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反命题作为一种可变(未知)边界问题近年来得到了广泛的研究。本文给出了亚声速平面叶栅反命题计算的势函数变域变分有限元解法。变域变分通过把可变边界结合在变分泛函中,使其与求解流场的控制方程结合起来,从而使可变边界求解和流场分析可以完全耦合进行。本文针对亚声速平面叶栅的反命题,根据泛函的驻值必要条件,介绍了变域变分有限元方法的求解过程,最后给出了两个数值算例。这两个算例均采用四节点矩形单元的插值基函数,第一个算例用于检验程序的可靠性,第二个算例设计了一个给定叶面马赫数分布的叶型,并与试验结果进行对照。 相似文献
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本文研究了含边裂纹的有限宽弹性长板条在反平面剪切冲击作用下的瞬态响应.考虑了两种情况,1.两边自由,2.板的一边自由,另一边固定.用Laplace和Fourier变换将问题化为在Laplace变换域内求解第一类Cauchy型奇异积分方程,并给出了动态应力强度因子和裂纹张开位移的数值结果。 相似文献
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多尺度有限差分方法求解波动方程 总被引:2,自引:1,他引:2
小波分析是多尺度分析方法,本文利用具有紧支集的正交小波变换对有限差分方程进行空间多尺度近似,提出适合于层状介质波传问题数值计算的多尺度有限差分方法,将波动方程的求解转换到小波域中进行。利用小波基的自适应性与消失矩特性,有效减少了计算量、提高了稳定性,扩大了可求解的速度范围。地球物理勘探中的数值实例显示了算法具有良好效率。 相似文献
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有限条法的一个显著优点,它使单元刚阵降阶,总刚阵极为稀疏且正定,这样易于在小容量计算机上求解问题。对于不存在泛函或者建立泛函很困难的问题中,迦辽金有限元法是十分有效的。本文提出迦辽金有限条法分析基础板问题。我们先将基础板的基本方程通过积分变换表达成矩阵形式,再对板离散为有限条元,从而导出基础板的有限条元基本方程,通过算例表明,精度较满意。 相似文献
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在非增量算法的基础上,提出了用最优控制变分原理形成过程最优控制迭代求解的基本思路,并给出求解的基本控制方程。这一工作为有限变形力学问题的数值求解提供了一个新的处理方法。 相似文献
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本文用分离变量法求解雷诺方程,在π油膜的假设下,求得雷诺方程应满足的特征值与用傅立叶级数表达的特征函数,进而求得有限长轴的非特急油膜力解析表达式。为分析轴承转子系统的非线性动力特性提供了帮助。 相似文献
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区别于基于半空间理论的传统直齿轮弹流润滑模型,本文基于有限长空间解建立考虑轮齿自由端面影响的渐开线直齿轮有限长弹流润滑模型. 采用叠加法构造自由端面,矩阵法和半解析法求解自由端面的影响,快速傅里叶变换算法加速齿面弹性变形计算;采用统一Reynolds方程法求解油膜压力和油膜厚度. 以啮合节点为特征位置,分析比较不同压力角下自由端面对直齿轮弹流润滑的影响. 结果表明:与半空间模型比较,考虑自由端面后端面峰值压力降低,压力分布更均匀,最小油膜厚度增大;增大轮齿压力角,节点压力水平减小,油膜厚度增大;当压力角不同时,自由端面对齿轮弹流润滑压力峰值的影响基本相当,对最小膜厚的影响较大. 相似文献
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考虑进油压力的滑动轴承非线性油膜力数据库 总被引:2,自引:0,他引:2
通过对ReyTlolds方程的非线性变换,提出了考虑进油压力边界条件时径向滑动轴承非线性油膜力数据库的建库方法,扩展了油膜力数据库计算方法的应用,通过引入2个有限数据域的新变量对转子轴心速度项和进油压力边界条件进行有限化处理,得到了更符合实际工况的连续性油膜力数据库及计算模型,同有限元法对比分析了非线性油膜力数据库的适用性.结果表明,非线性油膜力数据库模型的精度较高,所建立的非线性油膜力计算模型可用于对转子系统瞬态运动进行简便和快捷的分析. 相似文献
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非定常短轴承油膜力公式的变分修正 总被引:6,自引:0,他引:6
本文采用了变分方法对非定常短轴承的油膜压力分布公式进行了修正,既保留了短轴承公式的简洁形式,又使其适用于大长径比轴承。得出了具有足够精度、适合轴颈大扰动情况下的有限长圆柱轴承非定常油膜力的解析公式。与差分充零算法相比,短轴承公式的结果在轴承长径比为0.6时,误差已经超过百分之二百,而本方法计算结果的误差小于百分之五。因此采用本方法既提高了短轴承油膜力公式的计算精度,又保持了油膜力公式的简洁形式,不失为进行转子-轴承系统非线性动力分析的一种有效方法。 相似文献
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构筑了轴向解析、周向有限元压力分布的一维变粘度场有限宽轴承模型。在绝热边界条件下,忽略泊肃叶流项对速度的影响,不考虑温度轴向变化并沿油膜厚度方向积分,三维能量方程可降阶为平均温度场只沿周向分布的一维形式,结合滑动轴承非线性油膜力的一维直接解法,能量方程与雷诺方程可分别求解,既考虑了温粘效应对滑动轴承非线性动力学性能的影响,又提供了无需迭代直接确定油膜破裂边界和求解非线性油膜力的快速新方法。作为应用,针对进油槽位于水平两侧的椭圆瓦轴承进行了动力润滑热效应分析,与工程数据比较,计算结果吻合,证明该模型合理,适用于工程上多瓦轴承的分析计算。 相似文献
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The modeling and simulation process of oil-film bearing dynamics constitutes a rather essential task integrated in the workflow of various mechanical products. Specifically, in the turbo charger industry, the correct capture and understanding of the associated nonlinear rotating dynamics is of utmost importance, since the system’s efficiency and lifetime span depends on it. The root cause of the nonlinear rotordynamic effects is the oil-film concentrated in the rotor’s journal bearings. Its behavior is highly coupled with both the system’s geometric and dynamic configuration. The dynamics of the oil-film are described by the well-known Navier–Stokes equation, which under a series of assumptions and simplifications results to the, so-called, Reynolds equation. In this paper, the Reynolds equation