Nonlinearity of finite-amplitude waves in rectangular containers

Mohammed F. 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)
ISBN (Electronic)9780791850183
DOIs
StatePublished - 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

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume6

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

ASJC Scopus subject areas

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

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  • Cite this

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