加热弹性梁在热过屈曲构形附近的自由振动

基于轴向可伸长梁的几何非线性理论建立了弹性直梁在热过屈曲静态大变形附近自由振动的几何非线性模型。在小振幅振动假设下,简化得到热过屈曲梁线性振动的控制方程。采用打靶法分别获得了两端不可移简支(pinned-pinned)和两端固定(fixed-fixed)梁的前四阶固有频率与升温之间的特征关系曲线。数值结果表明,梁在未屈曲时,各阶频率都随升温而单调下降。在过屈曲后,两端不可移简支梁的前两阶频率随升温单调上升,三、四阶频率随升温而单调下降。但是,两端固定梁在过屈曲后的各阶频率都随升温而单调增加。因此,可以通过温度调控来实现对结构固有频率的调整。     

埋入形状记忆合金丝的复合材料圆柱壳壁板的热振动特性分析

采用有限元软件ABAQUS实现了埋入形状记忆合金（SMA）丝的复合材料圆柱壳壁板结构热振动特性分析．基于“ang-Rogers本构模型编写用户子程序（UMAT）模拟形状记忆合金材料的超弹性行为和形状记忆效应，并在不同温度和应力状态下验证了程序的正确性．基于此程序，计算了埋入SMA丝的复合材料圆柱壳壁板在温度和机械载荷作用下的一阶固有频率，分析了其热振动特性和屈曲特性．模拟结果表明：加热驱动SMA丝一般会提高结构的固有频率和屈曲临界，SMA丝的数量对结构的热振动和屈曲特性有显著影响。这些结论将对智能复合材料结构设计、抗热设计有一定的指导作用。     

嵌入形状记忆合金圆板在升温场内的自由振动

基于形状记忆合金Brinson一维热力学本构关系和圆板小振幅振动理论,研究了径向嵌入SMA丝的圆板在均匀升温场作用下的自由振动响应,获得了周边不可移简支和夹紧圆板的前三阶固有频率随温度变化的特征关系曲线。结果表明,形状记忆合金丝在从马氏体到奥氏体相变的过程中产生的回复力对板的固有频率具有显著增强作用。由此可见,通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节圆板的固有频率。     

具有形状记忆合金丝的复合材料轴转子系统的振动与稳定性

提出具有SMA丝的复合材料轴-盘-刚性支承转子系统的数学模型,研究转子系统的振动与稳定性。将轴视为一个平行于轴线方向埋入SMA丝的薄壁复合材料空心梁,盘为各向同性刚性圆盘,轴位于刚性轴承上。基于变分渐进法(VAM)描述复合材料薄壁梁的变形,基于Brinson热力学本构方程计算SMA丝的回复应力,采用Hamilton原理推导出系统的运动方程,采用Galerkin法进行模型离散化和近似数值计算。着重分析SMA丝含量和初始应变对复合材料轴振动固有频率和转子系统临界转速的影响。研究结果表明,所建立的动力学模型能够用于揭示SMA对转子系统的振动与稳定性的影响机理。     

热过屈曲正交异性圆(环)板的自由振动响应

基于vonKármán薄板几何非线性理论,建立了以中面位移为基本未知量的加热极正交异性圆板轴对称大挠度动力学控制方程。然后,将控制方程的响应分解为热过屈曲静态解和振动解两部分,并在小振幅振动假设下得到了板在热过屈曲静平衡构形附近自由振动的线性微分方程。最后,采用打靶法获得了板在热过屈曲前后的固有频率与升温参数之间的特征关系曲线。结果表明,周边面内约束板的前两阶固有频率在热屈曲前随着温度升高而降低,而一旦板进入过屈曲平衡状态,前两阶频率都随着升温而单调增加。     

热环境中功能梯度材料圆板的自由振动

基于von Kaman经典板理论,建立了功能梯度材料圆板在升温场内的大挠度动力学控制方程.将控制方程的响应分解为热过屈曲静态解和振动解两部分,得到了功能梯度材料圆板在热过屈曲平衡构形附近小振幅线性自由振动的微分方程.采用打靶法同时求热过屈曲和振动问题的控制方程,得到了随温度载荷变化的热过屈曲平衡路径以及前三阶固有频率的数值解.分析和讨论了板的材料梯度参数、温度场分布参数、边界条件等因素对过屈曲变形和振动响应的影响.分析中考虑了功能梯度板的组份材料的物性参数对温度的依赖性.     

