三合板梁弯曲问题

一.引言 三合板的弯曲问题在航空工业上有广泛的应用。近十年来出现了不少关于这方面的理论,但是这些理论都是以線性问题观点来处理的,在实际结果与理论出入太大时,一般都认为是材料的品质和结构的缺点的问题。本文的理论分析了非線性的因素,无论是線性及由線性扩展到非線性范围;而且根据本文的理论结果得到了很好的实验证明。     

三合板的一般弹性理论

一.引言 本文所指之三合板是一种轻质板材,在航空工业上近年来有广泛的应用。板由三层材料构成:外层为二硬薄钣(金属薄钣),夹心为较轻软之材料(如泡状醋酸赛璐珞、软木、或蜂巢状金属材料)。前者称为表钣,后者称为夹心,表钣与夹心胶合成一综合板。三合板之形变与应力之计算在十多年来曾引起力学家与工     

矩形晶格双折射多孔光纤宽带稳定拍长的优化设计

在矩形晶格多孔光纤的基础上,通过加入一对大直径圆孔,并进一步优化结构参数可以得到宽带稳定的双折射拍长。采用有限差分波束传播法计算了多孔光纤的模式双折射特性,分析了不同参数变化对模式双折射的影响。计算表明,这两种非对称结构分别具有正值和负值双折射,两者相互作用能够控制模式双折射随波长的变化斜率,在一定的波长范围内使模式双折射与波长呈现等比例的线性变化关系,从而得到基本不随波长变化的双折射拍长。通过优化结构参数,分别在1310 nm和1550 nm波长窗口获得了中心拍长为10 mm的平坦拍长曲线,相对带宽达到12%以上,这种光纤非常适合制作集成于全光纤大电流传感器之中的宽带光纤波片。     

固定边矩形板的弯曲问题

The problem of bending of orthotropic rectangular plates with clamped edges on elastic foundation may be reduced to the following differential equation and boundary conditions (?⁴w)/(?x⁴)+2λ(?⁴w)/(?x²?y²)+(?⁴w)/(?y⁴)+kw=q/D. w=0, (?w)/(?x)=0 at x=±a, w=0, (?w)/(?y)=0, at y=±b. In the case of isotropic plates, λ = 1. In this paper a perturbation method is proposed for the solution of this problem fay expanding w in power series of λ: w=w₀+w₁λ+w₂λ²+……. It is proved that this series is convergent when -1 ≤λ≤1.     

沟渠内杨木三合板架空燃烧的火灾行为的研究

建立了缩尺寸沟渠火灾试验模型,测量了沟渠以及平台入口附近的温度分布,研究了沟渠内杨木三合板架空燃烧的位置和沟渠的倾斜角度对火蔓延行为的影响,分析了火焰传播特征和火蔓延速率.试验结果表明:在沟渠效应和烟囱效应的综合作用下,火焰先从杨木三合板与沟渠底板之间的狭长空间传播到沟渠顶部,在入口处形成喷射状火焰;狭长空间内的温度先...     

矩形薄膜受迫横振动问题的求解及可视化

膜的横振动分析在乐器膜、耳膜以及植物细胞膜中有着广泛的应用价值.相比自由振动,受迫膜振动问题的研究更符合应用实际.本文采用数学物理定解问题的傅里叶级数法与冲量定理法,对四周固定的均匀矩形薄膜振动问题进行了研究,得到了此类问题在受迫振动下的解析解,并对其振动状态进行了可视化分析.研究发现：一维弦振动解法同样可为二维有界膜振动问题提供简便的求解途径,且膜振动将呈现更加丰富的特点.本文的二维非齐次振动问题的冲量定理解法还可推广到二维有源(汇)输运问题中去.     

稳定热传导问题的电比拟方法

根据稳定热传导问题与稳恒电流问题的相似性 ,导出了在几何形状及边界条件相似的条件下 ,热流强度Q与电流强度I的对应关系     

稳定热传导问题的电比拟方法

对于几何形状比较复杂,或几何形状虽然简单,但边界条件比较复杂的物体的稳定导热问题,一般的分析解法往往无能为力,而需采用数值解法或实验解法.无论是用数值解法还是实验解法,均是一件费时费力的事.利用热电比拟方法可以有效地解决这一问题.     

有分散热源时矩形区域内熔化问题的数值解

为了探索在电子设备冷却中应用固液相变冷却的可能性，本文用数值方法求解了一侧垂直壁上有三个分散热源、其余三个面均绝热时矩形区域内的二维熔化传热问题，对固液界面形状以及加热壁面温度沿高度方向的变化规律进行了讨论。     

矩形板声辐射预测中速度采样问题的研究

为减少系统的复杂度和成本,基于无限大障板上振动矩形板模型,研究了声辐射预测中板表面速度采样问题。从理论上分析了影响速度采样间隔选取的因素,得到了低频时采样间隔由振动模态决定,高频时采样间隔由振动频率决定的结论。数值结果显示临界频率应满足k_csinθ=const(k_c=2πF_c/c,F_c为临界频率,θ为观察点倾斜角,c为声波波速)的规律,并且通过数值模拟和实验验证了该规律的适用性。     

FORCED AND FREE VIBRATIONS OF RECTANGULAR SANDWICH PLATES WITH PARAMETRIC STIFFNESS MODULATION

An active control of the resonant vibrations of a rectangular sandwich plate performed by the parametric stiffness modulation is analyzed. The controlled vibrations are those of the dominantly flexural type excited by the transverse force acting at the first resonant frequency of dominantly flexural vibrations. The stiffness modulation is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. The method of direct partition of motions is used that predicts an existence of the modal interaction between these two modes of vibrations due to the parametric stiffness modulation. It is shown that such a parametric control can provide a significant shift of the first eigenfrequency of a controlled plate (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled plate. Heavy fluid loading conditions are accounted for as well as the energy dissipation in the material of a plate. It is demonstrated that although heavy fluid loading reduces resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases. Dynamics of an elementary two-degree-of-freedom model mechanical system is considered to illustrate the mechanism of modal interaction, which is involved in the suggested way of an active control of vibrations of sandwich plates.     

