粘弹性介质中输流碳纳米管的动态稳定性分

应用非局部粘弹性夹层梁模型分析粘弹性介质中输送脉动流碳纳米管的动态稳定性。在经典的欧拉梁模型中考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力,同时考虑纳米管道的非局部效应,得到了改进的欧拉梁模型。用平均法对其控制方程进行求解,得到了管道稳定性区域。数值算例揭示了纳米管的壁厚、粘弹性特性、表面效应及两个介质参数对管道动态稳定性的复杂影响,结论可为纳米流体机械的结构设计和振动分析提供理论基础。     

四边固支功能梯度矩形板的主共振分析

针对四边固支约束的陶瓷-金属材料功能梯度矩形板,在给出非均匀材料的应力应变关系及非线性几何方程基础上,应用虚功原理导出了横向简谐激励力作用下功能梯度板的非线性振动偏微分方程。通过位移函数的设定,利用伽辽金积分法推得了相应的达芬型非线性振动方程。应用多尺度法对非线性系统的主共振问题进行解析求解,得到了稳态运动下的幅频响应方程。基于李雅普诺夫稳定性理论,得到了共振下解的稳定性判别条件。作为算例,给出了不同参数下功能梯度矩形板共振的幅频曲线图和动相平面相轨迹图,讨论了不同参数对系统非线性振动特性的影响     

磁场下黏弹性基体中输流纳米管稳定性分析

基于非局部连续介质理论，应用哈密顿原理建立轴向磁场作用下黏弹性基体中固支输流单层碳纳米管（Single-walled Carbon Nanotube,SWCNT）系统振动微分方程，应用微分变换法(Differential Transformation Method,DTM)求解该振动方程，着重研究黏弹性基体、轴向磁场、小尺度效应耦合作用时该系统的振动稳定性问题。数值计算结果表明：输流碳纳米管无论是否嵌入黏弹性基体中，磁场的作用均能提高系统的稳定性，而小尺度系数的增加则降低系统稳定性。黏弹性基体的阻尼系数加大系统的振动耗能，当阻尼系数处于较大数值时，系统振动能量迅速耗散，在管内流体流速还处于较低数值时系统即产生发散失稳现象。进一步研究表明在考虑小尺度效应、轴向磁场与基体耦合作用时，较强的轴向磁场可以降低小尺度效应、基体阻尼系数对系统的影响；即使存在小尺度效应，对于弹性系数较大的基体，其阻尼系数对振动系统的影响程度仍大大降低。     

基于非局部弹性理论的充液双壁碳纳米管振动特性分析

基于非局部弹性理论和Flügge壳理论,建立了充液双壁碳纳米管振动方程,计算了简支边界条件下碳纳米管的振动固有频率。用数值计算方法,分析了波数、几何参数和材料参数对振动频率的影响,并对比了局部和非局部弹性理论对结果的影响。结果表明,随着碳纳米管长度和半径的增大,振动频率逐渐减小;且随着小尺度参数的增大,频率也呈下降趋势。     

Biot理论与修正的Biot理论比较及讨论

对Biot理论和修正的Biot理论中的波动方程进行了详细推导,注明了每个参数的量纲和准确含义,并基于修正的Biot理论导出了三种不同形式的波动方程;对两种理论进行比较,得到了Biot弹性系数表达式,并分析了两者的应力及其对应关系;最后,着重对易被混淆的孔隙流体压力符号的正方向和含义,以及基本方程中部分参数的定义式进行了讨论,有助于更好地理解、应用Biot理论和修正的Biot理论。     

考虑非局部效应的纳米梁非线性振动

以弹性理论为基础,建立考虑非局部效应和轴向非线性伸长的两端固支纳米梁物理模型,推导出其动力学方程,计算得到考虑非局部效应和轴向非线性纳米梁的固有频率,研究了考虑非局部效应的纳米梁主谐波共振响应。数值结果表明,非局部效应对两端固支纳米梁固有频率和幅频关系均有影响。     

混凝土泵车臂架系统振动机理的研究

结合悬臂输液管流固耦合理论,建立泵车臂架结构与混凝土的流固耦合动力学方程,从流固耦合的角度分析混凝土泵车臂架振动问题。通过试验测试获得混凝土脉动流速图以及仿真边界条件。采用Newmark-β法求解动力学方程,仿真分析了混凝土流动为脉动和常速流时臂架振动响应,发现振动位移响应基本吻合,说明脉动流速对臂架结构应力历程影响较小;仿真分析转台振动为零振动时,混凝土脉动和常速流时臂架振动响应,发现泵送油缸导致的车体振动激扰是臂架振动的主要因素,在臂架系统振动研究时应重点考虑。     

