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    An Efficient Analytical Method Based on Averaging and MemoryFree Principle for Variable Fractional Oscillators

    Source: Journal of Applied Mechanics:;2022:;volume( 089 ):;issue: 012::page 121002
    Author:
    Liu, Q. X.;Liu, J. K.;Chen, Y. M.
    DOI: 10.1115/1.4055617
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: It has been a difficult task to solve fractional oscillators analytically, especially when variableorder fractional derivatives (FDs) are included. The major difficulty consists in deriving analytical expressions for the variable FDs of trigonometric functions. To tackle this problem, a memoryfree transformation for constantorder FDs is modified to transform the variable FDs equivalently into a nonlinear differential equation of integer order. Based on the equivalent equation, an analytical solution is obtained for the variable FD, showing nice agreement with numerical results. According to the approximate analytical solution in closed form, the frequency amplitude curve and the backbone line of variable fractional oscillators are determined accurately. In addition, it provides us with convenience in analyzing the primary resonance.
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      An Efficient Analytical Method Based on Averaging and MemoryFree Principle for Variable Fractional Oscillators

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    contributor authorLiu, Q. X.;Liu, J. K.;Chen, Y. M.
    date accessioned2023-04-06T12:50:41Z
    date available2023-04-06T12:50:41Z
    date copyright10/6/2022 12:00:00 AM
    date issued2022
    identifier issn218936
    identifier otherjam_89_12_121002.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4288615
    description abstractIt has been a difficult task to solve fractional oscillators analytically, especially when variableorder fractional derivatives (FDs) are included. The major difficulty consists in deriving analytical expressions for the variable FDs of trigonometric functions. To tackle this problem, a memoryfree transformation for constantorder FDs is modified to transform the variable FDs equivalently into a nonlinear differential equation of integer order. Based on the equivalent equation, an analytical solution is obtained for the variable FD, showing nice agreement with numerical results. According to the approximate analytical solution in closed form, the frequency amplitude curve and the backbone line of variable fractional oscillators are determined accurately. In addition, it provides us with convenience in analyzing the primary resonance.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleAn Efficient Analytical Method Based on Averaging and MemoryFree Principle for Variable Fractional Oscillators
    typeJournal Paper
    journal volume89
    journal issue12
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.4055617
    journal fristpage121002
    journal lastpage1210028
    page8
    treeJournal of Applied Mechanics:;2022:;volume( 089 ):;issue: 012
    contenttypeFulltext
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