功能梯度三相复合材料圆柱壳的非线性振动研究

论文研究了一种由环氧树脂、石墨烯纳米片、碳纤维制成的功能梯度三相复合材料圆柱壳的非线性振动响应.基于一阶剪切变形理论和von-Karman几何非线性关系,考虑到温湿效应、气动力和外激励的共同作用,利用Hamilton原理建立了两端固支圆柱壳的非线性偏微分运动方程.利用Galerkin法将非线性偏微分运动方程离散成一组相互耦合的二阶非线性常微分方程,利用伪弧长延拓法求解非线性常微分方程组,给出对应的幅频响应曲线.本论文中仅考虑湿度和外激励等参数的变化对新型三相复合材料圆柱壳结构非线性振动响应的影响,分析了湿度和外激励的变化对功能梯度三相复合材料圆柱壳共振响应的影响.     

功能梯度薄壁圆柱壳的自由振动

研究了由功能梯度材料制成的薄壁圆柱壳的自由振动.采用幂律分布规律描述功能梯度材料沿厚度的梯度性质,根据Donnell壳体理论,导出了功能梯度材料薄壁圆柱壳线性振动的简化控制方程.基于此理论分析了功能梯度圆柱壳的自由振动特性,给出了两端简支功能梯度材料薄壁圆柱壳小挠度固有振动的频率公式.以简支圆柱壳作为算例,与前人结果及有限元法对比验证了该简化功能梯度薄壁圆柱壳理论的正确性,同时讨论了周向波数及梯度指数对其频率的影响.     

旋转Timoshenko输流管道的固有频率和稳定性分析

基于Timoshenko梁模型,本文研究了旋转输流管道在自由振动状态下的流固耦合振动特性.考虑流体压力、重力、初始轴应力作用,基于Hamilton原理和欧拉角转换,推导得到了旋转Timoshenko输流管道的偏微分方程.根据Galerkin截断法将运动方程进行离散,通过求解系统的特征方程即可得到输流管一阶复频率的实部和虚部,实部代表固有频率,虚部代表能量变化.在流速较高时,研究发现必须考虑4阶及以上Galerkin截断,才能得到稳定的结果.通过与EulerBernoulli梁模型对比,验证了本文的结果正确性.研究发现针对短粗型管道,Timoshenko梁模型更加精确.此外研究了多种参数对旋转Timoshenko输流管道固有频率和振动稳定性的影响.研究结果表明质量比、流速、剪切系数对Timoshenko输流管道流固耦合振动的稳定性影响显著,而转动惯量、重力、流体压力和初始轴应力在一定程度上也会影响管道振动的频率和稳定性.转速的出现将管道频率分为两个量值,但转速并不影响系统能量变化.     

功能梯度三相复合材料圆柱壳固有振动特性分析

本文以一种石墨烯与碳纤维协同增强三相复合材料圆柱壳为研究对象,研究了在任意边界条件下该新型功能梯度三相复合材料圆柱壳的自由振动特性.首先,基于一阶剪切变形理论、Von Karman几何非线性关系和Hamilton原理,推导了三相复合材料圆柱壳结构运动控制方程.然后,应用Galerkin法离散求解三相复合材料圆柱壳的固有频率和模态振型.最后通过将本文方法与Abaqus仿真结果进行对比,验证了本文方法的准确性.此外,本文进一步分析了石墨烯质量分数、功能梯度形式和边界条件等不同因素对新型三相复合材料圆柱壳固有振动特性的影响.     

Spar平台月池水晃动的等效力学模型及模型参数研究

研究深海Spar平台月池水晃动的等效力学模型,确定模型参数.基于势流理论推导了月池内水体运动的动力学方程,建立了月池内水体晃动的等效单摆模型.采用ANSYS软件建立模型并进行网格划分,采用Matlab软件进行数值计算.运用Galerkin方法求解水体晃动的固有频率、模态函数以及势函数离散解,确定等效单摆模型的模型参数.对比分析了数值模拟结果与解析解,验证了本文计算方法的正确性.建立了不同月池水高度的等效力学模型参数库,为进一步研究平台-月池内流体的耦合运动奠定了基础.     

风力机叶片大挠度挥舞振动特性分析

分析了风力机叶片大挠度挥舞振动特性.基于Hamilton原理,建立了叶片大挠度挥舞振动控制方程,其中非稳态气动力由Greenberg公式得出.使用瑞利-利兹法求解振动特征问题,得到振动的频率和无阻尼模态函数.基于得出的模态函数,使用Galerkin方法将控制偏微分方程离散,得到模态坐标方程.将振动位移分解为静态位移和动态位移,得到了静态位移和动态位移方程,考查了入流速度比对静态位移和气动阻尼的影响,并对大挠度挥舞振动动态响应进行了分析,得到如下结论：大挠度挥舞振动静态位移沿叶片展向随入流速度比的增大而增大,叶尖处位移最大；当入流速度比较小时,振动为小振幅的周期运动,入流速度比较大时,振动为大振幅的拟周期运动.     

