形状记忆合金纤维混杂正交对称铺层板的固有频率

形状记忆合金（SMA）混杂复合材料板是将有预应变的SMA纤维与普通纤维混杂单层内构成的。基于主动应变能调节（ASET）的概念,可实现对板的固有频率的调整。本文采用Galerkin法导出形状记忆合金（SAM）纤维混杂对称正交智能复合材料铺层板自由振动的频率的分析表达式。数值结果表明,SMA纤维的相变激发温度、体积含量、分布方式及其预应变对固有频率均有的影响,尤其是温度、SAM含量及其分布的作用更为显著,是结构振动控制的重要设计参数。     

复合材料层合板自由振动的谱切比雪夫解法EI北大核心CSCD

采用二维谱切比雪夫法(2D-ST),对一般边界条件下复合材料层合板的自由振动进行了分析。基于一阶剪切变形理论(FSDT),采用边界弹簧技术模拟任意边界条件,推导了复合材料层合板的能量方程表达式。利用二维谱切比雪夫法求解能量方程,得到了任意边界条件下复合材料层合板的自由振动特征方程。在数值算例中,通过与其它方法的计算结果进行对比,验证了所提出方法的收敛性和准确性,并在此基础上研究了弹性模量比和铺设角对复合材料层合板振动特性的影响。     

纤维增强粘弹性复合材料层合板的自由振动和应力分析

基于Reddy分层理论推导出纤维增强粘弹性复合材料层合板的动力学方程,得到了其自由振动频率和损耗因子;分析了自由振动时,纤维体积含量和纤维增强层厚度对自然频率和损耗因子的影响;且计算出了协调的横向应力,数值结果分析表明:结构频率和损耗因子随纤维体积含量的增加而增加;阻尼材料参数对结构损耗因子和横向应力影响较大,且阻尼材料模量存在最佳值;高阶模态下,较高的横向正应力是层合板脱层的主要因素。     

复合材料角铺设层合板非线性振动特性研究

本文运用渐进摄动法得到复合材料角铺设层合板系统的平均方程在此基础上研究了四边简支碳纤维增强复合材料角铺设层合板在外激励作用下的非线性振动和混沌运动。指出由于复合材料角铺设层合板的强耦合作用而引起该板系统运动控制方程的复杂性,系统平面的振动方程不仅与横向振动方程相耦合而且与中面法线的转角有关。考虑了复合材料角铺设层合板系统在1:1内共振和基本参数共振的情况下的动力学特性,数值模拟得到了复合材料角铺设层合板在参数激励和横向激励联合作用下的复杂周期和混沌运动。     

基于超弹性特性的SMA复合材料层合板低速冲击损伤数值模拟方法

基于ABAQUS有限元软件结合VC++6.0程序设计,建立了含不同铺层角度、不同排列密度形状记忆合金(SMA)纤维的复合材料层合板有限元模型。将基于Brinson本构模型的SMA分段线性超弹性模型以及判断复合材料层内失效的三维HASHIN失效准则编译至ABAQUS/VUMAT子程序,使用界面单元模拟复合材料层间区域,建立了SMA复合材料层合板的低速冲击损伤及冲击后剩余强度数值模拟方法。对比了不含SMA纤维层合板、含SMA纤维层合板、含普通金属丝层合板在不同冲击能量下的损伤响应。进一步分析了SMA纤维体积分数和直径变化对冲击响应的影响。冲击后剩余压缩强度模拟结果表明:冲击能量为16J时,含体积分数25%、直径0.5mm的SMA纤维层合板的冲击后剩余压缩强度相比不含SMA纤维层合板提高5.78%、相比含普通金属丝层合板提高4.69%。随着SMA纤维体积分数提高,层合板的抗低速冲击能力增强,当体积分数一定时,较细的(0.3mm)SMA纤维比粗的(0.6mm)SMA纤维对层合板的抗低速冲击能力增强效果更好。     

热载荷作用下嵌入SMA丝复合材料梁的横向自由振动

基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系。其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型。最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线。数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法。     

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.     

受热复合材料层合板的非线性热振动——Part:理论及数值分析

基于能综合考虑温度效应以及横向线应变和剪切应变的高阶计算模型 ,研究受热复合材料层合板的非线性热振动 ,推导了非线性有限元方程并给出了相应的数值分析方法 ,通过数值算例与已有文献相比较 ,证明了本文理论和算法的精确有效性。文中还以大量数值算例研究了温度效应对幅频曲线的影响。     

混杂纤维复合材料的拉伸刚度

对单向和多向混杂纤维复合材料的拉伸刚度进行了研究。在混合定律的基础上考虑混杂比和分散度对混杂效应的影响, 提出了单向混杂纤维复合材料拉伸模量的估算公式。通过实验得到了多向混杂纤维复合材料的拉伸模量, 并且采用经典层合板理论进行了估算, 基于混杂比以及分散度对拉伸模量的影响规律, 对多向混杂纤维复合材料拉伸模量的估算公式进行了修正。结果表明: 混杂纤维复合材料的拉伸模量与混杂比和分散度相关, 分散度的增大在一定程度上可以提高单向混杂纤维复合材料的纵向拉伸模量。采用经典层合板理论所得的拉伸模量与实验值有一定的误差, 而本文所提出的公式能够更加准确地估算混杂纤维复合材料的拉伸模量。      

受热复合材料层合板的非线性热振动--Part Ⅰ: 理论及数值分析

基于能综合考虑温度效应以及横向线应变和剪切应变的高阶计算模型,研究受热复合材料层合板的非线性热振动,推导了非线性有限元方程并给出了相应的数值分析方法,通过数值算例与已有文献相比较,证明了本文理论和算法的精确有效性.文中还以大量数值算例研究了温度效应对幅频曲线的影响.     

