Continuum model of dispersion caused by an inherent material characteristic length
Continuum model of dispersion caused by an inherent material characteristic length
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由固有材料特征长度引起的色散连续体模型
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
O. Gottlieb
中科院分区：
文献类型：
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作者：
M. Rubin;P. Rosenau;O. Gottlieb
提出了对亥姆霍兹自由能和与简单连续体的一般本构方程相关的应力的修改，以模拟固有材料特征长度的色散效应。这些修改不会改变热力学第一定律和第二定律对未修改本构方程的通常限制。考虑热弹性可压缩牛顿粘性流体的特殊情况，重点关注单轴应变。在此背景下，对于弹性响应的简单情况，考虑无限介质中的波传播和有限柱的自由振动的线性化问题。结果表明，所提出的模型预测了随着波长减小，波通过一系列弹簧和质量块传播时观察到的色散效应。此外，还讨论了在不存在粘性的情况下孤子稳态波传播和在存在粘性的情况下冲击波的非线性问题。特别是它...
Modifications of the Helmholtz free energy and the stress associated with general constitutive equations of a simple continuum are proposed to model dispersive effects of an inherent material characteristic length. These modifications do not alter the usual restrictions on the unmodified constitutive equations imposed by the first and second laws of thermodynamics. The special case of a thermoelastic compressible Newtonian viscous fluid is considered with attention focused on uniaxial strain. Within this context, the linearized problems of wave propagation in an infinite media and free vibrations of a finite column are considered for the simple case of elastic response. It is shown that the proposed model predicts the dispersive effects observed in wave propagation through a chain of springs and masses as the wavelength decreases. Also, the nonlinear problems of steady wave propagation of a soliton in the absence of viscosity and of a shock wave in the presence of viscosity are discussed. In particular it...