轴向力作用下非对称支承Euler-Bernoulli梁在过屈曲前后的横向自由振动

基于轴线可伸长杆的几何非线性理论，建立了Euler-Bemoulli梁在轴向载荷作用下过屈曲横向自由振动的精确模型，并采用打靶法数值求解了一端可移简支一端固定的Euler-Bemoulli梁在过屈曲前后的小振幅自由振动，获得了线性振动的响应。结果表明，轴向力对过屈曲前后梁的各阶固有频率均有影响。     

SMA纤维复合材料变截面板簧固有频率特性研究

研究了形状记忆合金(SMA)纤维混杂复合材料变截面板簧的固有频率特性.基于Brinson本构模型,讨论了SMA的受限回复特性.在建立具有SMA纤维的各向异性层合梁本构方程的基础上,利用瑞利-里兹能量法求板簧的固有频率,并给出板簧固有频率的表达式.应用MATLAB进行数值计算,得到板簧固有频率与温度、铺层角、SMA含量的关系曲线,揭示了形状记忆合金纤维复合材料变截面板簧的固有频率可调节机理.     

埋入SMA丝的复合材料层合板在热激励下的自由振动分析

采用Liang-Rogers的形状记忆合金(SMA)本构模型和相变动力学关系,编写了ABAQUS中的相应UMAT用户材料子程序,模拟了形状记忆合金材料的超弹性行为和形状记忆效应,并在不同温度和应力状态下验证了程序的正确性.基于此程序,建立了埋入SMA丝的复合材料层合板结构计算模型,仿真计算了两端固支边界条件下,热驱动SMA时的结构的固有振动特性,分析了SMA丝的热驱动温度,埋丝数量及埋设方式等对结构热振动特性的影响规律.模拟结果表明:加热驱动SMA丝一般会提高结构的固有频率,增加SMA丝的数量可以实现增大结构频率的目的;不同的埋设角度对结构的振动特性影响显著.这些结论将对智能复合材料结构设计、抗热设计有一定的指导作用.     

SMA纤维复合材料变截面板簧的固有频率特性研究

摘 要:研究了形状记忆合金（SMA）纤维混杂复合材料变截面板簧的固有频率特性。基于Brinson本构模型,讨论了SMA的受限回复特性。在建立具有SMA纤维的各向异性层合梁本构方程的基础上,利用瑞利-里兹能量法求板簧的固有频率,并给出板簧固有频率的表达式。应用MATLAB进行数值计算,得到板簧固有频率与温度、铺层角、SMA含量的关系曲线,揭示了形状记忆合金纤维复合材料变截面板簧的固有频率可调节机理。     

SMA纤维混杂层合梁的振动分析

提出一类形状记忆合金(SMA)纤维混杂层合梁的数学模型。采用多胞模型、形状记忆合金一维本构关系分析方法,同时考虑铁木辛柯剪切和马氏体相变的影响。目的是为了更进一步了解层合梁的振动控制。SMA纤维用来作为驱动器,它能够改变弹性模量和回复力,以此改变梁的频率。分析了SMA纤维含量、铺设角度和横向剪切变形的影响。结果表明,通过激活形状记忆合金纤维及改变初始变形,对层合梁的自振频率有很强的控制和调节能力。     

A simulation study on the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires

In this paper, numerical simulation analyses of the thermal buckling behavior of laminated composite shells with embedded shape memory alloy (SMA) wires were performed to investigate the effect of embedded SMA wires on the characteristics of thermal buckling. In order to simulate the thermomechanical behavior of SMA wires, the constitutive equation of the SMA wires was formulated in the form of an ABAQUS user subroutine. The computational program was verified by showing the response of the pseudoelasticity and shape memory effect (SME) at various temperatures and stress levels. Modeling of the laminated composite shells with embedded SMA wires and thermal buckling analyses were performed with the use of the ABAQUS code linked with the subroutine of the formulated SMA constitutive equations. The thermal buckling analyses of the composite shells with embedded SMA wires show that the critical buckling temperature can be increased and the thermal buckling deformation can be decreased by using the activation force of embedded SMA wire actuators.     

