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Search Results: 1 - 10 of 65845 matches for " 滕兆春 "
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Winkler-Pasternak弹性地基梁自由振动的二维弹性分析 Two-dimensional elastic analysis for free vibration of beams set on winkler-pasternak elastic foundations

蒲育,
- , 2016, DOI: 10.7511/jslx201602007
Abstract: 基于二维线弹性理论,应用Hamilton原理,获得Winkler-Pasternak弹性地基梁自由振动的控制微分方程,应用微分求积法(DQM)数值研究了梁自由振动的量纲频率特性。计算结果与已有的结果(Bernoulli-Euler梁和Timoshenko梁)比较表明,本文的分析方法对弹性地基长梁和短梁自由振动的研究都有效。最后考虑了几何参数对梁频率的影响,以及不同边界条件下地基系数对频率的影响和收敛性。
Based on the two-dimension linear elasticity theory and applied the Hamilton's principle,the governing differential equations of free vibration for beam set on Winkler-Pasternak elastic foundation are derived.Using differential quadrature method (DQM),the free vibration dimensionless frequencies of beams are investigated numerically.With application of DQM in this paper,it illustrated that the method was validated and accurate for Bernoulli-Euler beams as well as for Timoshenko beams by comparison of previously reported results.Finally,the effect of the geometrical parameter on the non-dimensional frequency parameter of the beams,the influence and the convergence for dimensionless frequency owing to elastic coefficients of foundation under different boundary conditions are considered.
加热压电纤维复合材料圆板的横向自由振动 Transverse free vibration of heated piezoelectric fibre composite materials circular plates
Transverse free vibration of heated piezoelectric fibre composite materials circular plates

王硕,
- , 2017, DOI: 10.7511/jslx201703004
Abstract: 基于经典薄板理论和极正交各向异性材料的本构理论,建立了加热压电纤维复合材料圆板的线性振动控制微分方程。采用打靶法分别获得了加热压电纤维复合材料圆板在周边固支和简支情况下,量纲固有频率随温度和电场强度变化的关系曲线,并分析了压电纤维体积分数、刚度参数、电场强度和温度变化对压电纤维复合材料圆板量纲固有频率的影响。结果表明,一定体积分数或者电场强度下,压电纤维复合材料圆板的量纲固有频率都随温度的升高而单调下降;同一温度下,刚度参数越小,量纲固有频率越低;电场强度越大,量纲固有频率越高。
Based on the classical thin plate theory and the constitutive theory for orthotropic materials,the linear differential equations of vibration for circular plate of heated piezoelectric fibre composite materials are derived.By using a shooting method,the relationship curves of the dimensionless natural frequencies of the heated piezoelectric fibre composite circular plate versus temperature rise and electric field strength change are presented with clamped and simply supported boundary conditions.And the influence of the volume fraction of piezoelectric fibre,stiffness parameters,electric field strength and temperature rise on the dimensionless natural frequencies of piezoelectric fibre composite materials circular plate is also discussed.The results show that the dimensionless natural frequency of the piezoelectric fibre composite material circular plate monotonically decreases with the temperature.It decreases with decreasing the stiffness parameters,but increases with increasing electric field strength at certain fixed values of temperature.
非均匀Winkler弹性地基上变厚度矩形板自由振动的DTM求解 Free vibration analysis for rectangular plates with variable thickness resting on a non-uniform Winkler elastic foundation by DTM
Free vibration analysis for rectangular plates with variable thickness resting on a non-uniform Winkler elastic foundation by DTM

