TY - GEN
T1 - Nonlinearity of finite-amplitude waves in rectangular containers
AU - Daqaq, Mohammed F.
AU - Xu, Yawen
AU - Lacarbonara, Walter
PY - 2016
Y1 - 2016
N2 - This paper investigates the two-dimensional nonlinear finite-amplitude sloshing dynamics of an irrotational, incompressible fluid in a rectangular container. In specific, the paper addresses the influence of surface tension represented by a coefficient, b, and the ratio between the fluid height and the container's width, represented by h=L, on the nonlinear normal sloshing modes. To achieve this objective, we first study the influence of, b, and, h=L, on the modal frequencies and generate a map in the (h=L, b) parameters' space to highlight regions of possible nonlinear internal resonances up to the fifth mode. The map is used to characterize the regions where a single uncoupled nonlinear mode is sufficient to capture the response of surface waves. For these regions, we study the influence of surface tension on the effective nonlinearity of the first four modes and illustrate its considerable influence on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, we investigate the response of the sloshing waves near internal resonance of the two-to-one type. We show that, in the vicinity of these internal resonances, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the higher frequency mode (uncoupled high-frequency mode response). We show that the regions where the coupled-mode uniquely exists has a clear dependence on the surface tension.
AB - This paper investigates the two-dimensional nonlinear finite-amplitude sloshing dynamics of an irrotational, incompressible fluid in a rectangular container. In specific, the paper addresses the influence of surface tension represented by a coefficient, b, and the ratio between the fluid height and the container's width, represented by h=L, on the nonlinear normal sloshing modes. To achieve this objective, we first study the influence of, b, and, h=L, on the modal frequencies and generate a map in the (h=L, b) parameters' space to highlight regions of possible nonlinear internal resonances up to the fifth mode. The map is used to characterize the regions where a single uncoupled nonlinear mode is sufficient to capture the response of surface waves. For these regions, we study the influence of surface tension on the effective nonlinearity of the first four modes and illustrate its considerable influence on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, we investigate the response of the sloshing waves near internal resonance of the two-to-one type. We show that, in the vicinity of these internal resonances, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the higher frequency mode (uncoupled high-frequency mode response). We show that the regions where the coupled-mode uniquely exists has a clear dependence on the surface tension.
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U2 - 10.1115/DETC201659908
DO - 10.1115/DETC201659908
M3 - Conference contribution
AN - SCOPUS:85007303949
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
Y2 - 21 August 2016 through 24 August 2016
ER -