恒定磁场中简支圆柱壳的磁弹性振动分析

依据电磁场方程及相应的电磁本构关系,给出了作用于圆柱壳体上的电磁力及力矩表达式.在此基础上,分别推得了纵向和横向磁场中圆柱壳体的磁弹性轴对称振动方程.针对两端简支约束条件,通过位移函数的设定,得到了相应的有阻尼振动微分方程.通过算例,给出了系统衰减振动的响应曲线图和相图,分析了磁感应强度和壳体厚度对系统振幅衰减速度的影响.结果表明,通过改变磁感应强度可以达到控制系统振动的目的.     

求解Navier-Stokes方程的一类有限元有限体积迎风方法及其实现

Navier-Stokes方程是一类非线性的鞍点问题,在高Reynolds数流的情形下,标准Galerkin有限元方法会导致数值伪震荡.迎风有限元方法在算法结构上表征了流体＂上游＂决定＂下游＂的流动性态,它能够有效地消除高Reynolds数流的对流占优扩散所产生的非物理震荡.基于此,将Navier-Stokes方程的对流项采用有限体积框架下的迎风离散,对其它项仍使用Galerkin有限元离散,研究了二维定常Navier-Stokes方程的数值求解,编程藉助于有限元程序自动生成软件FEPG.通过对方腔流动和圆柱绕流问题与基准测试已有数值结果的比较,验证了所构造方法的可行性和有效性.     

轴向冲击下非线性弹性圆柱壳轴对称响应仿真

采用增量数值解法分析了轴向冲击下非线性弹性圆柱壳的轴对称响应。应力一应变关系采用Ramberg-Osgood表示法，运动控制方程采用Karman-Donnell变形方程。对时间积分采用变步长Runge-Kutta方法，对壳单元离散采用有限差分法来求解运动方程，并采用科学计算软件Matlab对计算结果进行了动态仿真。     

基于板单元形函数的公路桥梁车桥耦合振动分析方法研究

为研究公路多片式梁桥的车桥耦合振动问题,提出一种基于矩形薄板形函数的车桥耦合振动分析方法.该方法以车轮与桥面接触点为界,将车桥耦合系统分为汽车与桥梁2个子系统,分别采用虚功原理与有限元法建立各自的运动方程,并通过车轮与桥面接触处的位移协调条件及车桥相互作用力的平衡关系相耦合,采用矩形薄板形函数实现车桥接触点位移与桥梁节点位移的联系以及车桥相互作用力的分配,通过迭代求解汽车和桥梁的运动方程得到其动力响应.根据分析方法的计算流程,编制了汽车 桥梁耦合系统的动力分析程序,并通过算例分析验证其可行性.研究结果表明,使用基于矩形薄板形函数的公路桥梁车桥耦合振动分析方法得到的车桥动力响应具有较好的精度,该方法具有广泛的适用性,可为多片式梁桥的车桥耦合振动分析提供一种新思路.     

圆柱壳弹性波超材料分级排列的带隙拓宽方法研究

圆柱壳弹性波超材料的弯曲波带隙拓宽问题限制其满足实际工程中的宽频隔振要求,针对该问题,本文首先研究了基于局域共振机理的圆柱壳弹性波超材料弯曲波带隙特点,研究局域谐振器质量和弹簧劲度系数的关系,然后将周期分级排列的组合方式应用于圆柱壳类弹性波超材料的带隙拓宽中,并利用有限元法进行能带结构和振动传输特性计算.研究结果显示：该方法可实现弯曲波带隙的拓宽;利用组合法构建的轴向周期分级排列圆柱壳弹性波超材料可实现705-1226Hz频率范围内弯曲波的高效衰减,带隙拓宽至分别为单一谐振器的2.55倍,这表明该方法在宽频减振方面具有明显优势,应用前景广阔.     

A Ritz procedure for optimisation of cylindrical shells, formed by a nearly symmetric and balanced angle-ply composite laminate, with fixed minimum frequency

The paper deals with the problem of optimisation of a cylindrical shell profile under a frequency constraint. The minimum value of the thickness has been established a priori. The structure considered is typical of aerospace craft vessels.The same value of the lowest vibration frequency of the reference cylindrical shell with uniform thickness, has been imposed. That is the minimization procedure of the structure weight must not affect its lowest vibration frequency.Instead of the currently applied finite element method (FEM), Ritz series expansions have been utilized in the analytical developments both for the dynamic variables and for the thickness axial distribution over the shell surface. Lagrange multipliers, together with governing equations and objective function, have been utilized to form the Lagrangian functional, as in the classical Euler–Lagrange method. Imposing the stationary conditions with respect to the Lagrangian degrees of freedom gives a non-linear algebraic equations system, whose solution can be found with an appropriate algorithm.A series of repeated optimisation operations have been performed to arrive at the minimized weight profile, but with the pre-established minimum value of the shell thickness.A simplified nearly symmetric and balanced multilayer composite angle-ply laminate of the shell structure is supposed, as in the case of the uniform thickness reference shell, previously considered for the dynamic analysis. Significant results of some computation application cases can be helpful to evaluate the efficiency of the proposed optimisation procedure applied to cylindrical structures.     