形状记忆合金梁在随机激励下的随机分岔与首次穿越

根据形状记忆合金（SMA）的等应变拉压实验的数据,利用van der Pol环模型模拟了形状记忆合金在加载和卸载过程中的应力应变迟滞环特性。并且根据弹性理论和Galerkin方法建立了形状记忆合金简支梁在受轴向高斯白噪声激励时的振动模型。应用拟不可积Hamilton随机平均法将函数表示为一维扩散过程后,通过最大Lyapunov指数判断系统的局部稳定性,同时用奇异边界理论讨论了系统的全局稳定性。随后通过分析稳态概率密度和联合概率密度的图形特征,得到了此模型的随机Hopf分岔现象,并讨论了系统产生随机Hopf分岔的条件。最后,用数值法模拟了系统在特定初始条件和边界条件下可靠性函数和首次穿越时间的概率密度函数所满足的BK(Backward Kolmogorov)方程,并且分析了系统发生首次穿越的条件。     

输流管道的流体诱发振动稳定性分析

考虑内、外部流体的联合作用,研究输流管道的流体诱发振动稳定性。将外部流体的作用简化为涡激升力,利用Kane方法建立输流管道的二维非线性涡激振动方程。将动力学方程在平衡位置附近线性化,进行输流管道的稳定性分析。探讨不同内外流流速、外部流体的粘滞力系数、管道跨度以及内外流联合作用对管道稳定性的影响。研究结果表明,非线性涡激振动模型更真实地反映输流管道的流体诱发振动稳定性,在内流和管道跨度的影响下,发生耦合模态颤振现象;外部流体粘滞力系数的变化对管道的动力特性有明显的影响;在内外部流体的联合作用下管道的振动特性与各因素单独作用时明显不同。     

振动时效在铝合金厚板应力消减中的局限与应用

运用振动时效对材料应力消减的作用,结合铝合金厚板残余应力消减后的分布及效果,认为振动时效对厚板结构残余应力消减作用有限。而运用位错理论和最小能量法分析,发现振动时效对材料因内部微结构差异而形成应力集中区域的应力松弛释放有所贡献,在一定激振频率和时效时间条件下,完全可以造成材料局部的微屈服,减小了微结构间残余应力水平,从而对板内应力的均匀化过程起到一定效果。借助实验对厚板振动时效前后表面应力强度和板形尺寸稳定性对比发现,振动时效对稳定板形和消减大梯度表面残余应力具有显著作用。     

Nonlocal,strain gradient and surface effects on vibration and instability of nanotubes conveying nanoflow

ABSTRACT

In this paper, the size-dependent vibration and instability of nanoflow-conveying nanotubes with surface effects using nonlocal strain gradient theory (NSGT) are examined. Hence, based on Gurtin-Murdoch theory, the nonclassical governing equations are derived by extended Hamilton's principle. To study the small-size effects on the flow field, the Knudsen number is applied. Applying Galerkin's approach, the partial differential equations converted to ordinary differential equations. The effects of the main parameters like nonlocal and strain gradient parameters, length to diameter ratio, thickness, surface effects, Knudsen number and different boundary conditions on the eigenvalue and critical fluid velocity of the nanotube are explained.     

Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection

Based on the nonlocal continuum theory, transverse vibration of a single-walled carbon nanotube (SWCNT) conveying fluid with immovable support conditions is investigated. Unlike previous similar studies, the SWCNT is assumed to be not perfectly straight and initially includes a slight geometrical curvature as an imperfection. The SWCNT is assumed to be embedded in a Pasternak-type foundation. Hamilton’s principle is applied to drive an efficient governing equation of motion, which covers stretching, large deformation, and imperfection nonlinearities. The perturbation method of multi scales (MMS) is applied and the nonlinear flow-induced frequency ratio is analytically calculated. The obtained results reveal that the imperfection of the nanotube at high flow velocities makes the model severely nonlinear, especially when considering the nonlocal effects. A noteworthy observation is that the nonlinear flow-induced frequency ratio is decreased as the imperfection of the nanotube increases. Whereas through a parametric study, the effects of the flow velocity, nonlocal parameter, the stiffness of the elastic foundation, and the boundary conditions (BCs) on this frequency reduction are calculated and discussed widely.     

轴向运动超薄梁的非局部动力学分析

基于非局部弹性理论,建立了两端受初始张力的轴向运动超薄梁横向振动的控制方程。与现有的一些仅仅在控制方程中考虑非局部效应的研究不同,该文同时将非局部效应引入到两种典型的边界条件中,考察了非局部参数对超薄梁横向振动行为尤其是固有频率和临界速度的影响。结果表明:超薄性使得轴向运动梁的自由振动固有频率及临界速度降低,经典弹性理论高估了纳米尺度结构的弯曲刚度,轴向运动超薄梁的动力学行为存在明显的非局部尺寸效应。     

Nonlocal continuum model and molecular dynamics for free vibration of single-walled carbon nanotubes

Free transverse, longitudinal and torsional vibrations of single-walled carbon nanotubes (SWCNTs) are investigated through nonlocal beam model, nonlocal rod model and verified by molecular dynamics (MD) simulations. The nonlocal Timoshenko beam model offers a better prediction of the fundamental frequencies of shorter SWCNTs, such as a (5, 5) SWCNT shorter than 3.5 nm, than local beam models. The nonlocal rod model is employed to study the longitudinal and torsional vibrations of SWCNT and found to enable a good prediction of the MD results for shorter SWCNTs. Nonlocal and local continuum models provide a good agreement with MD results for relatively longer SWCNTs, such as (5, 5) SWCNTs longer than 3.5 nm. The scale parameter in nonlocal beam and rod models is estimated by calibrations from MD results.     

Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid,Based on the Nonlocal Beam Model

Variational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.     

Stability of single-walled carbon nanotubes and single-walled carbon nanocones under self-weight and an axial tip force

Poorly designed structures buckle under the action of an unbearable axial force, self-weight or a combination of different axial forces. The increasing exploration of nanostructures for future devices dictates that the buckling of uniform single-walled carbon nanotubes (SWCNTs) and single-walled carbon nanocones (SWCNCs) should be well studied. Therefore in this paper, the investigation of the boundary value problems associated with the buckling of the SWCNTs and SWCNCs is carried out. The theoretical formulation of the mathematical model for these nanostructures is premised on the newly advanced nonlocal continuum theory. Predictions of the nN range critical loads of SWCNT and SWCNT under self-weight and an axial tip force are carried out with an optimized variant of the Galerkin method. The analysis reveals the degree of influence of the nonlocal parameter on the critical loads of the SWCNTs and the SWCNCs under different boundary conditions. A non-monotonically increasing trend is observed between the critical load values and increasing aspect ratio of the SWCNT. In the case of the SWCNC, the analysis reveals a positive linear relationship between the critical loads and the apex angles of the SWCNC. The apex angle also acts as a counterbalance to the small-scale coefficient.     

Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams

A class of higher-order continuum theories, such as modified couple stress, nonlocal elasticity, micropolar elasticity (Cosserat theory) and strain gradient elasticity has been recently employed to the mechanical modeling of micro- and nano-sized structures. In this article, however, we address stability problem of micro-sized beam based on the strain gradient elasticity and couple stress theories, firstly. Analytical solution of stability problem for axially loaded nano-sized beams based on strain gradient elasticity and modified couple stress theories are presented. Bernoulli–Euler beam theory is used for modeling. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. Both end simply supported and cantilever boundary conditions are considered. The size effect on the critical buckling load is investigated.     

Temperature effects on wave propagation in nanoplates

In this paper, the thermal effects on the ultrasonic wave propagation characteristics of a nanoplate are studied based on the nonlocal continuum theory. The nonlocal governing equations are derived for the nanoplate under thermal environment. The axial stress caused by the thermal effects is considered. The wave propagation analysis is carried out using spectral analysis. The influences of the nonlocal small scale coefficient, the room or low temperature, the high temperature and the axial half wave numbers on the wave dispersion properties of nanoplate are also discussed. Numerical results show that the small scale effects and the thermal effects are significant for larger half wavenumbers. The results are qualitatively different from those obtained based on the local plate theory and thus, are important for the development of graphene-based nanodevices such as strain sensor, mass and pressure sensors, atomic dust detectors, and enhancer of surface image resolution.     

A single variable shear deformable nonlocal theory for transversely loaded micro- and nano-scale rectangular beams

In this paper, a simple single variable shear deformable nonlocal theory for bending of micro- and nano-scale rectangular beams is presented. To incorporate small size effects, the theory uses Eringen’s nonlocal differential constitutive relations. The theory has only one fourth-order governing differential equation involving a single unknown variable. The governing equation and the expressions for the bending moment and shear force of the present theory are strikingly similar to those of nonlocal Euler-Bernoulli Beam Theory (EBT) formulated based on Eringen’s nonlocal elasticity theory. The theory assumes that the axial and lateral displacements have bending and shear components such that the bending components do not contribute towards shear force, and the shear components do not contribute towards bending moment. Also, the chosen displacement functions of the theory give rise to a realistic parabolic transverse shear stress distribution across the beam cross-section. Efficacy of the proposed theory is demonstrated through bending of simply supported, cantilever and clamped-clamped micro- and nano-scale beams of rectangular cross-section. The numerical results obtained by using the present theory are compared with those predicted by other nonlocal first-order and higher-order shear deformation beam theories. The results obtained are quite accurate.     

Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory

In this work, analytical solutions are presented for the wave propagation in functionally graded (FG) nanoplates using a nonlocal strain gradient theory and four-variable refined plate theory considering the magnetic field. The size effects are included using nonlocal strain gradient theory that has two length scale parameters, and the nanoplate is modeled as a plate using four-variable refined plate theory. From the knowledge of authors, it is the first time that the influences of magnetic field on the wave propagation in FG nanoplates are investigated based on present methodology.