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.     

基于有限差分法的端部约束同轴圆柱壳的流致失稳分析

本文基于经典壳体和理想势流理论建立圆柱壳流固耦合系统的运动方程,并引入有限差分法(FDM)对运动方程进行离散.为将壳体表面的扰动压力离散到差分网格节点,基于差分离散的原理,提出了以分段函数作为基函数的展开方法.本文对结构与压力控制方程均采用FDM方法进行求解,发展了一种基于FDM的同轴圆柱壳流固耦合求解策略.首先,利用本文方法计算了同轴圆柱壳在静态流体环境中的振动频率,并与有限元软件(ANSYS)的计算结果相比较,验证了本文方法的正确性；然后,探究了在静流体环境中同轴圆柱壳的结构参数变化对其振动频率的影响规律；最后,研究了同轴圆柱壳系统在运动流体环境中的流弹失稳问题.     

高灵敏度圆柱壳体振动陀螺的研究

灵敏度是陀螺的重要性能指标,灵敏度的提高可以直接带动精度提高,同时可以拓展陀螺的应用范围。影响圆柱壳体振动陀螺灵敏度的因素很多,本文通过考虑了科里奥利效应(Coriolis effect)的ANSYS谐响应分析,提取产生陀螺效应的圆柱壳体振动陀螺的输出位移,通过比较不同形状谐振子相同激励条件下的输出位移大小来反映灵敏度的大小。采用这种方法分别研究谐振子的各项参数对于陀螺灵敏度的影响规律,并基于仿真结果设计了高灵敏度的参数优化圆柱壳体振动陀螺谐振子,通过实验验证了该谐振子的高灵敏度。     

格栅夹层板抑振性能研究

为了有效降低铺板与圆柱壳体耦合结构中因铺板振动而引起的壳体振动,提出了以格栅夹层板作为一种铺板结构.以格栅夹层板安装于带有端板的圆柱壳体上作为研究模型,采用有限元软件对格栅夹层板的抑振性能展开了仿真分析,讨论了格栅结构参数对其抑振效果的影响,并实验验证了格栅夹层板的抑振效果.仿真和实验结果一致表明：格栅夹层板能有效降低圆柱壳体的振动响应,尤其是在中高频段抑振效果显著；格栅的结构参数对抑振效果影响规律比较复杂,格栅夹层的上层面板采用阻尼较大的材料利于提高其抑振效果.     

基于阶梯掩膜腐蚀的圆柱壳体振动陀螺谐振子的亚表面残余应力测试与分析

圆柱壳体振动陀螺是一种具有较高精度的金属振动陀螺,陀螺谐振子表面经过加工后会留下残余应力,对其性能影响较大。但目前国内外对圆柱壳体振动陀螺的表面和亚表面应力情况还缺乏深入的研究,针对圆柱壳体振动陀螺振动器件谐振子的几何结构和加工工艺特点进行研究,建立了谐振子切削加工的仿真模型,仿真分析了谐振子的亚表面残余应力的分布规律,并提出一种阶梯掩膜化学腐蚀的方法,对亚表面残余应力进行测试和分析,获得谐振子亚表面应力的分布规律,对实现谐振子的低应力制造和降低残余应力对圆柱壳体振动陀螺零偏稳定性的影响具有较好的指导意义。     

磨粒形态对滑油屑末监测器输出特性的影响

滑油屑末传感器基于磁场微平衡技术,能定量区分铁磁性和非铁磁性颗粒,可以为大型旋转部件健康监测提供重要数据.基于COMSOL建立有限元模型,分析了微平衡磁场下不同椭球磨粒和圆柱磨粒磁化场,并采用ANSYS Maxwell建立滑油屑末传感器模型,研究了不同长径比圆柱磨粒通过滑油屑末传感器时信号强度的变化.结果 表明,铁磁性颗粒经过平衡磁场时,轴线位置上磨粒中心处磁感应强度最大,随着离中心点距离增加磁感应强度衰减;切线位置上磁感应强度随着空间位置变化而改变,在切点处最小.对于不同的铁磁性颗粒形态,当磨粒体积相同时,长径比越大磁感应强度越大,信号强度越大.同时,搭建了滑油屑末测试系统,验证了有限元分析结果的正确性.     

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.     

电磁与机械载荷作用下导电梁式板的超谐波共振

研究了电磁与机械载荷共同作用下梁式薄板的非线性超谐波共振问题．在给出薄板的电磁弹性运动基本方程及电磁力表达式的基础上,推得了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程;应用伽辽金积分法,进一步导出了相应的非线性振动控制微分方程．采用多尺度法进行求解,得到了稳态运动下的幅频响应方程．最后,通过算例,给出了相应的幅频响应曲线图和时间历程图,分析了板厚、磁场及激励幅值对系统振动的影响．     

考虑双向振动耦合效应的声发射传感器的分析

由于声发射传感器属于低频超声传感器,其压电晶片工作频率决定了晶片的尺寸,使其不能简化为一维或二维弹性体来分析,考虑其径向和纵向振动不可忽视的耦合效应,借用表观弹性常数的定义,给出了短圆柱压电晶片包含直径和长度尺寸的频率方程。并根据频率方程制作了相应压电晶片,实验测试结果和理论预期相符。     

多物理场仿真开关磁阻电机定子的径向电磁振动

由于双凸极结构及磁饱和特性,开关磁阻电机较它型电机有较大的径向振动.通过多物理场仿真方法,开展定子壳体径向电磁振动耦合仿真.先通过二维电磁场有限元,分别在三相和六相工作模式下,计算额定转速下电机各定子齿所受径向电磁力密度的时程.再利用定子振动特征方程,进行了定子的模态分析.最后,将电磁力密度施加到相应定子齿作为外部激励,通过瞬态结构场分析获得了定子壳体的整体变形,以及关键节点加速度在时域和频域的振动特性.结果表明,在三相模式下,正方变形模态是壳体的典型振型;在六相模式下,椭圆变形是壳体振动的典型振型.正方变形时的加速度幅值要小于椭圆变形.该工作能从振动方面指导开关磁阻电机工作模式的选择和优化.     

