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    Exact and Nonlocal Solutions for Vibration of Axial Lattice with Direct and Indirect Neighboring Interactions

    Source: Journal of Engineering Mechanics:;2018:;Volume ( 144 ):;issue: 005
    Author:
    Challamel Noël;Wang Chien Ming;Zhang Hong;Kitipornchai Sritawat
    DOI: 10.1061/(ASCE)EM.1943-7889.0001441
    Publisher: American Society of Civil Engineers
    Abstract: This paper investigates the effect of long-range interaction forces in the longitudinal vibration of an axial linear elastic lattice. The eigenfrequencies of this axial lattice with direct and indirect linear elastic interactions are expressed in closed-form solutions for fixed-fixed and fixed-free boundary conditions. The paper starts with the two-neighbor interaction problem, and then generalizes the result to the more general N-neighbor interaction problem. Starting from a continualization of the higher-order difference equations, a nonlocal elastic continuum is constructed to approximate the behavior of the axial lattice with generalized short and long-range interactions. It is shown, while preserving the definite positiveness of the generalized lattice strain energy, that the associated nonlocal continuum is equivalent to a stress gradient type of Eringen’s nonlocal model, which is able to capture the main scale phenomena of the generalized lattice. The length scale factor of the nonlocal model is calibrated to the size of the influence domain for the long-range interaction. The paper ends with a discussion about the effect of the discrete interaction kernel on the sensitivity of the eigenfrequencies with respect to scale effects. Exact analytical natural frequencies are calculated for discrete power law or exponential-based kernels. The stress gradient nonlocal theory offers an efficient engineering continuum framework, which accurately fits the response of generalized lattice with N-neighbor interaction.
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      Exact and Nonlocal Solutions for Vibration of Axial Lattice with Direct and Indirect Neighboring Interactions

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4250523
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    contributor authorChallamel Noël;Wang Chien Ming;Zhang Hong;Kitipornchai Sritawat
    date accessioned2019-02-26T07:57:28Z
    date available2019-02-26T07:57:28Z
    date issued2018
    identifier other%28ASCE%29EM.1943-7889.0001441.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4250523
    description abstractThis paper investigates the effect of long-range interaction forces in the longitudinal vibration of an axial linear elastic lattice. The eigenfrequencies of this axial lattice with direct and indirect linear elastic interactions are expressed in closed-form solutions for fixed-fixed and fixed-free boundary conditions. The paper starts with the two-neighbor interaction problem, and then generalizes the result to the more general N-neighbor interaction problem. Starting from a continualization of the higher-order difference equations, a nonlocal elastic continuum is constructed to approximate the behavior of the axial lattice with generalized short and long-range interactions. It is shown, while preserving the definite positiveness of the generalized lattice strain energy, that the associated nonlocal continuum is equivalent to a stress gradient type of Eringen’s nonlocal model, which is able to capture the main scale phenomena of the generalized lattice. The length scale factor of the nonlocal model is calibrated to the size of the influence domain for the long-range interaction. The paper ends with a discussion about the effect of the discrete interaction kernel on the sensitivity of the eigenfrequencies with respect to scale effects. Exact analytical natural frequencies are calculated for discrete power law or exponential-based kernels. The stress gradient nonlocal theory offers an efficient engineering continuum framework, which accurately fits the response of generalized lattice with N-neighbor interaction.
    publisherAmerican Society of Civil Engineers
    titleExact and Nonlocal Solutions for Vibration of Axial Lattice with Direct and Indirect Neighboring Interactions
    typeJournal Paper
    journal volume144
    journal issue5
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)EM.1943-7889.0001441
    page4018025
    treeJournal of Engineering Mechanics:;2018:;Volume ( 144 ):;issue: 005
    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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