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广义能量耗散弹性理论(TEWED,G-NⅢ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究.提出了更普遍的有复杂参数的色散方程,通过运用Ieguerre 方法解决复杂条件下耦合磁-热-弹性波的问题,表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题.在G-NⅢ模型(TEWED)中,耦合磁-热-弹性波传播时发生衰减和色散,扩散的热量由热传播方程中的阻尼项考虑,而在G-N Ⅱ模型没有发生衰减和耗散.最后给出了类铜材料的数值结果. 相似文献
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本文讨论非线性扩散和色散方程隐式单支差分格式的稳定性,将证明:当 α=1-1/2s时,扩散方程单支差分解满足L_(2s)范广义极值原理,从而L_(2s)范无条件压缩性稳定.证明的方法适用于多维方程和方程组,而且扩散系数可以是退化的.类似地给出色散方程绝对稳 相似文献
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研究了一类星形弹性网络系统在热效应影响以及边界反馈作用下的稳定性问题及系统相应(广义)特征向量的Riesz基性质.基于Green和Naghdi第二类热弹性理论,假设在该热弹性系统中热以有限波速传播,并且在传播过程中无能量耗散.证明了该热弹性网络系统能量渐近衰减到零.并进一步通过系统算子谱分析,讨论得出该系统算子的(广义)特征向量构成状态空间的一组Riesz基. 相似文献
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研究了弹性力学中一退化波方程的Riemann问题.其应力函数非凸非凹,从而使得激波条件退化.通过引入广义激波条件下的退化激波,构造性地得到了各种情形下Riemann问题的整体解. 相似文献
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研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的. 相似文献
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对一般的热机械问题提出了一种有效的数值方法,并对二维的热弹性问题进行了测试.该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶,使之成为一组微分代数方程,应力应变关系被写成代数方程.所得到的微分代数系统采用全隐式的向后差分公式进行求解.对该方法进行了详细的说明.为了验证该方法的有效性,将其应用于一个动态非耦合的热弹性问题的求解和一个耦合的二维热弹性问题的求解. 相似文献
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色散方程的一类新的并行交替分段隐格式 总被引:14,自引:0,他引:14
本文给出了一组逼近色散方程的非对称差分格式,并用这组格式和对称的Crank-Nicolson型格式构造了求解色散方程的并行交替分段差分隐格式.这个格式是无条件稳定的,能直接在并行计算机上使用.数值试验表明,这个格式有很好的精度. 相似文献
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The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates. 相似文献
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The paper examines the problem of wave propagation in a random conducting magneto-non-simple thermo-viscoelastic medium. The medium has been assumed to be weakly conducting and weakly thermal. The thermomechanical coupling parameter and the conductivity are random functions, proportional to ε, with non-zero mean values, ε measuring the smallness of the scale of random fluctuation of inhomogeneities of the medium. The smooth perturbation technique enunciated by Keller (1964) has been employed to analyze the appropriate dispersion equation in non-simple thermoelastic medium. The longitudinal and transverse waves were discussed by using a particular form of thermomechanical coupling parameter representing the corresponding auto-correlation function. The effect of magnetic conductivity has been investigated. The phenomena of attenuation of waves and change of phase speed were discussed numerically in details. 相似文献
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Effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids
The effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids has been investigated. Elastic waves are reflected due to incident coupled longitudinal and coupled shear waves from a plane free boundary of micropolar thermoelastic materials with voids. The amplitude ratios corresponding to the reflected coupled longitudinal and coupled shear waves are derived by using appropriate boundary conditions. Energy partition in the free surface has been presented. The amplitude and energy ratios of the reflected waves are also computed numerically for a particular model. 相似文献
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Yeping Li 《Mathematical Methods in the Applied Sciences》2013,36(11):1409-1422
In this paper, we discuss a bipolar transient quantum hydrodynamic model for charge density, current density, and electric field in the quarter plane. This model takes the form of a classical Euler–Poisson system with the additional dispersion terms caused by the quantum (Bohn) potential. We show global existence of smooth solutions for the initial boundary value problem when the initial data are near the nonlinear diffusive waves, which are different from the steady state. We also show the asymptotical behavior of the global smooth solution towards the nonlinear diffusive waves and obtain the algebraic decay rates. These results are proved by elaborate energy methods. Finally, using the Fourier analysis, we obtain the optimal convergence rates of the solutions towards the nonlinear diffusion waves. As far as we known, this is the first result about the initial boundary value problem of the one‐dimensional bipolar quantum hydrodynamic model in the quarter plane. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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研究具有两个驰豫时间的、两个不同弹性和热性质的、广义传热立方晶体固体半空间的有缺陷结合面上,热弹性平面波的反射和折射问题.具有两个驰豫时间的广义热弹性理论,是1972年由Green和Lindsay提出并应用于问题的研究.对有缺陷边界,给出了反射系数和折射系数(即反射波和折射波振幅与入射波振幅之比)的表达式,并推演了法向刚性边界、横向刚性边界、接触传热边界、滑动边界和结合面边界时的表达式.给出了在不同边界条件及出射角时,不同的反射波和折射波的振幅比,在不同的入射波时的变化图.发现反射波和折射波振幅比受到介质刚性和热性质的影响. 相似文献
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The problem of symmetric and anti-symmetric vibrations in micropolar thermoelastic plate with voids has been investigated. The dispersive frequency equations are obtained for different surface waves propagating in the plate. The velocity curves are depicted for the symmetric and anti-symmetric vibrations, plate, Rayleigh and flexural waves. It is found that there exist two modes in the solution of frequency equation for the surface waves in micropolar thermoelastic plate with voids. We have observed that the first modes of velocity ratios of corresponding surface waves are lesser than those of second mode of vibration. 相似文献
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Narayan Das Soumen De Nantu Sarkar 《Mathematical Methods in the Applied Sciences》2020,43(3):1313-1336
The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. 相似文献
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The generalized thermoelasticity theory based upon the Green and Naghdi model II of thermoelasticity as well as the Eringen’s nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves which are dispersive in nature and associated with attenuation. In addition to the coupled waves, there also exists one independent vertically shear type wave which is dispersive but without any attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear type wave is found to to be associated with a critical frequency, while the coupled longitudinal waves may have critical frequencies under constraints. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on the phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients as well as the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. 相似文献
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D S Chandrasekharaiah 《Proceedings Mathematical Sciences》1983,92(2):109-120
Free surface waves of arbitrary form in a homogeneous and isotropic linear micropolar thermoelastic half-space with stress-free plane boundary are investigated. It is found that all physical quantities associated with the waves are derivable from two scalar functions and that there exist two families of waves in general. One of these is the classical thermoelastic wave modified under the influence of the microelastic field and the other is a new surface wave not encountered in classical elasticity. The waves are not necessarily plane waves and even when these are assumed to propagate in a fixed direction parallel to the boundary, unlike in classical elasticity, the problem is not one of plane strain. Explicit expressions for the displacement vector, microrotation vector and the temperature are obtained and the nature of deformation has been analysed. Several earlier results are deduced as particular cases of the more general results obtained here. 相似文献