,衡亚洲,刘露
- , 2018, DOI: 10.7511/jslx20170217002
Abstract: 针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法(DTM),研究其量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。
For free vibration problem of rectangular plates with variable thickness resting on a non-uniform foundation and by an effective solving numerical method called differential transformation method (DTM),the dimensionless natural frequency characteristics are investigated.Two opposite edges of plates are assumed to be simply supported and other two edges can be changed into simply supported,camped or free boundary conditions arbitrarily.By using DTM,dimensionless normalized governing differential equation of rectangular plates with variable thickness resting on a non-uniform Winkler elastic foundation and boundary conditions are transformed to the equivalent algebraic equations,which can derive equations of dimensionless natural frequency.The example results are back to cases for uniform Winkler rectangular plates and rectangular plates with variable thickness,which are compared with different methods in present literature.The result shows that DTM have very higher accuracy and stronger applicability.Finally,the influence of the varied foundation parameter,the varied thickness parameter and the aspect ratio on dimensionless natural frequencies are analyzed for different boundary conditions and deriving the first six mode shapes for CSCS plate with variable thickness resting on a non-uniform Winkler elastic foundations.
热载荷作用下嵌入SMA丝复合材料梁的横向自由振动
,李世荣,付小华
工程力学 , 2005,
Abstract: 基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系.其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型.最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线.数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法.
FGM圆环板面内自由振动的DQM求解
,蒲育,房晓林
北京理工大学学报 , 2014,
Abstract: 基于二维线弹性理论,假定材料物性沿圆环板的径向按照幂律梯度分布,建立了FGM薄圆环板面内自由振动的运动微分方程,采用微分求积法数值研究了FGM圆环板面内自由振动的量纲一频率特性,并与各向同性材料圆环板面内自由振动的量纲一频率进行了比较,说明本文的分析方法有效.结果表明,不同边界条件,FGM梯度指标以及FGM圆环板内、外半径比对量纲一频率均有影响,其计算结果和分析方法可供设计参考.
基于微分变分不等式的再制造闭环供应链网络动态模型
孙嘉轶,,
系统工程理论与实践 , 2015,
Abstract: ?针对一段时间内具有再制造的闭环供应链网络的博弈均衡状态问题,首先利用博弈理论,构建了具有多制造商(再制造商)及多零售商(回收商)的再制造闭环供应链网络动态模型,制造商(再制造商)及零售商(回收商)之间从事微分nash博弈.然后,利用微分变分不等式的方法得到了制造商(再制造商),零售商(回收商)及整个闭环供应链网络的均衡条件.进而,在正则条件下分析了闭环供应链网络动态模型解的存在性条件.仿真算例验证了模型的合理性和有效性.
基于回收价格与销售数量的再制造闭环供应链渠道选择模型
孙嘉轶,,
系统工程理论与实践 , 2013,
Abstract: ?针对现有刻画闭环供应链回收数量函数的不足,构建了与销售数量和回收价格均相关的回收数量函数.分析了三种情形下(两个零售商参与回收,一个零售商参与回收和制造商回收)供应链中成员的最优决策问题.研究表明:新品与再制品的成本差越大,制造商越倾向于选择两个零售商进行回收;然而,当新品与再制品的成本差较小时,选择一个零售商回收或制造商自行回收,会受到市场规模大小,吸引系数和游移系数的影响;并说明了消费者环保意识的提高对制造商、消费者和社会环境都是有利的,为制造商选择回收渠道提供了决策依据.
变刚度Winkler地基上受压非均质矩形板的自由振动与屈曲特性
,衡亚洲,,,,
- , 2019,
Abstract: 基于经典薄板理论,利用Hamilton原理建立变刚度Winkler地基上受压非均质矩形板自由振动与屈曲问题的控制微分方程并进行无量纲化。通过一种半解析方法?微分变换法(DTM)研究其无量纲固有频率和屈曲临界载荷特性。首先采用DTM将其无量纲控制微分方程及边界条件变换为等价的代数方程,得到含有频率和屈曲载荷的特征方程。再将该问题退化为面内变刚度矩形板情形,其DTM解与精确解进行对比,结果表明DTM具有非常高的精度和很强的适用性。最后计算出在不同边界条件下屈曲临界载荷并分析地基刚度变化参数、弹性模量变化参数、密度变化参数、面内载荷和长宽比对矩形板无量纲固有频率的影响,给出了不同边界条件下变刚度Winkler地基上受压非均质矩形板的前三阶振型。
Abstract:Based on the classical thin plate theory, the governing differential equation of free vibration and buckling of a compressed non-homogeneous rectangular plate on Winkler foundation with variable stiffness was established by using Hamilton’s principle, and then its dimensionless form was obtained.The characteristics of the plate’s dimensionless natural frequencies and buckling critical loads were studied with a semi-analytical method called the differential transformation method (DTM).DTM was used to convert dimensionless governing differential equation and boundary conditions into equivalent algebraic equations, and derive characteristic equations of frequencies and buckling loads.Then, the problem was degenerated into the case of an in-plane variable stiffness rectangular plate, and its DTM solution was compared with the analytical solution.The results showed that DTM have very higher accuracy and stronger applicability.Finally, the buckling critical loads were calculated under different boundary conditions, and the effects of foundation stiffness parameters, elastic modulus parameters, density parameter, in-plane loads and length-width ratio on the plate’s dimensionless natural frequencies were analyzed.The first three modal shapes of the compressed non-homogeneous rectangular plate on Winkler foundations with variable stiffness were deduced under different boundary conditions.
各种典型边界FGM矩形板面内自由振动的二维弹性分析
Two-Dimensional Elasticity Solutions for In-Plane Free Vibration of FGM Rectangular Plates under Different Boundary Conditions

