Energy approach for static and linearized dynamic studies of elastic structures containing incompressible liquids with capillarity: a theoretical formulation

Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity

“…Concerning the linear formulation for the compressible liquid with free surface, the sloshing is taken into account with surface tension (capillarity) effects. We refer the reader to [6,7] for the classical theory on capillarity, to [8,9,10] for developments of the behavior of liquids in microgravity environment, to [11,12] for general analyzes of sloshing problems for incompressible liquids in rigid structures, to [13,14,15,16,17,18] for sloshing problems of incompressible liquids without capillarity effects in elastic structures, to [13,19,20,21] for sloshing problems of incompressible liquids with capillarity effects in rigid structures, to [22,23,24,25,26,27,28,13,29] for the conditions of contact angle between the free surface and the structure, to [30] for sloshing problems of incompressible liquids with capillarity effects in elastic structures, to [31,32,33] for sloshing problems of compressible liquids with capillarity effects in rigid structures, to [1] for linear dissipative acoustic liquids with sloshing and capillarity effects in linear elastic structures. Concerning nonlinear sloshing and capillarity for incompressible liquids in rigid tanks submitted to rigid body motions, see [34,35,36,37,38].…”

Vibration of structures containing compressible liquids with surface tension and sloshing effects. Reduced-order model

“…The sloshing problems of incompressible liquids with capillarity effects in elastic structures exhibit a major difficulty induced by the boundary contact conditions on the triple line because the capillarity forces are forces per unit length while the elastic forces are forces per unit surface. An attempt to solve this problem has been presented in [35] using an energy approach, and without deriving and discussing the local equations.…”