轴向运动SMA层合梁的主共振分析

研究了均布横向载荷作用下轴向运动SMA(形状记忆合金)层合梁的横向非线性振动。考虑轴向运动效应、轴力等因素的综合影响,利用力平衡条件、变形协调方程及SMA多项式函数的本构关系,建立了SMA层合梁在均布横向载荷作用下的动力学方程。针对两端简支边界条件,通过伽辽金积分得到了轴向运动SMA层合梁横向振动微分方程。应用平均法得到了横向载荷作用下系统主共振幅频响应方程,对理论结果进行了数值验证;分析了轴向运动速度、温度、激励参数对系统稳态响应的影响。结果表明:轴向速度、轴向载荷的变化只对系统共振频率产生影响;在外激励幅值较大时,温度增加和SMA层增厚对系统产生了相同的减振效果。     

非对称混杂边界轴向运动Timoshenko梁橫向振动分析

研究两端带有扭转弹簧且弹簧系数均可任意变化的非对称混杂边界下的轴向运动Timoshenko梁的横向振动.利用非对称混杂边界条件推导对应任意弹簧系数的系统超越方程以及特征函数.运用数值方法计算系统的固有频率及其相应的模态函数,并研究确定梁的刚度、轴向速度以及边界处扭转弹簧的刚度的影响.通过数值算例,比较7imoshenko梁、瑞利梁、剪切梁和欧拉梁的固有频率随轴向速度的变化,分析转动惯量和剪切变形的影响.     

应用有限差分法的轴向流作用下叠层板的稳定性和模态分析

分析了轴向流作用下两端简支和固支叠层板的稳定性。基于势流理论建立轴向流作用下叠层板的流固耦合系统连续型运动方程,基于有限差分法建立了流场网格和结构网格统一的离散化格式,流场势函数用板的横向振动位移变量来表示,得到关于叠层板的横向振动位移变量的控制方程。求解控制方程的广义特征值,计算分析结果表明,两端简支和两端固支模型发生屈曲失稳,且得到了屈曲失稳临界速度与叠层板的层数和无量纲板间距的关系。此外,轴向流作用下叠层板的一阶模态并不是叠层板的同相弯曲模态。     

分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数，由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明，管道在弹性支承下的动力稳定性比较复杂，在较小的弹性支承刚度和较小 的参数范围内，管道主要表现为动态颤振失稳；在较大的弹性支承刚度和较大的参数作用下， 管道的失稳形式主要表现为静态失稳；并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降，随管截面轴向拉力的增加而上升.     

圆柱约束下细长压杆屈曲及后屈曲行为

研究了轴向力作用下受圆柱横向约束的弹性杆的屈曲和后屈曲行为。通过有限元模拟,分析了细长压杆发生正弦和螺旋屈曲的轴向临界力,提出了正弦和螺旋屈曲临界点判定方法,且与文献结果比较验证了分析的正确性。同时考察了长细比和边界条件等因素对临界力的影响。结果表明正弦屈曲临界力和螺旋屈曲临界力随杆的长细比减小而增大。杆在一定长度范围内,端部约束条件对临界屈曲载荷及模态的影响不可忽略;当杆的长度足够长时,可以忽略边界条件对临界载荷的影响。     

PELE垂直侵彻薄靶的机理分析

PELE(横向效应增强型侵彻体)撞击靶板能够产生明显的横向效应,横向效应的强弱受多种因素的影响。通过改变PELE的外壳材料、弹芯材料及着靶速度,对PELE垂直侵彻薄靶进行了实验研究。基于实验结果,对PELE侵彻靶板的过程进行了受力分析,阐明了横向效应产生的机理,建立了破片轴向剩余速度和径向速度的理论模型,模型计算结果与实验结果吻合较好。理论分析和实验结果表明,外壳材料的压拉强度比、弹芯材料的泊松比和弹性模量以及着靶速度等对PELE横向效应影响显著。本研究对PELE的设计和改进有一定的参考价值。     