蒲育,
PU Yu
, TENG Zhaochun

- , 2016, DOI: 10.3969/j.issn.0258-2724.2016.06.020
Abstract: 为获得功能梯度材料(FGM)矩形板面内自由振动的动力学响应,基于二维线弹性理论建立了功能梯度材料矩形板面内自由振动的控制微分方程.采用微分求积法(DQM)数值研究了9种典型边界下FGM矩形板面内自由振动的频率特性,分析了边界条件、长宽比及梯度指数对自振频率的影响.分析结果表明:通过设置梯度指数为0,将FGM矩形板退化为各向同性矩形板,与已有各向同性矩形板的文献结果进行比较,表明了DQM的适用性和精确性;9种边界下长宽比对FGM矩形板基频的影响不同,基频随长宽比的增大而增大的板分别为:C-C-C-C板、SS2-C-SS2-C板、C-C-C-F板、SS1-C-SS1-C板、C-C-F-F板和SS1-SS1-SS2-SS2板;基频随长宽比的增大而减小的板分别为:F-F-F-F板与C-F-C-F板;SS1-SS1-SS1-SS1板发生剪切自锁现象,基频随长宽比的增大而基本保持不变;基频随梯度指数的增大而快速减小,梯度指数p >10时,基频变化不再明显.
: In order to obtain the dynamic responses on in-plane free vibration of functionally graded material (FGM) rectangular plates, based on the two-dimensional linear elasticity theory, the governing partial differential equations for the in-plane free vibration of FGM rectangular plates were derived. Using differential quadrature method (DQM), the frequency characteristics for in-plane free vibration of FGM rectangular plates under 9 different boundary conditions were investigated. The effects of boundary conditions, geometrical parameters and material gradient indexes on the dimensionless frequencies of the FGM rectangular plates were analyzed. The material gradient index was set as zero to take FGM rectangular plates as isotropic rectangular plates. Then, the applicability and accuracy of the DQM were demonstrated by comparing the in-plane free vibration of the obtained isotropic rectangular plates with those in literature. The effect of the length-width ratio on the fundamental frequency of the FGM rectangular plates varies under different boundary conditions. The fundamental frequency increases with the length-width ratios for the plates C-C-C-C, SS2-C-SS2-C, C-C-C-F, SS1-C-SS1-C, C-C-F-F and SS1-SS1-SS2-SS2, and decreases with the increase of the length-width ratios for the plates F-F-F-F and C-F-C-F, but has no significant changes for SS1-SS1-SS1-SS1 plate because of shear locking. The fundamental frequency decreases rapidly with the increase of material gradient indexes, but it has no obvious change when the material gradient index p is more than 10
FGM环扇形板的面内自由振动分析 In-plane free vibration analysis of FGM annular sector plates
In-plane free vibration analysis of FGM annular sector plates

,朱亚文,蒲育
- , 2018, DOI: 10.7511/jslx20170703001
Abstract: 假定功能梯度材料(FGM)的物性参数沿环扇形板径向按照幂律梯度变化,基于平面线弹性理论,建立了FGM环扇形板面内自由振动的运动控制微分方程。采用二维微分求积法(DQM)对FGM环扇形板面内自由振动的量纲运动控制微分方程进行离散,数值求解了不同边界条件下FGM环扇形板面内自由振动的量纲固有频率,同时也给出了FGM环扇形板扇形角为π/4时有限元商用软件ANSYS的部分计算结果,验证了本文方法的正确性。结果表明,在相应边界条件下,FGM环扇形板的梯度指标、内外半径比以及扇形角对量纲固有频率均有影响,其计算结果和分析方法可供设计和研究参考。
Assuming that the material physical parameters of the annular sector plates follows a power law distribution along the radius and based on plane linear theory of elasticity,the governing differential equations of motion for in-plane free vibration of a functionally graded material (FGM) annular sector plate are established.Then using two-dimensional differential quadrature method (DQM),the dimensionless governing differential equations of motion of in-plane free vibration of FGM annular sector plates are discretized and the dimensionless natural frequencies of the in-plane free vibration of FGM annular sector plates under the corresponding boundary conditions are solved numerically.Some results of dimensionless natural frequencies of FGM annular sector plate with π/4 angle of the sector are computed by the finite element commercial software ANSYS.They show that the current method is effective and accurate.When the plates are under the corresponding boundary conditions,the results indicate that the gradient index of FGM,the internal and external radius ratio and the angle of the sector all affect the dimensionless natural frequencies,the calculation results and the analysis method can be used in design and research.
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