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利用Sinc-Galerkin法数值求解Burgers方程的初边值问题。首先,用Hopf-Cole变换将二阶非线性的Burgers方程变换为二阶线性方程,同时把第一类边界条件变为第二类边界条件。时间上的导数采用θ加权格式离散,空间导数采用Sinc-Galerkin法离散,端点处分别引入权函数处理变换后的第二类边界条件。最后,通过数值算例验证了Sinc-Galerkin法的指数收敛性,与精确解相比,本文构造的数值格式精度高,能够有效捕捉激波等物理现象。 相似文献
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The non-linear governing differential equations of immovably simply supported functionally graded material (FGM) rod subjected to thermal loads were derived. The thermal post-buckling behaviors of FGM rod made of ZrO2 and Ti-6Al-4Vwere analyzed by shooting method. Firstly, the thermal post-buckling equilibrium paths of the FGM rod with different gradient index in the uniform temperature field were plotted, and compared with the behaviors of the homogeneous rods made of ZrO2 and Ti-6A1-4V materials, respectively. For given value of end rotation angles, the influence of gradient index on the thermal post-buckling behaviors of FGM rod was discussed. Secondly, the thermal post-buckling characteristics of the FGM rod were analyzed when the temperature difference parameter is changed while the bottom temperature parameter remains constant, and when the bottom temperature parameter is changed while the temperature difference parameter remains constant, and compared with the characteristics of the two homogeneous material rods. 相似文献
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固—液耦合Timoshenko管道的稳定性分析 总被引:12,自引:0,他引:12
根据Hamilton原理的固-液耦合振同分方程用幂级数法计算了Timoshenko管道的固有频率和临界流速。给出了管道前三阶固有频率-流速的关系曲线,分析了转动惯量对该输流管道的稳定特性的影响。计算结果表明,转动一对两端简支的固-液合Timoshenko管道的静力失稳没有影响,但对其频率特性和动力失稳有影响。 相似文献
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将数学建模思想以及Matlab软件融入矩阵运算的教学中,降低了矩阵代数的抽象性和计算的繁杂性,增强了学生用数学知识和计算机编程来解决实际问题的能力,为线性代数的教学改革提供了一种新的模式. 相似文献
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从一维黏弹性本构方程出发,导出了黏弹性变截面直杆纵向振动微分方程的一般形式,采用了有限差分法,并以二阶矩阵表示的递推形式,建立了该问题的复特征值方程组。两种Maxwell黏弹性变截面(指数指数、线性函数)直杆的数值计算表明,该方法运算简单,计算精度高,能适用于求解任意变截面黏弹性直属的纵向自由振动问题。 相似文献
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Stability analysis of viscoelastic curved pipes conveying fluid 总被引:1,自引:0,他引:1
Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode. 相似文献
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