两种典型螺栓连接结构的刚度特性比较研究

针对法兰对接和径向套接两种典型舱段螺栓连接形式,基于有限元静刚度计算、动力学简化建模、冲击响应特性分析及结构冲击试验,系统研究了两种连接形式的轴向刚度特性及其对动力学冲击响应的影响.有限元静刚度分析揭示了法兰对接与径向套接的轴向拉压刚度分别是非对称的和对称的,而法兰对接的平均刚度更大.之后,为两种连接形式建立了统一的动力学模型,证明非对称的轴向拉压刚度导致结构在受到横向载荷作用时会产生附加的耦合轴向振动,并且利用高精度幂函数拟合刚度跳变,得到耦合轴向振动频率是弯曲振动频率的二倍的结论.最后,通过冲击动力学试验证明了法兰对接存在二倍频的耦合轴向振动,而径向套接则不存在该耦合振动.径向套接虽然一阶频率较低,但阻尼效果更好.     

刚性块轴向撞击杆的弹塑性动力屈曲

用特征线法分析了刚性块轴向撞击弹塑性直杆时应力波传播的全过程,得到了杆冲击端与固定端应力的变化规律及刚性块与杆首次分离的时间．基于能量原理,考虑了弹塑性应力波的传播与反射,建立了弹塑性杆在刚性块轴向撞击下的横向扰动方程,给出了问题的级数解,由解的稳定性得到了发生屈曲时的临界条件;通过数值计算和分析,给出了临界速度与冲击质量、线性强化模量及临界时间间的关系．     

THERMOELASTIC VIBRATION OF FLUID-CONVEYING MICROTUBES EMBEDDED IN ELASTIC MEDIUMS

研究热环境中被弹性介质包围的微米输流管道的横向振动问题. 根据Hamilton 原理及非线性热弹性理论建立管道横向振动控制方程,并利用复模态法对其进行求解,得到了系统的固有频率和屈曲失稳临界流速,讨论了环境温度和一些重要系统参数对管道振动特性的影响. 研究结果表明:环境温度变化、管道和流体的微尺度效应、管道外径及弹性介质刚度对输流微管道固有频率和临界流速都有很大影响.     

无人机捷联惯组隔振系统动力学分析与优化设计

针对捷联惯组在无人机中的特殊安装环境,提出了一种在偏移安装环境中实现三轴向等刚度与准解耦隔振系统的设计方法。首先建立了隔振系统的六自由度动力学模型及其动力学方程,对隔振系统进行动力学分析。分析结果表明:当隔振器的轴径刚度比为0.8左右且阻尼比大于0.125时系统可以实现设计要求。最后,设计并制造隔振系统,分别在振动台上以及无人机飞行环境中对其进行试验验证。试验结果与理论计算相吻合:隔振系统有效地削弱了偏移安装环境带来的捷联惯组振动问题,可以实现三轴向等刚度设计与准解耦状态。     

Transverse Stiffness of a Sinusoidally Corrugated Plate∗

Abstract

An analytical model for the initial transverse stiffness of a sinusoidally corrugated plate is derived, incorporating deformations due to extension, shear, and bending. A nondimensional plot is developed for determining transverse stiffness based on thickness and corrugation for a range of plate geometries. This model shows that for most corrugated plates the transverse stiffness is dramatically decreased from that of an uncomigated plate of the same thickness. For thin plates, a simple approximate polynomial expression for initial transverse stiffness is obtained. For thick plates with a small degree of corrugation, transverse stiffness is not negligible relative to longitudinal stiffness. The exact model is verified using a linear-elastic two-dimensional finite element model.     

Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media

This study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface between two orthotropic micropolar elastic half-spaces with different elastic and micropolar properties. There exist three types of coupled waves in xy-plane. The reflection and transmission coefficients of quasi-longitudinal (QLD) wave, quasi-coupled transverse microrotational (QCTM) wave and quasi-coupled transverse displacement (QCTD) wave have been derived for different incidence waves and deduced for normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding. The numerical values of modules of the reflection and transmission coefficients are presented graphically with the angle of incidence for orthotropic micropolar medium (MOS) and isotropic micrpolar medium (MIS). Some particular cases of interest have been deduced from the present investigation.     

