超磁致伸缩薄膜悬臂梁的非线性振动特性试验研究

超磁致伸缩薄膜(GMF)的振动特性是决定其驱动性能的重要因素。针对研制出的Cu基双层GMF(TbDyFe/Cu/SmFe),测量并分析了其磁致回线、矫顽力等磁化特性。在此基础上,采用基于激光位移传感器的薄膜振动特性试验装置,研究了Cu基GMF悬臂梁在低频低磁场下的振动特性,结果表明,Cu基GMF悬臂梁具有10阶超谐波共振特性,二、三阶超谐波共振的峰峰值均在35μm以上,且其一阶主共振呈现明显的"软弹簧"特征。最后,给出了直流偏置磁场和交流驱动磁场对Cu基GMF共振频率和振动幅值等驱动性能的影响规律,为设计开发低频低磁场驱动的GMF微执行器和微传感器提供试验参考。     

非轴对称载荷作用下圆柱薄壳的解析解

求解非轴对称载荷作用下圆柱薄壳的变形及应力状态问题,在工程中普遍存在。将电磁轨道发射装置中的发射管外壁,在工作状态下简化为非轴对称载荷作用下有限长的圆柱薄壳;给出了分析变形与应力状态的基本方程;在设定载荷及位移函数的基础上,应用Galerkin法求得了应力与位移的解析解;通过具体算例,将所得的计算结果与Ansys数值解进行了对比分析,验证了解析解的正确性。研究结果可供圆柱薄壳非轴对称问题的理论求解和相应的工程设计参考。     

齿轮系统谐波共振的多尺度分析方法

考虑齿轮啮合动态刚度、传递误差、齿侧间隙等非线性因素,将时变刚度按5次谐波展开,齿侧间隙按3次多项式拟合,运用多尺度方法分析了单对直齿轮传动系统的谐波共振响应特性,讨论了系统在非共振硬激励下消去长期项的条件,给出了系统中存在的多种频率因子,发现了系统中存在2阶、3阶超谐波共振和1／2阶、1／3阶次谐波共振,推导了稳态振动下的频率响应方程,并绘制了频率响应曲线,分析了静态激励、动态激励、参数激励以及系统中阻尼对稳态响应的不同影响作用。     

悬垂缆线的非线性振动

研究了在曲线平面内受到简谐激励力作用下的悬垂缆线的非线性振动。用Hamilton原理导出悬垂缆线面内运动的非线性偏微分方程。通过假设悬垂缆线的挠度曲线,运用Galerkin方法将偏微分方程转化为常徽分方程．用多尺度法研究悬垂缆线的主共振、超谐波共振和次谐波共振,得到了系统的定常周期解,平均方程和幅频曲线。研究了非线性对幅频曲线的影响和定常运动的稳定性。研究表明,由于非线性,系统不仅有激励频率接近固有频率的主共振,而且还会出现激励频率接近固有频率整数倍或分数倍的次谐波共振和超谐波共振。     

超磁致伸缩薄膜悬臂梁的非线性变形分析及试验

将双层超磁致伸缩薄膜(Giant magnetostrictive thin film,GMF)悬臂梁的磁致伸缩作用等效为分布弯矩作用,以简化磁机耦合模型。在几何非线性弹性变形理论基础上,根据哈密顿原理推导出超磁致伸缩薄膜非线性变形的控制方程,并给出超磁致伸缩薄膜悬臂梁静态几何非线性变形模型、非线性主共振和超谐波共振响应模型。采用悬臂梁式超磁致伸缩双层膜(铽镝铁—聚酰亚胺—钐铁)进行变形特性的试验研究,发现超磁致伸缩双层膜表现出明显的几何非线性变形特征,悬臂梁端部位移量约为厚度的2/3;同时检测到悬臂梁的超谐波共振现象,前三阶超谐波共振的驱动效率与一阶主共振的驱动效率具有可比性。将所提出的静态非线性变形模型和振动响应模型分别与试验结果对比发现,两个模型可较好地说明双层超磁致伸缩薄膜的非线性变形特性,为有效地利用超磁致伸缩薄膜设计开发微驱动器和微传感器提供依据。     

基于HB-AFT方法的不对中转子系统超谐共振分析

考虑球轴承的非线性支承力和联轴器不对中的影响,建立含套齿联轴器的偏盘转子系统动力学模型,研究系统在转子不平衡激励和联轴器不对中激励共同作用下的非线性响应特性。针对具有分段和分数指数强非线性特性的动力学方程,采用谐波平衡法-时频域转换技术(HB-AFT)求得系统的周期解,并与数值积分结果进行对比,证明HB-AFT方法的有效性。结合弧长延拓方法和Floquet理论分析转子系统的超谐波共振特性,在低速区发现若干超谐波共振区域,其中以第三次超谐波共振较为明显。在高速区发现二次超谐波共振,共振曲线具有明显的硬弹簧特征且上翘,共振峰值较大,容易发生剧烈的振动突跳行为,给转子系统造成冲击和损害。探讨轴承间隙、轴承阻尼、不对中和外加载力(定常载荷)对超谐波共振曲线的影响规律,为控制策略的制定提供了一定的参考依据。     

立式凝结水泵次谐波结构共振故障诊断及处理

立式凝结水泵在变频运行状态下普遍存在结构共振的问题,总结了该类故障的抑制措施及效果。常规的凝结水泵共振,主频率都是工频,机械缺陷引发的低频振动较为少见。某两台凝结水泵出现了低频主导的振动超标故障,全面测试分析后,发现振动信号中的次谐波频率与结构固有频率存在合拍特征,诊断为次谐波振动引发的结构共振,解析了低频振动来源于轴承缺陷,通过检查证实了诊断的正确性,有效地处理了凝结水泵次谐波共振故障。     

横向磁场中矩形导电薄板的内共振特性分析

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,得到横向磁场作用下矩形薄板的磁弹性振动方程。针对一边固定三边简支的矩形薄板,通过位移模态展开并利用Galerkin法分离时间和空间变量,得到两自由度内共振非线性振动微分方程。采用多尺度法对模态方程组进行求解,得到了系统1∶3内共振情况下前两阶振动模态相互耦合的特征方程。通过算例,得到了关于系统内共振幅值的时程响应图和相图,分别讨论了无阻尼情况下系统初值、板厚以及有阻尼情况下磁场强度对内共振特性的影响,结果表明系统呈现明显的非线性内共振特征。     

磁场中轴向运动导电板磁弹性主共振分析

给出轴向运动薄板动能、应变能以及电磁力虚功的表达形式。应用哈密顿变分原理,推得横向磁场中轴向运动条形导电薄板的非线性磁弹性振动方程。针对对边简支边界约束条件,通过位移函数的设定并应用伽辽金积分法,得到三阶位移展开形式下轴向运动板的非线性振动微分方程组。利用多尺度法对系统的主共振问题进行求解,分别得到三种频率关系条件下关于稳态解的幅频响应方程。依据李雅普诺夫稳定性理论对解的稳定性进行分析,得到相应的稳定性判别式。通过数值算例,得到轴向速度、磁感应强度、激励力幅值及板厚不同时的振幅变化规律曲线图,分析不同参量对共振幅值和非线性特征的影响,并对不同频率关系进行比较。     

耦合场中弹性圆形薄板在混沌状态下的应力分析

在给出圆薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上,得到在横向稳恒磁场、环向电流和机械载荷共同作用下简支圆薄板的振动方程,并采用四阶Runge-Kutta法求解方程,得出圆板的弹性变形及应力状态.通过变化磁感应强度和电流密度,使系统由周期状态进入混沌状态;由分岔图与最大Lyaponov指数图判定系统是否进入混沌状态;并讨论磁场与电流对系统应力状态的影响.     

Exact solutions for vibration of cylindrical shells with intermediate ring supports

This paper presents new exact solutions for vibration of thin circular cylindrical shells with intermediate ring supports, based on the Goldenveizer–Novozhilov shell theory (Theory of thin shells; The theory of thin elastic shells). An analytical method is proposed to study the vibration behaviour of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive the homogenous differential equation system for a shell segment and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented in tables and design charts for circular cylindrical shells having multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmark values for researchers to validate their numerical methods for such circular cylindrical shell problems.     

温度场中输电线在谐扰力作用下的3次超谐共振

研究输电线在温度场中谐扰力作用下的3次超谐共振问题,应用动力学方法建立温度场中受谐扰力作用输电线的非线性振动.根据非线性振动的多尺度解法,得到系统满足3次超谐共振情况的近似解,并对其进行数值计算.分析温差变化、外部激励、谐调值、阻尼等对系统的影响.得到系统失稳的临界温度,指出幅频响应曲线存在跳跃现象.     

