hydrodynamic coefficients are found analytically via the so-called Clebsch-Gordan coefficients emerging in quantum mechanics. The nonlinear free oscillations of the drop at frequency close to the primary natural one are considered. The results are compared with the experimental and numerical data obtained by other authors. |
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KEY WORDS: liquid drop, zero gravity, free oscillations, eigenfreqency, the Lukovsky-Miles variational method, nonlinear modal system |
| TEXT LANGUAGE: Russian |