Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions

J. A. Turner

doi:10.1016/S0022-460X(03)00791-0

Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions

J. A. Turner

Mechanical & Materials Engineering

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

The non-linear vibrations of a linear beam with cantilever-Hertizian contact boundary conditions are investigated. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. One primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. In addition, the associated non-linear normal modes of this system are derived. The modes include a non-linear modification to the linear, harmonic component as well as a static offset term and second and third harmonic components.

Original language	English (US)
Pages (from-to)	177-191
Number of pages	15
Journal	Journal of Sound and Vibration
Volume	275
Issue number	1-2
DOIs	https://doi.org/10.1016/S0022-460X(03)00791-0
State	Published - Aug 6 2004

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Acoustics and Ultrasonics
Mechanical Engineering

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title = "Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions",

abstract = "The non-linear vibrations of a linear beam with cantilever-Hertizian contact boundary conditions are investigated. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. One primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. In addition, the associated non-linear normal modes of this system are derived. The modes include a non-linear modification to the linear, harmonic component as well as a static offset term and second and third harmonic components.",

author = "Turner, {J. A.}",

note = "Funding Information: This work was sponsored by the Air Force Office of Scientific Research under Grant No. F49620-99-1-0254. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government. Support of the Center for Electro-Optics at the University of Nebraska-Lincoln is also gratefully acknowledged.",

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N1 - Funding Information: This work was sponsored by the Air Force Office of Scientific Research under Grant No. F49620-99-1-0254. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government. Support of the Center for Electro-Optics at the University of Nebraska-Lincoln is also gratefully acknowledged.

PY - 2004/8/6

Y1 - 2004/8/6

N2 - The non-linear vibrations of a linear beam with cantilever-Hertizian contact boundary conditions are investigated. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. One primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. In addition, the associated non-linear normal modes of this system are derived. The modes include a non-linear modification to the linear, harmonic component as well as a static offset term and second and third harmonic components.

AB - The non-linear vibrations of a linear beam with cantilever-Hertizian contact boundary conditions are investigated. The method of multiple scales is used to analyze this problem in which it is assumed that the beam remains in contact with the moving surface at all times. One primary result from this analysis is the amplitude-frequency relation for the various flexural modes. The amplitude-frequency curves exhibit softening behavior as expected. The amount of softening is shown to depend on the linear contact stiffness as well as the specific mode. In addition, the associated non-linear normal modes of this system are derived. The modes include a non-linear modification to the linear, harmonic component as well as a static offset term and second and third harmonic components.

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JF - Journal of Sound and Vibration

SN - 0022-460X

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ER -

Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions

Abstract

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