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。     

Free vibration of buckled SMA reinforced composite laminates

The effect of shape memory alloys (SMA) on the free vibration behavior of buckled cross-ply and angle-ply laminates by varying the SMA fiber spacing was investigated using the finite element method. The formulation of the location-dependent linear, nonlinear stiffness and mass matrices due to non-homogeneous material properties and the temperature-dependent recovery stress stiffness matrix were derived. Numerical results show that the increase of SMA fiber volume fraction and prestrain may generate more recovery stress, and increase the stiffness of SMA reinforced composite laminates. Therefore, the postbuckling deflections of the plate will be decreased considerably and the natural frequencies of the plate may be modified significantly. The buckling mode and fundamental natural mode are dependent on the graphite fiber orientation of the SMA reinforced angle-ply laminates. The relationship between the buckling mode and fundamental natural mode is clearly displayed and studied in detail.     

随从力作用下运动薄膜的非线性强迫振动特性研究

研究随从力作用下运动印刷薄膜的非线性强迫振动特性。基于Von Karman薄板理论推导出轴向运动薄膜的非线性振动方程,应用Galerkin方法对振动偏微分方程组进行离散,利用4阶龙格-库塔法对微分方程进行求解,得出薄膜非线性振动的时程图、相图、Poincare截面图和分岔图。分析了初始条件、随从力和长宽比对薄膜振动特性的影响。研究结果得出了薄膜稳定工作区间和发散失稳区间。     

叠层板在两项简谐激励作用下的组合共振分析

研究了在四边简支的边界条件下,正交各向异性矩形叠层板在两项横向简谐激励作用下的非线性组合共振及其稳定性问题。在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的无量纲化达芬型非线性强迫振动方程。应用多尺度法对组合共振问题进行求解,得到了系统在稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件。通过数值算例,对几种复合材料薄板的共振特性进行了分析,分别给出了不同条件下系统运动的响应图、幅频图和动相平面图,讨论了不同参数对系统非线性动力学行为的影响。     

Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium

Abstract

In this study, the nonlinear vibration analysis of the new generation nanostructures is investigated. The composite nanoplate is fabricated from the functional-graded (FG) core and two lipid layers on top and bottom of the FG core as face sheets. The nonlinear vibration analysis is studied in the presence of the external harmonic excitation force. The porosity effect on the free and force vibration analysis of the composite nanoplate is investigated. The nonlocal elasticity theory is utilized to obtain the nonlinear differential governing equation. The Kelvin–Voigt model is used to model the viscoelastic effect of the lipid layers. The Hamilton's principle is utilized to obtain the differential governing equation. The Galerkin's method is used to discrete the nonlinear partial differential governing equation to a nonlinear ordinary differential equation. The multiple scale method is used to solve the ordinary differential equation. The numerical results are compared with the reported results in the literature. A comparison between the presented numerical results and the Runge–Kutta results is done and good agreement is obtained. In the presence and absence of the porosity, the system vibration behavior is studied in the primary and secondary resonance cases. The results show that the porosity distribution types play an important role in the mechanical behavior of the composite nanoplate. Also, the numerical results show that the nonlinear frequency of the system decreases by passing time. This study can be useful to product the sensors and devices at the nanoscale with high biocompatibility.     

Effect of viscoelastic interface on three-dimensional static and vibration behavior of laminated composite plate

In this study, static and free vibration analysis of laminated cross-ply rectangular plate with special emphasis on incorporating viscoelastic interface is investigated using three-dimensional theory of elasticity. The laminated plate is assumed to be simply-supported at four edges and is subjected to uniform pressure at the top surface. State space technique is used along the plate thickness to investigate the space dependent behavior where as time dependent behavior can be discussed by solving first order differential equation of sliding displacement at the viscoelastic interfaces. Numerical results depicts that the present method converges rapidly and good agreement is exist between the present results and the published results. Moreover, the effects of elastic and viscous interfaces, time, aspect ratio and length to thickness ratio on the bending and vibration behavior of laminated plate are studied.     

Nonlinear free vibration of a shear deformable laminated composite annular elliptical plate

The nonlinear free vibration of a laminated composite annular elliptical plate with elliptically orthotropic plies is investigated. The effects of out-of-plane shear deformations, rotatory inertia and geometrical nonlinearity are taken into account. The problem is solved numerically using a new polynomially enriched sector elliptic p-element. The nonlinear equations of free motion are obtained using the harmonic balance method and solved iteratively by the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained. Comparison is made with published results for a polar orthotropic annular plate and shows very good agreement. The minor semi-axis ratio, thickness ratio, moduli ratio, number of plies, layup sequence, and boundary conditions are shown to influence the hardening behavior.     

复合材料圆柱壳非线性热弹耦合振动

根据复合材料圆柱壳的非线性动力方程,研究了复合材料圆柱壳的非线性热耦合振动,应用Galerlein原理及改进的L－P法对其非线性热耦合振动进行求解,并讨论分析了温度、长径比、厚径比对复合材料圆柱壳非线性热振动固有频率的影响。