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131.
董明德 《应用数学和力学(英文版)》1985,6(3):213-218
For Poiseuille flow the Orr-Sommerfeld equation is solved exactly. Regular solutions are obtained, thereby eigenvalue equation can be analyzed analytically and explicitly. The bifurcation solutions will be discussed subsequently. 相似文献
132.
本文给出了Z-阶化有限维单李超代数具有非退化亦型的一个必要条件。应用这一结果,我们可以得到Cartan型李超代数X(n)与X(m,n,t)的Killing型是退化的。 相似文献
133.
Ping-Kwan Tam 《Applied Mathematics Letters》1999,12(8):207-64
A mean ergodic theorem for a matrix is first proved from which a mean ergodic theorem for affine operators on a vector space without any topological structure is obtained. 相似文献
134.
圆环形的压电材料器件在智能结构中得到了广泛的应用。本文推导了横观各向同性功能梯度压电材料圆环在内、外边界上给定位移和电势情况下的一般解。极化方向在圆环的半径方向,材料常数的梯度方向也设定在半径方向,并可表示为半径r的幂,本构关系为线性。然后推导了压电圆环外壁固定、接地,内壁沿垂向有一微小位移、电势分别为余弦分布和均匀分布的问题的精确解,并计算了该问题在这两种电势情况下产生的无量纲形式的径向和环向位移、电势、应力及电位移沿径向分布的数值结果。计算中考虑了不同的材料梯度,以及内壁的位移与电势的不同比例。 相似文献
135.
基于三维弹性理论,导出了带有压电层的圆柱形梯度壳的动力学方程以及相应的边界条件,用幂级数展开法得到了求解该圆柱形梯度壳自由振动的三维精确公式.通过实例模型求解了该壳体的自由振动的固有频率;分析了不同电学边界条件对壳体的振动频率的影响。结果可评估各种近似理论解和数值解的正确性。 相似文献
136.
137.
In this paper, the effective pyroelectric coefficient
and polarization offset of
the compositionally step-like graded multilayer ferroelectric structures
have been studied by use of the first-principles approach.
It is exhibited that the dielectric gradient has a nontrivial influence
on the effective pyroelectric coefficient, but has a little influence
on the polarization offset; and the polarization gradient
plays an important role in the abnormal hysteresis loop phenomenon
of the compositionally step-like graded ferroelectric structures.
Moreover, the origin of the polarization offset is explored,
which can be attributed to the polarization gradient
in the compositionally step-like graded structure. 相似文献
138.
The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate. 相似文献
139.
By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material (FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one. 相似文献
140.
基于一种新的各向异性修正偶应力理论,建立了碳纳米管增强复合材料功能梯度板的自由振动模型。该模型能够描述尺度效应,且仅包含一个尺度参数。基于一阶剪切变形理论和哈密顿原理推演了板的运动微分方程,并以四边简支板为例给出了自振频率的解析解。讨论了板的几何尺寸、碳纳米管体分比含量和分布方式等因素对板的自振频率的影响。结果表明,本文模型所预测的板的自振基频总是高于经典弹性理论的Mindlin板模型的预测结果,两者间的差异在板的几何尺寸接近尺度参数的值时非常明显,且会随着板的几何尺寸的增大而逐渐消失。 相似文献