Usefulness of passive non-linear energy sinks in controlling galloping vibrations

The suppression of vibration amplitudes of an elastically-mounted square prism subjected to galloping oscillations by using a non-linear energy sink is investigated. The non-linear energy sink consists of a secondary system with linear damping and non-linear stiffness. A representative model that couples the transverse displacement of the square prism and the non-linear energy sink is constructed. A linear analysis is performed to determine the impacts of the non-linear energy sink parameters (mass, damping, and stiffness) on the coupled frequency and onset speed of galloping. It is demonstrated that increasing the damping of the non-linear energy sink can result in a significant increase in the onset speed of galloping. Then, the normal form of the Hopf bifurcation is derived to identify the type of instability and to determine the effects of the non-linear energy sink stiffness on the performance of the aeroelastic system near the bifurcation. The results show that the non-linear energy sink can be efficiently implemented to significantly reduce the galloping amplitude of the square prism. It is also shown that the multiple stable responses of the coupled aeroelastic system are obtained as well as the periodic responses, which are dependent on the considered non-linear energy sink parameters.     

齿轮箱非线性耦合系统的动力学分析

分别建立了啮合齿轮子系统弯扭耦合振动模型、弹性轴子系统的弯曲振动和扭转振动模型以及齿轮箱弹性箱板子系统的横向振动模型,通过轴承多维刚度矩阵和子结构之间的受力变形协调关系将各子结构的振动模型联立起来,从而得到整个齿轮箱耦合系统的动力学模型。结合相图和庞加莱映射图分析了系统的运动特性,采用功率流方法研究了系统振动能量传递特性及其影响因素,揭示了外部激励和轴承刚度等因素对系统特性的影响,为齿轮箱系统的振动控制与结构设计提供了新的分析方法和理论依据。     

考虑弯扭耦合作用的转子-挤压油膜阻尼器系统的碰摩响应特性分析

研究了支承在挤压油膜阻尼器上的Jeffcott转子系统的转静件碰摩的弯扭耦合振动特性。建立了系统运动方程，分析了各参数对系统响应的影响。仿真计算结果表明碰摩刚度对系统响应的影响十分明显，增大碰摩刚度更容易使系统响应的周期解失稳；不平衡参数增大，导致系统响应的振动幅度增大，系统更容易出现碰摩现象，进而导致系统周期解失稳；随着扭转刚度的增大，扭转角度变化幅度与快慢均发生变化，在刚度较低时，扭转角变化幅度随时间变化较慢；随着扭转刚度的增大，扭转角幅度变化明显加快；当扭转刚度继续增大，扭转角的幅度变化反而变慢。研究发现，系统响应具有两条通向混沌的道路，即阵发性通向混沌的道路和拟周期通向混沌的道路。     

The effect of transverse normal strain in contact of an orthotropic beam pressed against a circular surface

The contact problem of a straight orthotropic beam pressed onto a rigid circular surface is considered using beam theories that account for transverse shear and transverse normal deformations. The circular nature of the rigid surface emphasizes the difference between Euler Bernoulli theory behavior, where point loads develop at the edge of contact, and the higher order theories that predict non-singular pressure distributions. While Timoshenko beam theory is the simplest theory that addresses this behavior, the prediction of a maximum value of pressure at the edge of contact contradicts the elasticity theory result that contact pressure must drop to zero. Transverse normal strain is therefore introduced, both to study this fundamental discrepancy and to include an important effect in many contact problems. To investigate this effect, higher order beam theories that account for both constant and linear transverse normal strain through the beam thickness are derived using the principle of virtual work. The resulting orthotropic beam theories depend on the bending stiffness (EI), shear stiffness (GA), axial stiffness (EA₁) and transverse normal stiffness (EA₂), which are independent stiffness parameters that can differ by orders of magnitude. The above mentioned contact problem is then solved analytically for these theories, along with the Timoshenko beam model which assumes zero transverse normal strain. The results for different orthotropic materials show that inclusion of transverse normal deformation has a significant effect on the contact pressure solution. Furthermore, the solution using higher order beam theories encompasses the two extremes of a Hertz-like contact pressure when the half contact length is smaller than the thickness of the beam, and the Timoshenko beam theory case when the half contact length is much larger than the thickness. Concerning the behavior of the pressure at the edge of contact, adherence to the boundary conditions required by the principle of virtual work, shows that while the pressure does tend to zero, it does not become zero unless artificially enforced. In this regard the solution for the case of linear strain is better than that for constant strain. All beam solutions are validated with plane elasticity solutions obtained using the commercial finite element software ABAQUS.     

