计算梁弯曲变形的一种特殊叠加法

梁的弯曲变形是材料力学的核心内容之一。本文基于梁的弯曲变形理论,以悬臂梁的弯曲变形为基础,给出了一种求解梁弯曲变形的“特殊叠加法”,该方法对于计算简支梁、外伸梁以及变刚度梁的变形问题尤为方便和有效。     

转动刚体上固结悬臂梁系统的动力学数值分析

本文首先用Ｊｏｒｄａｉｎ变分原理建立了转动刚体上固结悬臂梁系统的动力学方程，然后用数值方法分析了转动梁的变形频率，对系统的自由振动、受迫运动及共振现象等仿真结果作出了解释。     

阶跃载荷作用下弹塑性悬臂梁的变形机制与能量耗散

基于大挠度动力控制方程，应用有限差分离散求解，研究了阶跃载荷作用下弹塑性悬臂梁的动力行为。通过对动力响应早期内力、变形以及能量分布规律的分析，考察了悬臂梁的弹塑性响应模式和变形机制，并与已有的刚塑性分析进行了系统的比较。数值计算表明，阶跃载荷的不同幅值使得梁的响应模式存在较大差异，弹塑性分析肯定了刚塑性理论在处理中载情形的准确性，同时也指出了其在处理低载和高载情形时的缺陷。通过与小变形理论计算结果的比较，指出了考虑大变形效应的必要性，为今后的大变形刚塑性动力分析提出了建议。     

弹性撞击作用下弯扭耦合梁的动力响应

对于质量块以一定初速度撞击悬臂梁端部问题,基于弯扭耦合Timoshenko梁模型,把质量块与悬臂梁作为一个整体振动,动力响应以Duhamel积分表示,使用模态叠加法给出动力响应与撞击力的结果.对于悬臂梁受质量块撞击的算例,分别分析了弯扭耦合梁、弯扭耦合系数很小的梁和各向同性Timoshenko梁,对比讨论了撞击力结果.     

悬臂梁集中载荷大挠度弯曲变形的一种解

利用数值积分法求解了细长杆悬臂梁受集中载荷时大挠度弯曲问题，并分别对无限长及有限长细杆悬臂梁进行了讨论，提出细长杆悬臂梁所受最大弯矩计算方法，为梁的强度校核提供了依据     

Timoshenko固端梁特征值问题近似计算方法

利用模态摄动法将Timoshenko梁特征值问题的求解转化为一组非线性代数方程组的求解，不仅可以简化计算过程，而且计算结果具有较高的精度，对同一类问题具有适用性。通过算例，计算了在不同长细比条件下，剪切变形和转动惯量对固端梁的各阶主频率的影响。     

二维复合材料结构模态分析的边界元法

将边界元方法用于分析二维复合材料结构的自由振动模态，利用特解处理体积力（惯性力）仅需静态基本解就可求解问题，对一各向同性悬臂梁，用该法得到的结果与用有限元或各向性边界元法得到的结果符合得很好，但该法可解各向异性问题，对层状复合材料简支梁，用该法得到了数值结果与用一维层状复合材料梁的理论解的比较表明，当结构的长厚比大于２０时，二者符合得很好，当结构的长厚比小于２０时，一维层状材料梁的理论将产生很大的     

欧拉-伯努利梁的静态响应分析

欧拉-伯努利梁,即通常所称的工程梁或弯曲梁(不考虑剪切变形和转动惯量),其静态响应分析包括求解梁的挠度、转角、弯矩和剪力,亦即求解梁的变形和内力。求解梁的挠度的方法很多,诸如能量法、力矩面积法、差分法等,前不久有人撰文“用奇异函数法求解某些变截面梁的变形”。本文用传递矩阵法分析     

A MODAL TESTING METHOD FOR CANTILEVER BEAM1)

基于欧拉-伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁-传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁-传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为 1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

一种悬臂梁模态测试方法

基于欧拉–伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁–传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁–传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

Atomic beam magnetometer

The application of a novel atomic beam magnetic resonance technique to the measurement of magnetic fields is described. The technique has been used previously in electric field experiments to determine the upper limit to the permanent electric dipole moment of the cesium atom. Two different electric field modulation schemes were used which demonstrate the sensitivity of the technique. In one scheme (sinusoidal modulation) the sensitivity to magnetic field changes is inferred; in the second scheme (squarewave modulation) small magnetic field changes were measured directly.     

