边缘简支等边三角形板平衡问题的影响函数

过去研究过边缘简支等边三角形板平衡问题的作者有:纳达埃、富诺斯基-克里格、孙、斯蒂芬生、赛斯等。其中多数作者仅讨论了均布载荷的问题,只有纳达埃及富诺斯基-克里格两位作者曾经论述集中载荷的问题。关于简支等边三角形板在其上任意一点有集中载荷作用时的平衡问题,纳达埃建议用反映法把三角形板反映成一块无限大板及十二类集中载荷網来解泱,富诺斯基-克里格建议用反映法把三角形板反映成一条无限长板及六串集中载荷末解决。可是他们建议的这些方法所需要的数学运算十分繁复,因此他们在自己的著作中都没有把这个问题的一般解答求出来。所以到目前为止,简支等边三角形板的平衡问题实际上是没有完全解决的。     

一种简支式光学矩形保护窗口强度的通用计算方法研究

光学窗口的强度分析是光电设备设计的重要依据,而现有文献中只提供材料泊松比为0.3的简化的计算公式,而针对不同泊松比的简支矩形板强度原始计算公式以复杂的级数形式表示不方便直接应用,为了方便设计者得到准确的强度理论分析结果,提供了一种简单的方法推导出适用于不同泊松比的简支式矩形保护窗口的强度简化计算公式,并验证了该方法推导...     

单层石墨烯片的非线性板模型

基于实验得到的非线性本构关系和板理论,本文建立了包含三次及五次非线性项的单层石墨烯片的板动力学模型.针对四边简支矩形板,使用Ritz法研究了在板中点作用集中力时的静力弯曲,以及边界均匀受力时的静力屈曲问题.结果显示,基于非线性本构关系的板模型能很好的描述单层石墨烯片的力学行为,而且模型中的五次非线性项对结构的弯曲变形有显著影响.     

功能梯度压电材料矩形板自由振动方程的精确解

从压电材料基本方程出发，针对沿厚度方向极化且材料常数沿极化方向梯度变化的矩形压电板，导出并求解了四边简支、接地条件下板的自由振动方程。     

水声作用下矩形弹性-粘弹性复合板的振动和散射声近场(Ⅱ)——矩形弹性-粘弹性复合板散射声近场研究

本文根据作者前一篇文章导出的复合粘-弹性薄板弯曲振动方程给出板振动简正模式的级数解,计算和分析了声波入射时,矩形复合粘弹性障板的振动;研究了密介质中,复合板简正模振动和其二次辐射场之间作用,以及不同模式振动之间由于辐射场引起的互耦合作用;数值计算了简支矩形板各号简正模的自耦合和互耦合系数随kl_1的变化关系,(r=l_2/l_1作为参变量,k为波数,l_1,l_2分别为板的两对边边长);并计算了复合障板在不同频率声波作用下各号模的复数振幅值;进而计算了不同频率声波作用下,板振动二次辐射声的近场声压分布。     

求解水中加肋板声辐射特性的虚拟声源法*

发展一种利用虚拟声源离散声场的方法求解加肋板在水中的声振耦合问题。由波叠加原理和单元体积速度匹配的原则,根据离散的结构单元满足的动力方程和结构与介质的交界相容性条件,确定虚拟声源强度,计算结构的声辐射功率。本文以简支矩形加肋板为例,在不获得结构表面振速和声压的情况下,计算了结构在水中的声辐射功率,并与解析方法计算的结果进行了比较,表明了该方法具有较好的计算精度。     

思考题（四）

思考题（四）一、在均匀磁场中有矩形线圈ａ．ｂ．ｃ．ｄ。在ａｂ和ｃｄ两边连接有一条可以滑动、且与两边接触良好的导线ＥＦ。若ＥＦ向有以速度ｖ滑动时如图１所示，则在矩形线圈上有没有电流产生，如果有电流，其方向如何？二、有两平行导线Ａ与Ｂ。导线Ａ中通以电流Ｉ...     

弯曲振动矩形板辐射阻抗的计算

本文推导了四边简支矩形板的辐射阻抗表达式, 利用高斯数值积分方法, 计算了其相对辐射阻抗的数值解. 由不同模态下相对辐射阻抗与频率以及不同长宽比对应的相对辐射阻抗与频率的关系可知, 在中低频段, 模态越低, 辐射阻抗越大, 也就意味着辐射声功率和同振质量越大; 对于一定面积和模态的矩形板, r (r=a/b, 长与宽之比)值越接近1, 即越接近正方形, 辐射阻和辐射抗越大. 本文的方法能对其他复杂边界条件下的、无振动解析解的矩形板的辐射阻抗数值量级大小提供一个参考, 也可由计算弯曲振动的阻抗自然地过渡到活塞振动阻抗的计算.     