EXACT BUCKLING AND VIBRATION SOLUTIONS FOR STEPPED RECTANGULAR PLATES

This paper is concerned with the determination of exact buckling loads and vibration frequencies of multi-stepped rectangular plates based on the classical thin (Kirchhoff) plate theory. The plate is assumed to have two opposite edges simply supported while the other two edges can take any combination of free, simply supported and clamped conditions. The proposed analytical method for solution involves the Levy method and the state-space technique. By using this analytical method, exact buckling and vibration solutions are obtained for rectangular plates having one- and two-step thickness variations. These exact solutions are extremely useful as benchmark values for researchers developing numerical techniques and software for analyzing non-uniform thickness plates.     

DSC ANALYSIS OF RECTANGULAR PLATES WITH NON-UNIFORM BOUNDARY CONDITIONS

This paper introduces the discrete singular convolution (DSC) for the vibration analysis of rectangular plates with non-uniform and combined boundary conditions. A systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach. The validity of the DSC approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported, clamped and transversely supported (with non-uniform elastic rotational restraint) edges. The present results are in excellent agreement with those in the literature.     

GEOMETRICALLY NON-LINEAR FREE VIBRATION OF FULLY CLAMPED SYMMETRICALLY LAMINATED RECTANGULAR COMPOSITE PLATES

The geometrically non-linear free vibration of thin composite laminated plates is investigated by using a theoretical model based on Hamilton's principle and spectral analysis previously applied to obtain the non-linear mode shapes and resonance frequencies of thin straight structures, such as beams, plates and shells (Benamar et al. 1991Journal of Sound and Vibration149 , 179-195; 1993, 164, 295-316; 1990 Proceedings of the Fourth International Conference on Recent Advances in Structural Dynamics, Southampton; Moussaoui et al. 2000 Journal of Sound and Vibration232, 917-943 [1-4]). The von Kármán non-linear strain-displacement relationships have been employed. In the formulation, the transverse displacement W of the plate mid-plane has been taken into account and the in-plane displacements U and V have been neglected in the non-linear strain energy expressions. This assumption, quite often made in the literature has been adopted in reference [2] and (El Kadiri et al. 1999 Journal of Sound and Vibration228, 333-358 [5]), in the isotropic case and has been mentioned here because the results obtained have been found to be in very good agreement with those based on the hierarchical finite element method (HFEM). In a previous study, it was assumed, based on the analogy with the isotropic case, that the fundamental carbon fibre reinforced plastic (CFRP) plate non-linear mode shape could be well estimated, by using nine plate functions, obtained as products of clamped-clamped beam functions in the x and y directions, symmetric in both the length U001and width directions [3]. In the present work, a convergence study has been performed and has shown that, although such an assumption may yield a good estimate for the non-linear resonance frequency, 18 plate functions should be taken into account instead of nine in the first non-linear mode shape and associated bending stress patterns calculations. This allows the anisotropy induced by the fibre orientations to be taken into account. Results are given for the fundamental mode of fully clamped CFRP rectangular plates, for various plate aspect ratios and vibration amplitudes. The non-linear mode shows a higher bending stress near the clamps at large deflection, compared with that predicted by linear theory. Some experimental measurements are presented which are in good qualitative agreement with the theory.     

矩形柱电容器电容的简单计算方法

用简单方法计算矩形柱电容器的电容 ,并指出文献 [1 ]中的“电容特性普遍公式”实质上就是无限多个平行板电容器电容的串联公式 .     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES: PART II—FIRST AND SECOND NON-LINEAR MODE SHAPES OF FULLY CLAMPED RECTANGULAR PLATES

In a previous series of papers, a semi-analytical model based on Hamilton's principle and spectral analysis has been developed for geometrically non-linear free vibrations occurring at large displacement amplitudes of clamped-clamped beams and fully clamped rectangular homogeneous and composite plates. In Part I of this series of papers, concerned with geometrically non-linear free and forced vibrations of various beams, a practical simple “multi-mode theory”, based on the linearization of the non-linear algebraic equations, written in the modal basis, in the neighbourhood of each resonance has been developed. Simple explicit formulae, ready and easy to use for analytical or engineering purposes have been derived, which allows direct calculation of the basic function contributions to the first three non-linear mode shapes of the beams considered. Also, various possible truncations of the series expansion defining the first non-linear mode shape have been considered and compared with the complete solution, which showed that an increasing number of basic functions has to be used, corresponding to increasingly sized intervals of vibration amplitudes; starting from use of only one function, i.e., the first linear mode shape, corresponding to very small amplitudes, for which the linear theory is still valid, and ending by the complete series, involving six functions, corresponding to maximum vibration amplitudes at the beam middle point up to once the beam thickness. For higher amplitudes, a complementary second formulation has been developed, leading to reproduction of the known results via the solution of reduced linear systems of five equations and five unknowns. The purpose of this paper is to extend and adapt the approach described above to the geometrically non-linear free vibration of fully clamped rectangular plates in order to allow direct and easy calculation of the first, second and higher non-linear fully clamped rectangular plate mode shapes, with their associated non-linear frequencies and non-linear bending stress patterns. Also, numerical results corresponding to the first and second non-linear modes shapes of fully clamped rectangular plates with an aspect ratio α=0·6 are presented. Data concerning the higher non-linear modes, the aspect ratio effect, and the forced vibration case will be presented later.