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    Models of Viscoelasticity with Complex‐Order Derivatives

    Source: Journal of Engineering Mechanics:;1993:;Volume ( 119 ):;issue: 007
    Author:
    Nicos Makris
    ,
    M. C. Constantinou
    DOI: 10.1061/(ASCE)0733-9399(1993)119:7(1453)
    Publisher: American Society of Civil Engineers
    Abstract: In this paper it is shown that the order of time derivative and the coefficients in linear viscoelastic models can be generalized to complex quantities. In this approach, the storage and loss moduli are not regarded as two independent real functions but rather as the real and imaginary parts of a complex function. The problem of calibration of models with complex parameters is solved by resorting to methods of nonlinear regression in the complex space. The conditions for existence of complex‐order time derivatives are examined and the transformation of these derivatives in the frequency domain is derived. The procedure is applied in the development of models for viscous dampers. The models are shown to produce results in good agreement with experimental data.
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      Models of Viscoelasticity with Complex‐Order Derivatives

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    contributor authorNicos Makris
    contributor authorM. C. Constantinou
    date accessioned2017-05-08T22:15:22Z
    date available2017-05-08T22:15:22Z
    date copyrightJuly 1993
    date issued1993
    identifier other40007058.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/75301
    description abstractIn this paper it is shown that the order of time derivative and the coefficients in linear viscoelastic models can be generalized to complex quantities. In this approach, the storage and loss moduli are not regarded as two independent real functions but rather as the real and imaginary parts of a complex function. The problem of calibration of models with complex parameters is solved by resorting to methods of nonlinear regression in the complex space. The conditions for existence of complex‐order time derivatives are examined and the transformation of these derivatives in the frequency domain is derived. The procedure is applied in the development of models for viscous dampers. The models are shown to produce results in good agreement with experimental data.
    publisherAmerican Society of Civil Engineers
    titleModels of Viscoelasticity with Complex‐Order Derivatives
    typeJournal Paper
    journal volume119
    journal issue7
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)0733-9399(1993)119:7(1453)
    treeJournal of Engineering Mechanics:;1993:;Volume ( 119 ):;issue: 007
    contenttypeFulltext
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