Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers

Mohammed Daqaq, Yawen Xu, Walter Lacarbonara

Research output: Contribution to journalArticle

Abstract

This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

Original languageEnglish (US)
Article number031002
JournalJournal of Applied Mechanics, Transactions ASME
Volume84
Issue number3
DOIs
StatePublished - Mar 1 2017

Fingerprint

liquid sloshing
Liquid sloshing
containers
Containers
Surface tension
nonlinearity
interfacial tension
coupled modes
Fluids
uncoupled modes
Contacts (fluid mechanics)
Contact angle
Hardening
incompressible fluids
hardening
softening
fluids

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers. / Daqaq, Mohammed; Xu, Yawen; Lacarbonara, Walter.

In: Journal of Applied Mechanics, Transactions ASME, Vol. 84, No. 3, 031002, 01.03.2017.

Research output: Contribution to journalArticle

@article{53545c9e270d43dd97a99568cfbea361,
title = "Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers",
abstract = "This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.",
author = "Mohammed Daqaq and Yawen Xu and Walter Lacarbonara",
year = "2017",
month = "3",
day = "1",
doi = "10.1115/1.4035363",
language = "English (US)",
volume = "84",
journal = "Journal of Applied Mechanics, Transactions ASME",
issn = "0021-8936",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "3",

}

TY - JOUR

T1 - Nonlinearity of Finite-Amplitude Sloshing in Rectangular Containers

AU - Daqaq, Mohammed

AU - Xu, Yawen

AU - Lacarbonara, Walter

PY - 2017/3/1

Y1 - 2017/3/1

N2 - This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

AB - This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.

UR - http://www.scopus.com/inward/record.url?scp=85007496565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007496565&partnerID=8YFLogxK

U2 - 10.1115/1.4035363

DO - 10.1115/1.4035363

M3 - Article

AN - SCOPUS:85007496565

VL - 84

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 3

M1 - 031002

ER -