YaBeSH Engineering and Technology Library

    • Journals
    • PaperQuest
    • YSE Standards
    • YaBeSH
    • Login
    View Item 
    •   YE&T Library
    • ASME
    • Journal of Vibration and Acoustics
    • View Item
    •   YE&T Library
    • ASME
    • Journal of Vibration and Acoustics
    • View Item
    • All Fields
    • Source Title
    • Year
    • Publisher
    • Title
    • Subject
    • Author
    • DOI
    • ISBN
    Advanced Search
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Archive

    Nonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities

    Source: Journal of Vibration and Acoustics:;1995:;volume( 117 ):;issue: 002::page 199
    Author:
    A. H. Nayfeh
    ,
    S. A. Nayfeh
    DOI: 10.1115/1.2873898
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: We use two approaches to determine the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic nonlinearities. In the first approach, we use the method of multiple scales to treat the governing partial-differential equation and boundary conditions directly. In the second approach, we use a Galerkin procedure to discretize the system and then determine the normal modes from the discretized equations by using the method of multiple scales and the invariant manifold approach. Whereas one- and two-mode discretizations produce erroneous results for continuous systems with quadratic and cubic nonlinearities, all methods, in the present case, produce the same results because the discretization is carried out by using a complete set of basis functions that satisfy the boundary conditions.
    keyword(s): Boundary-value problems , Equations , Frequency , Functions AND Manifolds ,
    • Download: (673.1Kb)
    • Show Full MetaData Hide Full MetaData
    • Get RIS
    • Item Order
    • Go To Publisher
    • Price: 5000 Rial
    • Statistics

      Nonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/116276
    Collections
    • Journal of Vibration and Acoustics

    Show full item record

    contributor authorA. H. Nayfeh
    contributor authorS. A. Nayfeh
    date accessioned2017-05-08T23:48:51Z
    date available2017-05-08T23:48:51Z
    date copyrightApril, 1995
    date issued1995
    identifier issn1048-9002
    identifier otherJVACEK-28820#199_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/116276
    description abstractWe use two approaches to determine the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic nonlinearities. In the first approach, we use the method of multiple scales to treat the governing partial-differential equation and boundary conditions directly. In the second approach, we use a Galerkin procedure to discretize the system and then determine the normal modes from the discretized equations by using the method of multiple scales and the invariant manifold approach. Whereas one- and two-mode discretizations produce erroneous results for continuous systems with quadratic and cubic nonlinearities, all methods, in the present case, produce the same results because the discretization is carried out by using a complete set of basis functions that satisfy the boundary conditions.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleNonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities
    typeJournal Paper
    journal volume117
    journal issue2
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.2873898
    journal fristpage199
    journal lastpage205
    identifier eissn1528-8927
    keywordsBoundary-value problems
    keywordsEquations
    keywordsFrequency
    keywordsFunctions AND Manifolds
    treeJournal of Vibration and Acoustics:;1995:;volume( 117 ):;issue: 002
    contenttypeFulltext
    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian
     
    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian