Nonlinear supersonic flutter of truncated conical shells

A numerical model was developed to investigate the flutter instability of truncated conical shells subjected to supersonic flows. The exact solution of Sanders’ best firstorder approximation was used to develop the finite elements model of the shell. Nonlinear kinematics of Donnell’s, Sanders’ and Nemeth’s theories, in conjunction with the generalized coordinates method, were used to formulate the nonlinear strain energy of the shell. A pressure field was formulated using the piston theory with the correction term for the curvature. Lagrangian equations of motion based on Hamilton’s principle were obtained. A variation of the harmonic balance method was used for developing the amplitude equations of the shell, and a numerical method was used for solving these equations. Results of linear and nonlinear flutter of truncated conical shells were validated against the existing data in the literature. It was observed that geometrical nonlinearities have a softening effect on the stability of the shell in supersonic flows.     

一种有效消除超声测量拖尾的新方法

本文介绍了一种消除超声波拖尾的方法，从超声波的波动原理和压电陶瓷的振动机理入手，推导出压电陶瓷的振动方程，分析了产生拖尾的原因和影响超声波拖尾周期、幅值和持续时间的各因素，利用波的叠加原理提出一种叠加消除法来消除超声波拖尾，计算机软件模拟达到了完全消除拖尾的理想效果。实验中，叠加消除法使超声波拖尾的幅值衰减率达到90％，对近距离测晕不造成影响，达到了消除拖尾影响的目的。理论和实践证明，叠加消除超声波拖尾方法简单易行、效果显著，具有很高的实用价值。     

Neural potentials and micro-signals of non-linear deep and shallow conical shells

Conventional sensors, such as proximeters and accelerometers, are add-on devices usually adding additional weights to structures and machines. Health monitoring of flexible structures by electroactive smart materials has been investigated over the years. Thin-film piezoelectric material, e.g. polyvinylidene fluoride (PVDF) polymeric material, is a lightweight and dynamic sensitive material appearing to be a perfect candidate in monitoring structure's dynamic state and health status of flexible shell structures with complex geometries. The complexity of shell structures has thwarted the progress in studying the distributed sensing of shell structures. Linear distributed sensing of various structures have been studied, e.g. beams, plates, cylindrical shells, conical shells, spherical shells, paraboloidal shells and toroidal shells. However, distributed microscopic neural signals of non-linear shell structures has not been carried out rigorously. This study is to evaluate microscopic signals, modal voltages and distributed micro-neural signal components of truncated non-linear conical shells laminated with distributed infinitesimal piezoelectric neurons. Signal generation of distributed neuron sensors laminated on conical shells is defined first. The dynamic neural signal of truncated non-linear conical shells consists of microscopic linear and non-linear membrane components and linear bending component based on the von Karman geometric non-linearity. Micro-signals, modal voltages and distributed neural signal components of two different truncated non-linear conical shells are investigated and their sensitivities discussed.     

Influence of initial pressure on frequency characteristics of a rotating truncated circular conical shell

As a new global numerical approximate technique, the generalized differential quadrature (GDQ) method is used in this paper to study the influence of initial pressure load on the free vibration of a rotating thin isotropic truncated circular conical shell. The present motion governing equations include the influence of initial stress field due to the initial uniform pressure. The effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation are also considered. The influence of initial pressure on the frequency characteristics of the rotating conical shell is discussed in detail. For the examination of present work, frequency numerical comparisons are made with those available in published works, and very good agreement is achieved.     

机电非线性振动系统参、强联合激励的分岔

建立机电耦联非线性电机模型的数学方程：利用非线性振动理论中的非固定参数的渐近法，研究由电磁力激发的参数激励、强迫激励联合作用下非线性振动系统的动力学特性，由理论分析、数值计算得到系统的分岔转迁集和四种分岔响应曲线。在实验的基础上揭示各种电磁参数及机械参数对主参数共振的振幅、运动稳定性及共振曲线的拓扑结构的影响，同时显示系统的运动状态及其稳定域，分析结果为有效地控制电机的稳定运行提供依据。     

Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells

Non-linear buckling analyses of imperfect functionally graded truncated conical shells with simply supported boundary conditions and subjected to an axial compressive load have been presented in this work. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The non-linear prebuckling deformations and initial geometric imperfections of an FGM truncated conical shell are both taken into account. The fundamental relations, modified Donnell type non-linear stability and compatibility equations of an imperfect FGM truncated conical shell are obtained and are solved by superposition and Galerkin methods, and the upper and lower critical axial loads has been found analytically. The numerical illustrations concern the non-linear buckling response of FGM truncated conical shells with different values of truncated conical shell parameters, initial imperfections and compositional profiles. Comparing the results of this study with those in the literature validates the present analysis.     

复合结构研齿换能器的动力学特性与设计

利用4段复合式变幅杆及夹心式压电陶瓷换能器的结构,研制了一种用于超声辅助研磨弧齿锥齿轮的新型换能器。首先,根据牛顿定律和超声波传输线理论,推导得到了超声研齿换能器的频率方程,依据压电陶瓷的谐振频率、振动模式和输入功率,确定了复合式超声研齿换能器的结构参数;其次,运用等效声学参数修正法和质量互易法,对设计的换能器进行了声学和结构参数的修正;然后,利用ANSYS分析软件进行了模态分析和谐响应分析,对换能器的谐振频率、振动幅度、振动速度比和导纳等动力参数进行了研究;最后,进行了阻抗特性测试和振动特性实验和通过5对弧齿锥齿轮的超声研磨实验,进一步证实了复合结构研齿换能器的超声研磨性能。     

摩擦自激系统的分岔控制研究

研究应用Washout滤波器技术对摩擦系统自激振动的分岔控制.首先确定需要引入的Hopf分岔点,然后按Hopf分岔条件确定滤波器的线性增益和非线性增益系数,将系统的亚临界Hopf分岔变为超临界Hopf分岔,使受控系统产生的自激振动幅值大大降低.理论分析和数值仿真表明Washout滤波器法在分岔控制中的有效性.     

旋转机械耦合传动系统参激振动分析与控制

以一类旋转机械传动系统的扭振为研究对象,考虑轴系时变刚度变化和非线性摩擦阻尼力的影响,根据Lagrange原理建立了一类旋转机械传动系统的耦合非线性动力学方程,利用多尺度方法推导出了系统的平均方程,并根据Hopf分岔理论给出了系统发生Hopf分岔的充要条件及周期运动稳定性的判别方法,分析了参数共振和内共振条件下系统的分岔特性。为抑制传动系统因亚临界Hopf分岔引起的失稳振荡,引入非线性反馈控制,对系统的Hopf分岔点进行转移并控制周期运动的稳定性和幅值。研究结果为非线性旋转机械参激振动的分析及控制提供了有效方法。     

Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator

Shell type components and structures are very common in many mechanical and structural systems. Modeling and analysis of adaptive piezothermoelastic shell laminates represent a high level of sophistication and complexity. In this paper a finite element model is developed for the active control of thermally induced vibration of laminated composite shells with piezoelectric sensors and actuators. The present model takes into account the mass, stiffness and thermal expansion of the piezoelectric patches. A C_o continuous nine-node degenerated shell element is implemented to model the structure. The piezoelectric sensing layer senses the structural vibration and a suitable voltage applied in the piezoelectric actuator layer suppresses the oscillation. Actuator and sensor are coupled together with a control algorithm so as to actively control the dynamic response of the structure in a close loop. Numerical results are generated for a cylindrical shell and it is observed that thermally induced vibration of a laminated cylindrical shell can be suppressed through the application of piezoelectric sensor and actuator. Effects of variation in control gain and piezoelectric layer area coverage (PAC) have been studied. Higher control gain is more effective in damping out the vibration. Although the damping is enhanced by increase in PAC, increase beyond a certain level may not be useful in view of smaller efficacy and increased weight.     

时滞阻尼液固混合介质隔振系统的动力学研究

针对单一线性阻尼被动隔振无法兼顾共振区与隔振有效区的隔振性能问题,提出了时滞立方非线性主动阻尼控制策略。以具备分段线性刚度液固混合介质受控隔振系统为研究对象,运用多尺度摄动法对受控系统进行主共振分析,建立了等效刚度和等效阻尼的概念,并考察时滞对受控系统幅频特性与传递率特性的影响。研究结果表明:由于主动时滞的引入,立方非线性速度反馈增益既可调控阻尼,还可以调整隔振系统的等效刚度;与单一线性阻尼相比,立方速度反馈在不改变隔振有效区隔振效果的同时,显著降低了共振区的传递率;对于因鞍结分岔在主共振造成的幅值跳跃,通过选择合适的反馈时滞可以有效抑制跳跃的出现;通过稳定性分析发现,受控系统并非是全时滞稳定,因此最后给出控制器中反馈增益和时滞的参数区间设计方法。     

Winkler地基上四边自由矩形薄板的亚谐共振与奇异性分析

研究Winkler地基上四边自由矩形薄板的亚谐共振问题.按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程.利用Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法求得系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算.分析激励、阻尼等对系统响应曲线的影响.应用奇异性理论对1/3次亚谐共振幅频响应方程进行奇异性分析,得到选取不同分岔参数时开折参数平面的转迁集和分岔图.     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

基于钻头-岩石碰撞的激振冲击系统的非线性动力学研究

为了提升旋转冲击钻井过程中轴向冲击的辅助破岩效果,设计了一套用于测试钻头与岩石之间激振碰撞的试验装置,通过对钻头的激振频率、激振振幅和施加的静态压力3项可控参数的调节,研究了该激振冲击系统的动力学行为演化规律,且试验测试结果与数值模拟结果具有很好的一致性。通过进一步的分岔分析和相平面分析发现,由于激振冲击系统具有典型的接触非线性结构,其动态响应也呈现出复杂的非线性特征,钻头在与岩石发生激振碰撞后,主要保持单周期的振动状态,但随着控制参数的变化,钻头与岩石之间在一个激励周期内的碰撞次数会不断改变;此外,钻头的振动状态还会经由倍周期分岔转变为双周期振动,但最终又会经由逆倍周期分岔或者折叠分岔重新回到单周期振动状态。由于钻头的振动状态直接决定了其轴向冲击力的大小,因而会影响其破岩效率;因此,为了获得破岩效率最高的一周期一次碰撞的钻头振动状态,应该采用较高的激振频率和振幅,但应该避免较高的静态压力,因为它将触发钻头的颤振,反而降低其破岩效率。     

基于Taylor变换法的转子系统分岔与稳定性研究

对双盘转子系统的非线性动力学模型，引入求解非线性微分方程的Taylor变换法，分析转子振动系统动力学特性以及激振频率等参数对系统的影响，利用非线性动力学分析中的打靶法求该系统的周期解，并利用Floquet主导特征乘子判断不同周期轨道的失稳方式。结果表明，考虑非线性油膜力影响后，转子系统的运动状态随转速增加由周期至二倍周期再至周期再至拟周期，或者经周期运动直接至混沌运动．不平衡质量影响转子系统的分岔阈值和分岔类型，阻尼对分岔阈值和系统的运动稳定性有一定的影响。     

考虑螺栓联接结构的轴承-转子系统振动特性分析

针对含螺栓联接结构的轴承-转子系统,建立考虑陀螺力矩及因螺栓预紧力不均匀产生的初始变形量的非线性转子系统动力学模型。采用法求解转子系统运动方程,通过分岔图、时域曲线、频谱及Poincaré映射图研究存在轴承游隙时转子系统的混沌路径,并分析不同初始变形量及轴承游隙对转子系统非线性振动特性的影响,通过试验验证所得结论的准确性。研究表明,当存在轴承游隙时,预紧力不均匀产生的初始变形量增加会抑制低转速下盘的混沌运动,拟周期运动进入混沌运动状态的转速升高,临界转速附近的振动幅值增加,系统混沌路径发生变化;存在初始变形量时,随着轴承径向游隙增大,系统在低转速工作状态下即进入混沌运动运动状态,拟周期运动进入混沌运动状态的转速降低。研究结果可为含螺栓联接结构的轴承-转子系统设计提供理论参考。     

有挤压油膜阻尼器支承的多故障转子系统的非线性特性研究

研究了有挤压油膜阻尼器、转子与静子碰摩和转轴上的横向裂纹等多种非线性因素作用下的转子系统的非线性响应特征。数值研究发现 ,这类转子系统具有丰富的非线性特性 ,三条通向混沌的道路都存在 ,即阵发性通向混沌、倍周期分叉通向混沌和拟周期通向混沌的道路。系统响应的最大振幅曲线包含了大量的跳跃现象 ,发生这些跳跃所对应的参数点与周期解分叉的参数点相重合 (以前已经发现了这种跳跃现象 ,但没有发现与周期解分叉有关系 )。保持不平衡参数在一个小区间内能够使系统抑制多种故障引起的振幅 ,并使系统能够保持稳定的周期一解。较大的挤压油膜阻尼器参数对系统的振动有明显的抑制作用。当裂纹正方向与不平衡方向成反方向时 ,系统具有最小的振动幅度。     

外部激励下行星换向机构的分岔及混沌

为分析行星换向机构在动态外部激励即转速和扭矩作用下的分岔及混沌特性,建立了该行星系统的非线性扭转振动模型。采用变步长4-5阶Runge-Kutta算法对动力学方程进行数值求解,根据仿真结果绘制了系统分岔图,并结合典型工况下的相图和庞加莱截面图,得到系统响应随外部激励的变化历程。另外,借助混沌时间序列分析理论,计算最大Lyapunov指数,对系统是否处于混沌状态进行判定。结果表明:在一定的扭矩作用下,随着转速的增大,系统在较长范围内维持单周期运动状态,但在共振频域附近因啮合冲击的出现而产生频繁的分岔行为、振幅跳跃及状态突变,且期间出现了倍周期、拟周期等状态以及状态之间的交替现象,并最终由周期状态突变为混沌状态;与此相反,扭矩的增大对系统随转速增大而进入混沌状态的趋势有一定的抑制作用,且扭矩增大至一定程度时可使系统由混沌状态退化为单周期运动状态。     

被动隔振体的hopf分岔分析

本文建立了被动隔振体的非线性动力学方程。根据非线性振动理论,设立系统在弱非线性情况下的一次谐波解,通过平均法先求得系统的一次谐波的振幅随时间的变化方程,然后通过分析一次谐波的振幅发生hopf分岔的条件得到了被动隔振体系统发生hopf分岔的条件。     

液压缸非线性弹簧力下的轧机特性及控制

建立了非线性弹簧力约束作用下的轧机辊系振动模型,采用平均法求得轧机辊系的幅频响应方程。仿真分析了不同非线性弹簧力和活塞杆初始位移的幅频特性曲线,以及系统分岔响应随外激励幅值的变化规律。引入吸振器控制装置,比较了吸振器加入前后的时域曲线和幅频曲线,仿真分析了吸振器质量、弹簧力和摩擦力对幅频曲线的影响。研究结果表明：非线性弹簧力和外激励都会改变轧机辊系振动特性的规律,吸振器的控制效果与吸振器质量、弹簧力和摩擦力有关。