Vibrational energy flow models for out-of-plane waves in finite thin shell

In this paper, an approximate energy flow model for the out-of-plane vibration of a finite thin shell was developed. The derived energy governing equation for the model was expressed in terms of the time- and locally space-averaged far-field wave energy density which can be used as the main equation for the prediction of the out-of-plane structural vibration levels of the energy density and intensity in medium-to-high frequency ranges. The derived model can be applied to the vibration energy problems of a cylindrical shell, spherical shell and doubly-curved shell, whose radius of curvature in each direction is constant, regardless of the position, assuming that the in-plane motion is relatively small. To verify the results of the derived model, wave numbers were obtained using an energy flow analysis and classical analysis, such as the method using Donnell-Mushtari equations. For the case of various types of finite thin shell, the derived energy equations were applied. The results for the spatial distributions and levels of the energy density and intensity were compared with classical displacement solutions, according to the changes in the frequency and internal loss factor of the shell.     

Thermoelastic damping in cylindrical shells with application to tubular oscillator structures

Thermoelastic vibration and damping of cylindrical shell structures is studied in this paper. The general thermoelastic coupled equations for cylindrical thin shells are presented first. Since the general governing equations are quite complicated, they are then simplified with Donnell–Mushtari–Vlasov approaches for the cylindrical shells under transverse deflection-dominated vibrations. By solving the simplified thermoelastic equations with Galerkin method, the approximate solutions for thermoelastic damping in a cylindrical shell structure are obtained. The solutions are suitable for the predictions of thermoelastic damping of tubular oscillator structures. Some numerical examples for micro- or nano-tube resonators are provided to illustrate the results.     

Vibration of cylindrical shells with ring support

In this paper, a study on the vibration of thin cylindrical shells with ring supports is presented. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which imposed a zero lateral deflection. The study is carried out using Sanders' shell theory. The governing equations are obtained using an energy functional with the Ritz method. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.     

Vibrational energy flow analysis of coupled cylindrical thin shell structures

In this study, a method for energy flow analysis was developed to predict the vibrational responses of coupled cylindrical thin shell structures in the medium-to-high frequency ranges. To extend the application of the energy flow model for out-of-plane waves in the thin shell to coupled structures, the wave transmission analyses of general coupled cylindrical thin shell structures are performed. Power reflection and transmission coefficients on the coupled line were calculated using the coupling relationships established for coupled cylindrical thin shells. Using these coefficients, an energy flow analysis in which a junction was considered, was performed for coupled cylindrical thin shell structures. The junction consisted of an arbitrary number of cylindrical thin shells coupled along a junction line. Through numerical simulations, the energy flow solutions of coupled cylindrical thin shell structures were compared with those of classical displacement solutions, and they showed well-developed energy density global propagation and decay patterns.     

Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions

Based on the Reissner-Naghdi’s thin shell theory, this paper concentrates on the free vibration of a joined cylindrical-spherical shell with elastic-support boundary conditions by a domain decomposition method. The joined shell is first separated from the elastic-support boundary and then subdivided into some cylindrical and spherical shell segments along the axis of revolution. The elastic-support boundary is regarded as a combination of distributed linear springs and can be treated as a special interface as well as the interface between two adjacent shell segments. Through the variational operation of the whole energy functional, the discretized equations of motion are derived by the expansions of the displacement field for each shell segment with Fourier series and Chebyshev orthogonal polynomials in the circumferential and longitudinal direction, respectively. To analyze the numerical convergence and precision of the present method, a number of case studies have been conducted and the solutions are compared with those derived by ANSYS and those presented in the previous literature to confirm the reliability and accuracy.     

空间光学镜筒结构参数的探讨

空间光学镜筒是一个典型的圆筒形薄壳结构,而圆筒形薄壳在航空、航天等机械领域得到了广泛的应用,为减轻薄壳质量、提高薄壳强度和提高其制造工艺性,通常的圆柱形薄壳都具有加强筋,很显然,加强筋使薄壳的强度及制造工艺性大大提高。但是,加强筋使空间光学镜筒的动力学特性如何变化,至今还没有被深入的探讨。本文对航天相机中筒处的具有轴向和径向加强筋的圆筒进行动力学分析,研究加强筋对空间光学镜筒动力学特性的影响。     

Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions

A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E_z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

封闭圆柱壳振动响应特性研究

用均值导纳法分析了复杂的圆柱壳组合结构振动响应特性 ,取得了较好的结果。主要是将均值导纳法用于封闭圆柱壳体振动能量比的研究 ,实验结果证明用均值导纳法来研究封闭圆柱壳的振动响应是可行的。