结构振动模态之间耦合对预测结构声功率的影响

以简支矩形板为例,分析结构振动模态之间的耦合对声功率的影响。通过对声功率传递矩阵计算方法的改进,得到计算声功率传递矩阵对角元素和非对角元素(模态耦合项)的解析解,并进行数值计算和分析。所得解析解结果同前人发表的数值解非常吻合。     

基于Galerkin法研究应力波作用下复合材料板的动力学失稳

基于Kirchhoff薄板理论和Hamilton原理,考虑应力波效应,对含初始几何缺陷的三边简支、一边固支的复合材料板,建立了振动控制方程,得到了其屈曲临界荷载表达式。采用MATLAB编程进行数值计算,讨论了初始几何缺陷、初相位、铺层角度、屈曲模态阶数及铺层层数对板屈曲临界荷载的影响。结果表明:复合材料板的屈曲临界载荷随临界长度增大、铺设厚度减小、初始几何缺陷系数增大、振型函数初相位减小而减小。此外,复合材料板的各层铺层角度与荷载作用方向的夹角越小,屈曲临界载荷越大,当板的对称铺设层数达到7层时,临界荷载趋于稳定。     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

Self-assembled triangular and labyrinth buckling patterns of thin films on spherical substrates

We investigated the possibility of controlling thin film buckling patterns by varying the substrate curvature and the stress induced therein upon cooling. The numerical and experimental studies are based on a spherical Ag core/SiO(2) shell system. For Ag substrates with a relatively larger curvature, the dentlike triangular buckling pattern comes out when the film nominal stress exceeds a critical value. With increasing film stress and/or substrate radius, the labyrinthlike buckling pattern takes over. Both the buckling wavelength and the critical stress increase with the substrate radius.     

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

We present the application of differential quadrature(DQ) method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.     

Assessment of sandwich models for the prediction of sound transmission loss in unidirectional sandwich panels

The consistent higher-order approach and the two-parameter foundation formulation are used for the derivation of sound transmission loss in symmetric unidirectional (infinitely wide) sandwich panels with isotropic face sheets. In both models, transmission loss is calculated using decoupled equations representing symmetric and anti-symmetric motions of a sandwich panel. The closed-form expressions for impedances and transmission coefficient of a symmetric sandwich panel with an isotropic core are derived for the two-parameter foundation model. A comparison between the numerical predictions based on the two sandwich models and available experimental data shows that the consistent higher-order formulation can be used to predict the transmission loss in symmetric sandwich panels with both honeycomb and isotropic cores. For prediction of transmission loss of symmetric sandwich panels with an isotropic core, the two-parameter foundation model is more convenient, while the consistent higher-order approach is more accurate.     

Buckling of a compressed elastic membrane: a simple model

The buckling of a folded membrane submitted to a bi-axial compression is studied in the framework of the continuum non-linear elasticity theory. We show that the formation of the fold patterning can be quantitatively well described with a simple non-linear model. As a matter of fact, with this model, we recover the experimental phase diagram of a secondary buckling instability with a very good precision. In addition, depending on the anisotropy of the applied compressive stress, we find that the buckling coarsening dynamics can be described as a 1D spinodal decomposition (for a uni-axial stress) or as a 2D XY model (for an isotropic bi-axial stress) with an irrotational non-scalar order parameter. For an isotropic bi-axial stress, we indeed recover the famous coarsening exponent: n=1/4. This exponent has to be confirmed experimentally.     

Anisotropic colloids through non-trivial buckling

We present a study on buckling of colloidal particles, including experimental, theoretical and numerical developments. Oil-filled thin shells prepared by emulsion templating show buckling in mixtures of water and ethanol, due to dissolution of the core in the external medium. This leads to conformations with a single depression, either axisymmetric or polygonal depending on the geometrical features of the shells. These conformations could be theoretically and/or numerically reproduced in a model of homogeneous spherical thin shells with bending and stretching elasticity, submitted to an isotropic external pressure.     

Buckling instability of circular double-layered graphene sheets

In this paper, we study the buckling properties of circular double-layered graphene sheets (DLGSs), using plate theory. The two graphene layers are modeled as two individual sheets whose interactions are determined by the Lennard-Jones potential of the carbon-carbon bond. An analytical solution of coupled governing equations is proposed for predicting the buckling properties of circular DLGSs. Using the present theoretical approach, the influences of boundary conditions, plate sizes, and buckling-mode shapes on the buckling behaviors are investigated in detail. The buckling stability is significantly affected by the buckling-mode shapes. As a result of van der Waals interactions, the buckling stress of circular DLGSs is much larger for the anti-phase mode than for the in-phase mode.     

Vibration and buckling of tapered rectangular plates with two opposite edges simply supported and the other two edges elastically restrained against rotation

The paper describes an application of a method of power series expansions to the free vibration and buckling problems of isotropic rectangular plates with linear thickness variation. The plates are simply supported on the two opposite edges parallel to the direction of thickness variation and the other two edges are elastically restrained against rotation. By the present method, one can solve exactly the governing equation with variable coefficients. The choice of the origin for the power series expansion plays an important role in obtaining rapid convergence and accurate results. The effects of thickness variation and rotational stiffness of the elastic spring on the eigenvalues and mode shapes are shown numerically and graphically on the basis of new results obtained by the present exact analysis.     

Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.