Due to spatial variability of material property, Young＇ s modulus is assumed to be a stochastic process. This paper proposes a new method of calculating stochastic field, which includes the information of nodes and t...Due to spatial variability of material property, Young＇ s modulus is assumed to be a stochastic process. This paper proposes a new method of calculating stochastic field, which includes the information of nodes and the midpoint. The method is of high accuracy, and is easy to program. It is an improvement of the midpoint method of stochastic field. In the case of material properties, geometry parameters and applied loads are assumed to be stochastic, the vibration equation of a structure is transformed into a static problem using Newmark method. The Taylor expansion stochastic finite element method（TSFEM） is extended for the structure vibration analysis. An example is given and the calculated results are compared to validate the proposed methods.展开更多
基于改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对任意边界条件下环扇形板的面内自由振动特性进行计算分析,任意边界条件可采用沿各边界均匀分布的法向和切向线性弹簧来模拟。环扇形板的径向和切向位移函数被不变地表示...基于改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对任意边界条件下环扇形板的面内自由振动特性进行计算分析,任意边界条件可采用沿各边界均匀分布的法向和切向线性弹簧来模拟。环扇形板的径向和切向位移函数被不变地表示为改进傅里叶级数形式,并通过引入正弦函数项来克服弹性边界的不连续或跳跃现象。将位移函数的傅里叶展开系数看作广义坐标,并采用瑞利-里兹方法对其进行求解,得到一个关于未知傅里叶系数的标准特征值问题。通过求解标准特征值问题而简单地求解环扇形板面内振动的固有频率及其振型。通过不同边界条件下环扇形板模型结果与文献解及有限元法结果相对比来验证了本文方法的正确性及可靠性。展开更多
基金supported by the National Natural Science Foundation under Grant No.10202016
文摘Due to spatial variability of material property, Young＇ s modulus is assumed to be a stochastic process. This paper proposes a new method of calculating stochastic field, which includes the information of nodes and the midpoint. The method is of high accuracy, and is easy to program. It is an improvement of the midpoint method of stochastic field. In the case of material properties, geometry parameters and applied loads are assumed to be stochastic, the vibration equation of a structure is transformed into a static problem using Newmark method. The Taylor expansion stochastic finite element method（TSFEM） is extended for the structure vibration analysis. An example is given and the calculated results are compared to validate the proposed methods.
文摘基于改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对任意边界条件下环扇形板的面内自由振动特性进行计算分析,任意边界条件可采用沿各边界均匀分布的法向和切向线性弹簧来模拟。环扇形板的径向和切向位移函数被不变地表示为改进傅里叶级数形式,并通过引入正弦函数项来克服弹性边界的不连续或跳跃现象。将位移函数的傅里叶展开系数看作广义坐标,并采用瑞利-里兹方法对其进行求解,得到一个关于未知傅里叶系数的标准特征值问题。通过求解标准特征值问题而简单地求解环扇形板面内振动的固有频率及其振型。通过不同边界条件下环扇形板模型结果与文献解及有限元法结果相对比来验证了本文方法的正确性及可靠性。