is numerically solved based on a finite difference scheme and several parameter variation studies are conducted in an effort to pinpoint the most influential parameters—journal bearing geometric dimensions, oil-film properties and rotor-velocity-driven inputs—with respect to designated responses—friction, oil-film pressure force, minimum oil-film thickness and boundary oil-flow—all of which are regarded as important in terms of the aforementioned system’s efficiency and lifetime span. Based on multivariate analysis algorithms, correlation outcomes and global sensitivity results are presented. In an effort to capture possible nonlinear phenomena, which might not be possible via linear data mining tools, the Spearman rank-order coefficient and self-organizing maps methodology are applied. 相似文献
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To overcome the shortcomings of extreme time-consuming in solving the Reynolds equation, two efficient calculation methods,
based on the free boundary theory and variational principles for the unsteady nonlinear Reynolds equation in the condition
of Reynolds boundary, are presented in the paper. By employing the two mentioned methods, the nonlinear dynamic forces as
well as their Jacobians of the journal bearing can be calculated saving time but with the same accuracy. Of these two methods,
the one is called a Ritz model which manipulates the cavitation region by simply introducing a parameter to match the free
boundary condition and, as a result, a very simple approximate formulae of oil-film pressure is being obtained. The other
one is a one-dimensional FEM method which reduces the two-dimensional variational inequality to the one-dimensional algebraic
complementary equations, and then a direct method is being used to solve these complementary equations, without the need of
iterations, and the free boundary condition can be automatically satisfied. Meanwhile, a new order reduction method is contributed
to reduce the degrees of freedom of a complex rotor-bearing system. Thus the nonlinear behavior analysis of the rotor-bearing
system can be studied time-sparingly. The results in the paper show the high efficiency of the two methods as well as the
abundant nonlinear phenomenon of the system, compared with the results obtained by the usual numerical solution of the Reynolds
equation. 相似文献
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基于稀薄效应的微气体径向轴承稳态性能 总被引:2,自引:0,他引:2
针对微气体轴承给出参考努森数的定义,根据空气不同温度时的黏度,得到参考努森数的分布范围;考虑气体稀薄效应,给出基于Burgdorfer一阶滑移速度边界的微气体径向轴承润滑Reynolds方程的修正形式; 采用有限差分法求解修正的Reynolds方程,得到不同参考努森数$Kn_0$, 轴承数以及轴颈偏心率情况下轴承的压力分布、无量纲承载能力及偏位角. 数值分析表明:随气体稀薄程度的增强,气体径向轴承的压力明显降低,无量纲承载力降低,而轴承偏位角增大. 当偏心率小于0.6时,轴承偏位角变化平缓,受$Kn_0$数的影响不明显. 当轴承数较小时,气体稀薄程度对轴承的无量纲承载力、偏位角影响较小. 相似文献
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基于二阶摄动法求解区间参数结构动力响应 总被引:3,自引:0,他引:3
在处理区间参数结构动力响应问题时,现有的分析方法大多局限于一阶区间分析方法. 如果参数的不确定量稍大,采用一阶区间分析方法对结构动力响应范围进行估计可能会失效,所以需要考虑二阶区间分析方法.但是采用基于区间运算的二阶区间分析方法得到的结果将会对动力响应范围过分高估. 为了克服以上缺点,首先基于二阶摄动法得到结构动力响应广义函数. 然后通过求解此动力响应函数的最大和最小值,将结构动力响应区间的问题转化为序列低维箱型约束下的二次规划问题. 最后采用DC 算法(di erence of convex functionsalgorithm) 对这些箱型约束下的二次规划问题进行求解. 这样可以在不引入过多计算量的情况下,避免了对动力响应范围的过分估计. 通过数值算例,将该方法和其他区间分析方法进行比较,验证了该方法的有效性与精确性. 相似文献
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A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy’s flow problem, the exact analytical solution for the case of Darcy’s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem. 相似文献