Nonlinearity of finite-amplitude waves in rectangular containers

Mohammed Daqaq, Yawen Xu, Walter Lacarbonara

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    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.

    Original languageEnglish (US)
    Title of host publication12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
    PublisherAmerican Society of Mechanical Engineers (ASME)
    Volume6
    ISBN (Electronic)9780791850183
    DOIs
    StatePublished - Jan 1 2016
    EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
    Duration: Aug 21 2016Aug 24 2016

    Other

    OtherASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
    CountryUnited States
    CityCharlotte
    Period8/21/168/24/16

    Fingerprint

    Liquid sloshing
    Sloshing
    Container
    Containers
    Internal Resonance
    Nonlinearity
    Surface tension
    Surface Tension
    Fluids
    Nonlinear Resonance
    Surface waves
    Softening
    Hardening
    Surface Waves
    Incompressible Fluid
    Parameter Space
    Sufficient
    Fluid
    Influence
    Coefficient

    ASJC Scopus subject areas

    • Mechanical Engineering
    • Computer Graphics and Computer-Aided Design
    • Computer Science Applications
    • Modeling and Simulation

    Cite this

    Daqaq, M., Xu, Y., & Lacarbonara, W. (2016). Nonlinearity of finite-amplitude waves in rectangular containers. In 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201659908

    Nonlinearity of finite-amplitude waves in rectangular containers. / Daqaq, Mohammed; Xu, Yawen; Lacarbonara, Walter.

    12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2016.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Daqaq, M, Xu, Y & Lacarbonara, W 2016, Nonlinearity of finite-amplitude waves in rectangular containers. in 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. vol. 6, American Society of Mechanical Engineers (ASME), ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016, Charlotte, United States, 8/21/16. https://doi.org/10.1115/DETC201659908
    Daqaq M, Xu Y, Lacarbonara W. Nonlinearity of finite-amplitude waves in rectangular containers. In 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6. American Society of Mechanical Engineers (ASME). 2016 https://doi.org/10.1115/DETC201659908
    Daqaq, Mohammed ; Xu, Yawen ; Lacarbonara, Walter. / Nonlinearity of finite-amplitude waves in rectangular containers. 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2016.
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