Vibration characteristics of SMA composite beams with different boundary conditions

Recently, the development of shape memory alloy (SMA) actuators, in the forms of wire, thin film and stent have been found increasingly in the fields of materials science and smart structures and engineering. The increase in attraction for using these materials is due to their many unique materials, mechanical, thermal and thermal-mechanical properties, which in turn, evolve their subsequent shape memory, pseudo-elasticity and super-elasticity properties. In this paper, a common type of SMA actuator, Nitinol wires, were embedded into advanced composite structures to modulate the structural dynamic responses, in terms of natural frequency and damping ratio by using its shape memory and pseudo-elastic properties. A simple theoretical model is introduced to estimate the natural frequency of the structures before and after actuating the embedded SMA wires. The damping ratios of different SMA composite beams were measured through experimental approaches. The natural frequencies changed slightly at a temperature above the austenite finish temperature of composite beams with embedded non-prestrained SMA wires. However, the increase of the natural frequencies of the beams with embedded prestrained SMA wires were found in both the theoretical prediction and experimental measurements. The damping ratios of SMA composite beams increased with increasing the temperature of the embedded wires with and without being pre-strained. Compressive and local failures of the beams with high wire content are a possible explanation.     

Analytical layerwise solution of nonlinear thermal instability of SMA hybrid composite beam under nonuniform temperature condition

Abstract

Thermal buckling and post-buckling behavior of composite beam reinforced with shape memory alloy (SMA) wires under nonuniform temperature distribution is explored. Thermo-mechanical behavior of SMA wires is formulated by using the one-dimensional Brinson SMA model. Considering von Karman strain–displacement relation, corresponding nonlinear governing equations are obtained and solved analytically. Heat conduction equation is employed and through-the-thickness temperature distribution is obtained by discretization scheme of layerwise method. Influence of SMA-wire positioning across the thickness, temperature distribution, SMA wire pre-straining level and volume fraction of SMAs upon the thermal buckling and post buckling of reinforced beam are examined and discussed in detail.     

Thermal buckling and postbuckling analysis of a laminated composite beam with embedded SMA actuators

In this paper, the thermal buckling and postbuckling behaviours of a composite beam with embedded shape memory alloy (SMA) wires are investigated analytically. For the purpose of enhancing the critical buckling temperature and reducing the lateral deflection for the thermal buckling, the characteristics of thermal buckling are investigated through the use of the shape recovery force associated with SMA wire actuators. The results of both thermal buckling and postbuckling behaviours present quantitatively how the shape recovery force affects the thermal buckling behaviour. The analytical results show that the shape recovery force reduces the thermal expansion of the composite laminated beam, which results in both an increment of the critical buckling temperature and also a reduction of the lateral deflection of postbuckling behaviours. A new formula is also proposed to describe the critical buckling temperature of the laminated composite beam with embedded SMA wire actuators.     

形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动

研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率, 建立了SMA纤维混杂复合材料大挠度层合板的本构方程, 基于对称层合各向异性弹性板的非线性理论, 建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有三次非线性项的Duffing型常微分方程, 采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明: 非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征, 马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著, 同时也讨论了SMA纤维含量、 板的纵横比以及自由振动幅值对板的非线性频率比的影响。      

The active buckling control of laminated composite beams with embedded shape memory alloy wires

In this paper, the results of an experimental analysis on the active buckling control behaviour of a laminated composite beam with embedded shape memory alloy (SMA) wires are presented. For the purpose of enhancing the critical buckling load, active buckling control was investigated through the use of the reaction time associated with the shape recovery force of SMA wires. An increased critical buckling load and altered deflection shape due to the effects of activation of embedded SMA wires are represented qualitatively and quantitatively on the load–deflection behaviour records. The results obtained from this active buckling control test confirm that the buckling resistance in a composite beam with embedded SMA wires can be increased by the use of an activation force of the embedded SMA wires. Based on our experimental analysis, a new formula for the behaviour control of active buckling in a laminated composite beam with embedded SMA wires is also suggested.     

Bending of shape-memory alloy-reinforced composite beam

Based on the one-dimensional thermo-mechanical constitutive relation of a shape-memory alloy (SMA) in which the dependence of the elastic modulus of SMA upon the martensite fraction is considered, a constitutive relation for the bending of a composite beam with eccentrically embedded SMA wires has been developed. The deflection-temperature relation upon heating and cooling has been analysed for the SMA-reinforced composite beam.