磁约束阻尼悬臂壳的轴对称振动分析

提出了一种新型有效的方法来降低悬臂壳的轴对称振动．该方法的原理是在约束层端部上及固定端分别设置引力排列的永磁体,振动时磁体间的动态磁力可使阻尼层获得比传统约束阻尼处理方法更高的剪应变,阻尼层耗能增加,从而降低结构的共振峰．从夹层单元微元体受力分析出发,建立了局部磁约束悬臂壳的轴对称振动分析模型,得到分别用约束层纵向位移u30、积分常数c和径向位移w表示的夹层壳体单元的纵向和周向力平衡方程．在此模型中,考虑了振动时因u30引起动态磁力的变化,使得此模型能描述MCLD结构的动态及阻尼性能．此外,通过比较MCLD处理与传统的约束阻尼处理对磁约束悬臂壳的轴对称振动的控制效果,分析表明：磁约束处理可同时控制悬臂壳前几阶模态的振动．     

A new energy harvester using a cross-ply cylindrical membrane shell integrated with PVDF layers

In this paper, we proposed a smart cylindrical membrane shell panel (SCMSP) model for vibration-based energy harvester. The SCMSP is made of an orthotropic elastic core covered by outer PVDF layers with transverse polarization vector. Electrodynamics governing equations of motion are derived by applying extended Hamilton’s principle. The governing equations are based on Donnell’s linear thin shell theory. The SCMSP displacement fields are expanded by means of double Fourier series satisfying immovable edges with free rotation boundary conditions and coupled system of linear partial differential equations are obtained. The discretized linear ordinary differential equations of motion are obtained using Galerkin method. The output power is taken as an indicating criterion for the generator. A parametric study for MEMS applications is conducted to predict the power generated due to radial harmonic ambient vibration. Optimal resistance value is also obtained for the particular electrode distribution that gives maximum output power. A low vibration amplitude (5?Pa), and a low-frequency (471.79?Hz) vibration source is targeted for the resonance operation, in which the output power of 0.4111?μW and peak-to-peak voltage of 0.2952?V are predicted.     

A geometrically nonlinear shell finite element for tire vibration analysis

An axisymmetric finite element is developed which includes such features as orthotropic material properties, doubly curved geometry, and both the first and second order nonlinear stiffness terms. This element can be used to predict the equilibrium state of an axisymmetric shell structure with geometrically nonlinear large displacements. Small amplitude vibration analysis can then be performed based on this equilibrium state. The nonlinear path is predicted by using the self-correcting incremental procedure and any point on the path can be checked by using the Newton-Raphson iterative scheme. The present formulation and solution procedure are evaluated by analyzing a series of examples with results compared with alternative known solutions. Examples include: free vibration of an isotropic cylindrical shell, a conical frustum, and an orthotropic cylindrical shell; buckling of a cylindrical shell; large deflection of a clamped disk, a spherical cap, and a steel belted radial tire. The final example is a free vibration analysis of the inflated tire and the natural frequencies obtained compared well with published experimental data.     

An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends

In this paper, a new exact solution based on the classical shell theory (CST) for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends is proposed. The present exact solution can be summed up in the following steps: Firstly, the displacement functions are constructed by the governing differential equations with the exact closed form solutions; Then, the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell; Thirdly, the equation for natural frequencies is obtained by means of the method of reverberation-ray matrix (MRRM); Lastly, the vibration results are presented by the modified golden section search (MGSS) algorithm. By comparing the present method with published papers, the accuracy of present method is verified. On the basis of that, some new exact nature frequencies and mode shapes of the cross-ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future.     

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.     

Linear programming and limit analysis of shell roofs

Limit analysis for cylindrical shell roofs has been formulated as a linear programming problem based on lower bound theorem. The differential equations of equilibrium for a circular cylindrical shell element are transformed into algebraic equations by finite differences. The equilibrium equations and the linearized non-linear yield conditions at various points of the shell are linear functions of the stress resultants. These form the linear constraints of the problem. The load parameter is taken as an objective function and it is maximized using revised simplex method. For a shell of given geometry, stress resultants at various points are obtained to give the optimum collapse load. Thus the versatile technique avoids various trial solutions to achieve best lower bound for complicated shell problems.     

Optimal design of dynamic absorbers on vibration and noise control of the fuselage

Optimum design of dynamic absorbers for reducing the vibration and the interior noise of an aircraft’s fuselage is studied. Herein, a thin, elastic cylindrical shell is adopted as a simple model of the fuselage. The sound source of the noise in the acoustic field comes from the vibration of the shell. Several dynamic absorbers are then attached to the shell for vibration and noise control. The vibration of the shell and its interior sound pressure, caused by the propellers or the engines are formulated. Optimum design of the absorbers is studied for obtaining the minimum vibration of the fuselage or the minimum noise level in the cylindrical cavity. From the numerical results, the absorbers are found to be effective for vibration and noise control of the fuselage. Some general guidelines on optimum absorber design are also offered in conclusion.