球面扁薄圆壳的跳跃问题

一.引言 扁薄壳和波纹薄板在加载荷或去截荷过程中所产生的跳跃现象,是比较容易观察到的。可是这方面的理论问题却直到最近才有人研究。很显明的,跳跃问题是一个非缐性的问题,因此它的解决必须求诸非線性的理论。在1945年,В.и.费奥道斯也夫应用巴蒂夫提出的非線性弹性力学中的伽遼金方法,研究了波纹薄圆板在均布载荷作用下的大挠度问题,并讨论了可能产     

Frohlich极化子的能带非抛物性效应理论

本文对Frohlich极化子的能带非抛物性效应进行了理论研究。所使用的模型是用一个简化的双能带近似。我们发现能带非抛物性对极化子束缚能和有效质量重整化会产生影响。与早期的理论相对照,我们考虑了能带非抛物性,并附加了极化子效应。本文的理论与实验结果符合。     

泥沙在静水中的沉淀运动——(Ⅱ)沉速在时间过程里的变化

一.引言 在工程上一般碰到泥沙在水中运动的时侯,都应用斯托克斯公式来计算泥沙所受到的阻力。但是斯托克斯公式是一个圆球在无穷的粘性流体中作匀速运动时的阻力定律,对于很多砂子同时下沉作非匀速运动时,斯托克斯公式显然不能应用。本文根据了流体力学在小瑞诺数情况下的理论来讨论比较稀薄的泥沙在静水中的非匀速的沉淀问题。     

Fr?hlich极化子的能带非抛物性效应理论

本文对Fr?hlich极化子的能带非抛物性效应进行了理论研究。所使用的模型是用一个简化的双能带近似。我们发现能带非抛物性对极化子束缚能和有效质量重整化会产生影响。与早期的理论相对照,我们考虑了能带非抛物性,并附加了极化子效应。本文的理论与实验结果符合。 关键词：     

Rosenberg问题的对称性与守恒量

Rosenberg问题是一个典型而不太复杂的非完整系统问题.本文利用非完整系统的Noether对称性理论来求这个非完整力学问题的守恒量,进而得到问题的最终解.     

矩形三合板的稳定问题

一.引言 矩形三合板的稳定问题为高速飞机结构设针中经常遇到的实验问题,本文根据[1]所得的一般方程配合边界条件以求解。文中处理在一个方向受有均匀分布载荷、四边简支的矩形板及两边简支两边自由的矩形板,在形变初起的情况下若仅求临界载荷以供设计用则方程可以考虑作为線性,因之可以藉双三角函     

關於“透鏡光心”的討論

在講到透鏡成像的作圖法前,總要提到“光心”一詞,由於教師們的忽略,常常容易造成学生的某些誤解。当進行到这里的時候,講解上常有出入,譬如,有的講解為:“通过光心的光線不起折射作用”;有的講解为:“通过光心的光線沿直線進行”;还有的講解为:“光心是在透鏡的中心”;“光心是在透鏡的內部”等等。其实对光心的这些解释是不恰当的。在人民教育出版社出版的高級中学課本物理学第三册中,对光心的叙述可算相当簡明,其叙述為:“任何一個透鏡的主軸上都有一個特殊的點。凡是通过这個點的光線,都不因透鏡的存在而改变方向。这個特殊的点叫作光     

大气中光的传播——一种综合研究方法

要描述光波在低能见度天气条件下通过地球大气层传播的特性是非常困难的,在本质上需要解决多路散射的一般问题。本文叙述了利用综合研究法对光波通过混浊大气层传播的研究结果,在这种综合研究方法中,实验用来确定传播效应的大小并提供能简化理论近似式的经验关系式。具体来说,本文报告了多路展宽、角度展宽、光束扩展的直视通路激光测量结果和角度展宽、功率传输与距离关系的非相干光源测量结果。从这些数据导出了两种关于传播的近似理论,即多路向前散射理论和强多路散射理论。     

磁力線铁屑的固定

高三电學磁場一章的教学中,磁力線的演示頗为不便。其中磁体磁力線的敲製本身並不困难,但課堂中傳現時,三、四傳就散乱了,又要重新敲过。最好能把铁屑固定下來。並預先制好,經常可用。我們用这样的方法來固定磁体的磁力線:在光滑的木板上撒上铁屑,製成磁力線圖形。然後在白紙上塗以白色磁漆一薄层,覆在已做好的磁力線的铁屑上,能將铁屑黏起,陰乾后铁屑就固定了。在上述基礎上,我們亦研究了通电线蟠磁     