梁主共振情形下索梁结构1∶1内共振分析

研究梁产生主共振情形下索梁组合结构的1∶1内共振问题。基于斜拉桥中的索梁组合结构模型,忽略索梁纵向惯性力的影响,考虑弯曲刚度、几何非线性及垂度等因素,利用索梁连接处的变形协调条件,采用Hamilton变分原理建立了索梁结构面内耦合非线性偏微分方程,运用Galerkin离散和多尺度法研究了梁主共振情形下索梁的1∶1相互作用问题,获得了内共振时的平均方程和分叉响应曲线方程。以某斜拉桥中索梁结构参数为例,研究了内共振时索梁结构之间的相互影响及时程曲线。结果表明,索容易出现共振情形,并呈现出较强的非线性特点;梁振动对索振动影响显著,索振动对梁振动影响较小;索梁内共振时能量相互交换,索梁振幅呈现此消彼长的现象。     

Atomic beam magnetometer

The application of a novel atomic beam magnetic resonance technique to the measurement of magnetic fields is described. The technique has been used previously in electric field experiments to determine the upper limit to the permanent electric dipole moment of the cesium atom. Two different electric field modulation schemes were used which demonstrate the sensitivity of the technique. In one scheme (sinusoidal modulation) the sensitivity to magnetic field changes is inferred; in the second scheme (squarewave modulation) small magnetic field changes were measured directly.     

Creeping of a rotating beam

We determine the critical time in the problem of buckling of a beam rotating about its axis corresponding to the unstrained state. We draw an analogy between the transverse bending of a rotating beamand the problem of longitudinal bending [1], which is topical in applied geomechanics.     

Large deformations of in-plane beam

A theory of large deformations of straight slender in-plane beam is presented, based on the assumption of uniaxiality of the strain tensor. The integration of the compatibility conditions gives the parabolic variation of the axial component of the strain tensor over the cross-section of the beam. The integration of the kinematic equations gives linear variation of the displacement components over the cross-section. The equilibrium equations are written on a deformed configuration and numerically solved for linear elastic cantilever, subjected to concentrated or distributed conservative and nonconservative loads.     

Nonlinear motion of a beam

The investigation reported herein analyzes the vibration of a uniform beam with hinged ends which are restrained. The beam is subjected to a linearly-varying distributed load which has a maximum intensity w ₀ at the center and is released from rest when the load is suddenly removed. The motion is found to be inherently nonlinear, even for small vibrations, and there is dynamic mode-coupling. The mode frequencies are functionally related to initial conditions, particularly the amplitudes of all modes.     

Array realization of complex-source beam

An array is constructed to radiate the far-field pattern of a single complex point source. For any nonzero error tolerance, the physical dimension of the array is smaller (sometimes much smaller) than the diameter of the branch-cut disk of the complex point source. The inverse source problem is formulated for non-resonant arrays with reactive zones that do not extend significantly beyond the physical dimensions of the array. Both time-harmonic and pulsed beams are considered. In numerical examples, each array element consists of real point sources in an end-fire configuration.     

Dynamic response of viscoelastic beam

Dynamic analysis of the viscoelastic simple supported beam has been made in accordance with the relationship between stress and strain expressed by the simplest Voigt mechanical model, from which several analytic expressions have been obtained.It is shown that the reduction of the ratio of natural frequencies progresses with the increase of the exciting frequency for high modes (Tab.1). In the final part of this paper, the forced vibration of simple supported beam subjected to a random and harmonic excitation has also been dealt with, and the representations of the beam deflection have been derived.This paper was read at the 1980 Annual Meeting of Shanxi Association of Mechanics.     

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The nonlinear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge–Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance (10⁻⁵). The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.     

Electron beam moiré

A method of writing very high frequency line and dot pattems, in excess of 10,000 lines/mm, is described. This method uses a very small diameter, 10 to 20 nm, beam of electrons to sensitize a 100-nm thick layer of electron resist. The line and dot patterns are produced by etching the sensitized resist. Moiré fringe patterns occur when the line arrays are observed in the scanning electron microscope. Moiré fringes with excellent contrast have been produced at magnifications as high as 1900x. This capability permits e-beam moiré to be employed in micromechanics. Examples of line arrays, dot arrays and moiré fringe patterns on a brass disk and on a tensile specimen fabricated from glass-fiber-reinforced plastic are demonstrated to introduce the possibilities for micromechanics applications.