横向流中细长圆柱的热弹性颤振

研究了细长圆柱体在热环境下的横向流致振动.应用迦辽金法将非线性运动控制偏微分方程离散为常微分方程组,首先分析了热载荷对系统临界流速的影响,然后采用数值方法得到了系统分岔区,以及它在参数空间的分布情况.应用分岔图、相图对系统的运动性质进行了判定.系统随着参数的变化呈现周期运动,温度增加,系统发生颤振的临界速度减小.当温度载荷不变时,流速增加,系统周期振动的振幅越来越大,系统发生极限环振动,周期3运动、拟周期运动和混沌运动.     

A coupled boundary element/finite difference method for fluid–structure interaction with application to dynamic analysis of outer hair cells

Outer hair cells (OHC) in the inner ear, which resemble fluid-filled and fluid-surrounded cylinders, are known to exhibit motility and play a critical role in our keen sense of hearing. In this study, we investigate the OHC frequency response using a mathematical model of the OHC, which consists of a two-layered anisotropic cylindrical lateral wall, and both the intracellular and extracellular fluids. We use the boundary integral equations to model the intracellular and extracellular fluids, and these are coupled to the anisotropic cylindrical shell equations (discretized using the finite difference method). Since the geometry is axisymmetric, the dynamic analysis is performed by decomposing the motion into Fourier modes in the circumferential direction. For the boundary element method, this leads to two sequences of line integrals along the generator of the domain, and the singular kernels need to be evaluated with elliptic integrals. The coupled fluid–structure equations are solved for several modes of deformation (axisymmetric, cylindrical beam-bending, and pinched modes), and the frequency responses are obtained. The frequency response of the model with viscous fluid is found to be significantly different from that using inviscid fluid. For the small length scale of the OHC (which is of micron size), the viscosity of the fluid is found to have significant damping effects on the OHC frequency response.     

Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners

The effect of the boundary conditions on the natural frequencies for rotating composite cylindrical shells with the orthogonal stiffeners is investigated using Love’s shell theory and the discrete stiffener theory. The frequency equation is derived using the Rayleigh–Ritz procedure based on the energy method. The considered boundary conditions are four sets, namely: (1) clamped–clamped; (2) clamped–simply supported; (3) clamped–sliding; and (4) clamped–free. The beam modal function is used for the axial vibration mode and the trigonometric functions are used for the circumferential vibration mode. The composite shells are stiffened with uniform intervals and the stiffeners have the same material. By comparison with the previously published analytical results for the rotating composite shell without stiffeners and the orthogonally stiffened isotropic cylindrical shells, it is shown that natural frequencies can be determined with adequate precision.     

The response behaviour of a submerged cylindrical shell using the doubly asymptotic approximation method (DAA)

This paper presents experimentally measured and theoretically calculated responses of a flexible cylindrical shell subjected to an impulsive excitation in air and in water. The flat-ended, thin cylindrical shell of overall length 1284 mm, external radius 180 mm, thickness 3 mm is made of mild steel. The predicted responses are derived from a method using the doubly asymptotic approximation (DAA) models in order to uncouple the motion of the fluid from that of the structure. The DAAs enable the radiated pressure to be specified in terms of surface motion of the structure. The method, which employs the DAAs, is applied to determine the responses, i.e. acceleration, velocity and displacement, of the finite length cylindrical shell excited by an impulsive mechanical force. The calculated acceleration responses are compared with the experimental measurements.     

A semi-analytical coupled finite element formulation for shells conveying fluids

A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid–structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed.     

微重力环境下刚液耦合系统液体晃动混沌现象研究

微重力下,柱形贮箱内液体晃动的速度势模态和表面位移模态难以解析表达,为揭示液-刚耦合运动的非线性特性,不失一般性地用常重力下液体晃动的速度势模态和表面位移模态近似表示微重力下液体晃动的速度势模态和表面位移模态.用泰勒级数展开法分析了微重力下柱形贮箱内的液体晃动,运用Lagrange方法导出了微重力下贮箱内液体与结构耦合系统的无量纲动力学方程组,并用Matlab软件对该方程组进行数值计算,发现当系统稳定时,面内、外模态分别具有同类的稳态动力学行为,包括静止、周期运动、准周期运动和混沌运动;在不同的外激励参数下,面内、外模态的稳态动力学行为发生变化.     

变速旋转圆柱薄壳动力稳定性研究

本文开展了变速旋转圆柱薄壳动力稳定性研究.基于Donnell薄壳理论建立同时考虑变转速和周期 轴向力的圆柱壳体振动微分方程;采用多尺度方法,推导系统主参数不稳定区和组合不稳定区边界的解析 表达式;分别探讨仅考虑周期轴向力、仅考虑变转速以及同时考虑两种时变因素时,系统主参数不稳定区和 组合不稳定区的变化规律;通过与文献结果以及数值结果的对比,验证了解析结果的准确性.