高中电流定律的教学(续)

2.電流的本性在進而講解電流的本性就是電荷的定向運動時,我們的方案是從考查引入電場的導線來開始講解的,在這里强調指出,導線中的電荷的移動是在電場力的作用下進行的,這個導線中的電場力一直存在到導線兩端間的電勢差消失時為止。實際上,在導線中電勢趨於一致是瞬時的事情,但如果我們用兩個靜電計,事先使其中的一個帶電,在它们上面分别固定一個小球,並用半導體來連通小球(圖5),那我們     

Flexural effects of sandwich beam with a plate insert under in-plane bending

The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study. An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stress.The shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces. The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure. The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads. The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert.     

Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature.     

Structural synthesis of sandwich beams with outer layers of box-section

It is proved by model measurements that, for sandwich beams constructed from two rectangular tubes and a damping layer glued between them, the following calculation methods can be applied. Static bending and shear stresses as well as deflections of simply supported beams may be calculated by Allen's formulae for sandwich beams with flexurally stiff faces. The first eigenfrequency and the loss factor can be determined by using the diagrams given in reference [1]. For the loss factors Ungar's formula gives a suitable approximation. A minimum cost design procedure is presented for a sandwich beam with constant cross-section. The unknown dimensions of the cross-section are determined which satisfy the design constraints and minimize the material costs. In a numerical example, constraints relating to the maximal dynamic stresses and deflection as well as local buckling of plate elements are considered. In the optimization the backtrack combinatorial discrete programming method is applied. A numerical comparison shows that the material costs of a sandwich beam are lower than those of a homogeneous box one.     

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.     

Bending and springback theory of metal-polymer sandwich laminates

In this report an analysis is made of the behavior of sandwich beams in which the core polymer is laminated on both sides with surface metal sheets, each of which has a different thickness and mechanical properties when they are loaded with a uniform bending moment which is then released resulting in springback of the bent sandwich beam. It is assumed that the polymer behaves elastically because the bending strain in the core is small and its elastic limit is much larger than that of metals. Sandwich beams have various elastoplstic stess distributions when bent depending on the mutual relationships between their dimensions, the mechanical moduli, and the applied bending moment. Further, residual curvatures, shifting position of neutral axis, and residual stress distributions in sandwich beams variously elastoplastically stressed initially on the decrease of applied bending moment are analyzed.     

A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

The semi-analytical approach to the non-linear dynamic response of beams based on multimode analysis has been presented in Part I of this series of papers (Azrar et al., 1999 Journal of Sound and Vibration224, 183-207 [1]). The mathematical formulation of the problem and single mode analysis have been studied. The objective of this paper is to take advantage of applying this semi-analytical approach to the large amplitude forced vibrations of beams. Various types of excitation forces such as harmonic distributed and concentrated loads are considered. The governing equation of motion is obtained and can be considered as a multi-dimensional form of the Duffing equation. Using the harmonic balance method, the equation of motion is converted into non-linear algebraic form. Techniques of solution based on iterative-incremental procedures are presented. The non-linear frequency and the non-linear modes are determined at large amplitudes of vibration. The basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated. The percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution. Also, the percentage contributions of the higher modes to the bending moment near to the clamps are given, in order to determine accurately the error introduced in the non-linear bending stress estimated by different approximations. Solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency. The non-linear deflection shapes in various regions of the solution, the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes. The numerical results obtained here for the non-linear forced response are compared with those from the linear theory, with available non-linear results, based on various approaches, and with the single mode analysis.     

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     

Optimal design of beams under flexural vibration

The minimum weight design of a cantilever beam in flexural vibration is considered. The aim is the maximization of a given natural bending frequency (usually the first) for a given beam weight or equivalently the minimization of beam weight for a specified value of a natural frequency. The beams considered are of rectangular section and are subject, in a range of cases presented, to a variety of constraints on lower and upper bounds on the cross-section dimensions or to the specification of a point mass at the end of the beam. Simple bending theory is regarded as applicable to the problem. A variational statement of the problem is made and the necessary conditions for a minimum are obtained as a system of non-linear equations which are solved numerically. Results are given in the form of tables and of figures showing computed optimum profiles. Some experiments on a sample set of beams of equal mass are described briefly. The optimum profile beam was found to have the greatest fundamental frequency, in support of the theoretical predictions.