{"title":"Dynamic Stability of Wave-Convection Transport:","authors":"M. Greenberg, C. Harrell","doi":"10.1243/JMES_JOUR_1982_024_042_02","DOIUrl":null,"url":null,"abstract":"A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.","PeriodicalId":114598,"journal":{"name":"Archive: Journal of Mechanical Engineering Science 1959-1982 (vols 1-23)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1982-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive: Journal of Mechanical Engineering Science 1959-1982 (vols 1-23)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1243/JMES_JOUR_1982_024_042_02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract

A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.
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波对流输运的动力稳定性:
假定一个有弹性的不可扩展的水平带是由紧密间隔的垂直推杆形成的,形成一个行进的正弦波。当波传播时,位于波谷底部的球形物体将倾向于与波谷发生对流。考虑了这种波对流输运的动力稳定性。假设波是浅的,控制非线性方程在“浅参数”中展开(通过二阶),从而简化为单个方程,本质上是强制Duffing型,在实际感兴趣的参数空间上进行数值积分,以产生稳定性判据。
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