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    A Study of the Nonlinearly Related Modal Solutions of Coupled Nonlinear Systems by Superposition Techniques

    Source: Journal of Applied Mechanics:;1965:;volume( 032 ):;issue: 002::page 359
    Author:
    C. P. Atkinson
    ,
    Beverly Taskett
    DOI: 10.1115/1.3625807
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of m1ẍ1 + k = 1n akx1k + k = 1n Ak(x1 − x2)k = 0m2ẍ2 + k = 1n bkx2k − k = 1n Ak(x1 − x2)k = 0 (1)with k = 1, 3, 5, . . . . . . are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form m1ẍ1 + akx1k + Ak(x1 − x2)k = 0m2ẍ2 + bkx2k − Ak(x1 − x2)k = 0 (2) whose force fields are superimposed to yield the force field of equations (1).
    keyword(s): Nonlinear systems , Force AND Equations ,
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      A Study of the Nonlinearly Related Modal Solutions of Coupled Nonlinear Systems by Superposition Techniques

    URI
    https://yetl.yabesh.ir/yetl1/handle/yetl/104312
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    contributor authorC. P. Atkinson
    contributor authorBeverly Taskett
    date accessioned2017-05-08T23:27:55Z
    date available2017-05-08T23:27:55Z
    date copyrightJune, 1965
    date issued1965
    identifier issn0021-8936
    identifier otherJAMCAV-25803#359_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/104312
    description abstractThe coupled nonlinear oscillating systems studied do not possess linear normal modes. The nonlinearly related modes of m1ẍ1 + k = 1n akx1k + k = 1n Ak(x1 − x2)k = 0m2ẍ2 + k = 1n bkx2k − k = 1n Ak(x1 − x2)k = 0 (1)with k = 1, 3, 5, . . . . . . are expressed as superpositions of the linear normal modes of each of the homogeneous systems of the form m1ẍ1 + akx1k + Ak(x1 − x2)k = 0m2ẍ2 + bkx2k − Ak(x1 − x2)k = 0 (2) whose force fields are superimposed to yield the force field of equations (1).
    publisherThe American Society of Mechanical Engineers (ASME)
    titleA Study of the Nonlinearly Related Modal Solutions of Coupled Nonlinear Systems by Superposition Techniques
    typeJournal Paper
    journal volume32
    journal issue2
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3625807
    journal fristpage359
    journal lastpage364
    identifier eissn1528-9036
    keywordsNonlinear systems
    keywordsForce AND Equations
    treeJournal of Applied Mechanics:;1965:;volume( 032 ):;issue: 002
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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