Strani, Massimo Free vibrations of a meniscus with edge constraints. (English) Zbl 0592.76024 Meccanica 21, 15-22 (1986). Summary: The gravity capillary small vibrations of the meniscus of a fluid contained in a trough, when the line of contact on the lateral walls is fixed, are studied for the incompressible inviscid case. The two cases when the bottom end of the trough is closed or open are considered. It is found that the vibration frequencies and modes may be determined as eigenmodes and eigenvalues of a linear operator whose components, in a suitable basis of \(L_ 2(-1,1)\), are given analytically. The influence of the relevant nondimensional parameters and the distinguishing features of the case of an open channel are then determined, and substantiated by numerical results. Cited in 1 Document MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M99 Basic methods in fluid mechanics Keywords:gravity capillary small vibrations; meniscus of a fluid; trough; vibration frequencies; modes; eigenmodes; eigenvalues of a linear operator; open channel PDFBibTeX XMLCite \textit{M. Strani}, Meccanica 21, 15--22 (1986; Zbl 0592.76024) Full Text: DOI References: [1] Benjamin T.B., Scott J.C., 1979, J. Fluid Mech., 92, 241–267. · Zbl 0409.76020 · doi:10.1017/S0022112079000616 [2] Benjamin T.B.,Scott J.C., 1981, Trends in applications of pure Mathematics to Mechanics, vol. III, Pitman. [3] Lamb H., 1932, Hydrodynamics, 6-th Edition, Dover. [4] Strani M., Sabetta F., 1984, J. Fluid Mech., 141, 233–247. · Zbl 0571.76101 · doi:10.1017/S0022112084000811 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.