运动车辆横向振动半车模型分析

通过半车模型, 数值研究平滑路面上运动车辆车体的前两阶横向振动频率. 将车体模型化为两端自由的Euler-Bernoulli梁, 半车模型的车轮模型化为两个弹性不等的弹簧. 建立半车模型的数学模型描述车体的横向振动. 以两端自由的静态梁的模态为试函数和权函数, 通过高阶Galerkin截断计算车体横向振动的频率, 并研究车辆运行速度、车体刚度、弹簧刚度等参数对车体振动频率的影响.     

基于高阶变形理论的夹层板的弯曲与振动

考虑面板和夹芯的面内刚度和横向剪切刚度以及抗弯刚度,考虑了高阶剪切变形,根据横向剪应变分布情况给出横向剪切转角的位移函数,基于哈密尔顿原理,推导了基于高阶变形理论、适用于软、硬夹芯情况夹层板的基本方程。作为算例,以四边简支条件下的夹层板的弯曲与振动,在不同的面板与芯层的弹性模量比和厚度比下进行了计算,并与Reissner理论、Hoff理论以及邓宗白基于Reissner理论的修正模型的计算结果进行了对比。与前述理论与方法相比,本文方法考虑因素更为全面,对夹层板的适用范围更为广泛,计算结果更为精确。针对Nastran软件计算夹层板的振动问题,对其适用范围作了简要分析。     

The averaged mechanical properties of prismatic lattice formed by ellipsoidal inclusions

Summary The objective of this paper is to evaluate the averaged elastic properties of 3-D grained composites in which identical inclusions form a prismatic network interacting with the matrix material. The inclusions are of ellipsoidal shape with transverse circular sections located at the nodes of a doubly-periodic lattice with an orthogonal elementary cell. When the arrays of inclusions are set at equal spacings in normal directions through the thickness of the matrix, the material formed is an anisotropic composite with tetragonal symmetry at planes transverse to the fiber axis. The longitudinal and transverse elastic and shear moduli as well as the longitudinal Poisson's ratios of such composites are evaluated in this paper. The averaged properties are studied in terms of the aspect ratio and volume fraction of the inclusions as well as the relative rigidity of the constituent phases. Employing the Eshelby's theory for the stress field around a single ellipsoidal inhomogeneity, which is surrounded by the effective anisotropic material, and considering the Mori-Tanaka's concept for the mutual interaction of the neighboring inclusions, we may evaluate the averaged elastic properties of grained composites with aligned ellipsoidal inclusions at finite concentrations. The results provided in a closed-form solution concern the stiffness of 3-D grained composites with parallely dispersed ellipsoidal inclusions forming a prismatic network inside the principal material. It is shown that the stiffness is affected by both the geometry of the inclusions and their concentration. The use of different composite models in the analysis shows that intense variations of stiffness occur mainly in hard composites weakened by soft ellipsoidal inclusions. These findings come in full verification with experimental or theoretical results from the literature. Received 10 February 1998; accepted for publication 27 November 1998     

Constitutive relations for a rubber cord under three-dimensional stress states

The transverse modulus of a rubber cord is experimentally determined. It is shown that, in the framework of the effective layer model, it is problematic to find both the bending stiffness and the lateral compression stiffness with equal adequacy.