弹性支承输流管道的动力学特性

研究两端弹性支承输流管道横向振动的动力学特性。根据梁模型横向弯曲振动模态函数,由两端弹性支承的边界条件得到其模态函数的一般表达式。根据特征方程具体分析弹性支承刚度、质量比、流体压力和流速、管截面轴向力等主要参数对管道固有特性及失稳临界流速的影响。数值计算结果表明,管道固有频率随弹性支承刚度、管截面轴向拉力的增加而增大,随流体流速、流体压强和管截面轴向压力的增加而下降;静态失稳临界流速则随弹性支承刚度、流体压强、管截面轴向压力的增加而下降,随管截面轴向拉力的增加而上升。     

随从力作用下悬臂裂纹梁的稳定性分析

基于Adomian修正分解法研究悬臂裂纹梁的稳定性,悬臂梁的自由端具有弹簧支承和轴向随从力。将梁的裂纹模拟为无质量的等效扭转弹簧。通过Adomian修正分解法可以把裂纹梁的特征微分方程转换成递归代数公式,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的量纲一固有频率及相应的振形函数解析表达式。通过与前人的计算结果比较,验证了所提方法的有效性。讨论裂纹位置和深度对颤振或屈服失稳的临界随从力的影响。讨论不同失稳形式时裂纹梁支承的临界弹簧刚度。数值计算结果表明,当裂纹位于悬臂梁固定端附近时,对梁的固有频率影响最大。研究还表明裂纹的存在有可能提高梁的稳定性。     

轴向运动Rayleigh梁固有频率的微分求积法

轴向运动梁的振动和稳定性问题是振动力学问题研究的重要内容之一,它有着重要的理论和实际意义。研究了轴向运动Rayleigh梁的固有频率。根据广义哈密顿原理建立轴向运动Rayleigh梁横向振动的控制方程。采用微分求积法数值求解两端简支和两端固支边界条件下轴向运动Rayleigh梁的次临界固有频率。数值例子给出了变化梁的弯曲刚度和支撑刚度情况下第一阶和第二阶固有频率和速度之间的关系曲线。通过曲线间的关系可得到:高阶固有频率比低阶固有频率大,固有频率随着刚度系数的增大而增大,并且随着支撑刚度的增大而增大。     

进给系统参数对丝杠振动频率的影响

考虑轴承的支承刚度,建立了丝杠在两端弹性支承条件下纵向振动、扭转振动和横向振动的频率方程。对于纵向振动和扭转振动,分析了轴承支承刚度对其振动频率的影响。对于丝杠的横向振动,采用Timoshenko模型,综合考虑了转动惯量、涡动效应和预拉伸力对丝杠振动的影响,分析了轴承支承刚度、旋转速度和预拉伸力对丝杠横向振动频率的影响,分析了丝杠在启动过程中的共振,为回转系统减少或消除共振提供了理论依据。     

不同支承条件下梁结构弯曲振动的固有特性

根据梁模型端部的四种不同支承条件,将梁模型区分为一般支承梁、弹性支承梁、约束简支梁和约束悬臂梁四种,分别由各自的边界条件和梁弯曲振动模态函数的一般表达式推导出了这四种不同支承条件下梁模型弯曲振动的模态函数及其频率方程,计算得到了四种支承条件下梁模型的前两阶振动模态,具体分析了支承刚度对其特征值的影响.根据该方法,可以得出任意约束刚度下梁弯曲振动的任一模态及其特征值,其结果可以直接用于工程设计与分析.对于各种支承条件下的弹性约束刚度,根据梁的实际支承情况合理选取.     

基于解析弹性基础的重载轮胎动力学建模与分析

以重载大扁平比轮胎为研究对象,基于弹性基础的柔性胎体模型为基础,分别从大扁平比胎侧曲梁的刚度建模、基于解析弹性基础的轮胎动力学建模两方面开展研究。建立考虑预紧力弦效应和结构弯曲效应的大扁平比胎侧曲梁解析刚度模型,并研究胎侧曲梁非均匀截面特性和几何、结构参数对解析刚度的影响规律。结果表明：（1）重载轮胎在0～180 Hz范围以结构周向弯曲振动为主,与基于弹性基础的柔性梁模型一致;（2）大扁平比胎侧曲梁的解析刚度与胎侧的几何、结构和充气压力参数直接相关;（3）轮胎充气压力影响柔性胎体梁的轴向预紧力和胎侧的弦刚度,进而影响轮胎弯曲振动特性。     

轴向力作用下连续梁固有振动分析

采用整体分析的方法,推导出轴向力作用下两端简支多跨均匀连续梁横向振动的频率方程和振型函数的解析式。所得公式包括了连续梁中间支座约束反力不全为零和全为零两种情形,对拉压轴向力、零轴向力和任意跨数均匀连续梁都适用。最后通过实例分析,说明了轴向力对连续梁固有频率的影响。     

支承轴承对高速主轴系统特性的影响

结合轴系变形方程,对支承部位轴承与主轴的位移耦合以及对系统轴向力平衡条件进行了分析,提出用迭代法求解高速主轴系统刚度和临界转速的概念。计算结果表明,支承轴承的非线性对系统性能影响明显,当轴承预加轴向载荷增加时,轴承支承刚度增大,导致主轴系统刚度和临界转速随之增大。     

滑动轴承支承人字齿轮行星传动固有特性分析

考虑滑动轴承支承刚度不对称和耦合特性,建立计入内齿轮轴向振动的人字齿轮行星传动动力学模型。利用4个刚度系数描述行星轮滑动轴承支承油膜刚度。分析系统的自由振动特性,发现系统存在5种振动模式:中心轮扭转—轴向振动模式、内齿轮扭转—轴向振动模式、中心轮横向振动模式、内齿轮横向振动模式和行星轮振动模式。根据每种振动模式的振型特征,推导出5种模式固有特性的低阶计算公式。系统固有频率的分布范围比直齿、斜齿行星传动系统小。结果表明,油膜刚度不对称不会对振型特征产生影响,但是刚度耦合不对称时中心轮横向振动模式会发现显著变化:对应的二重固有频率变成两个不同的单重频率,振型呈现新特征。     

高速电主轴支承刚度计算及模态分析

以某型号数控磨床用高速电主轴为研究对象,基于滚动轴承静力学推导了高速电主轴常用支承—角接触球轴承计及预紧接触角变化的径向刚度和多联组配轴向刚度计算公式,结果显示该计算公式比现有文献中相关计算更准确,讨论了轴向预紧力对支承刚度的影响规律。在得到支承刚度的基础上,在ANSYS中采用弹簧单元COMBIN14模拟主轴轴承支承,基于ANSYS对主轴部件进行了不同轴向预紧力和不同转速下的模态分析,讨论了转速和轴向预紧力对电主轴模态的影响。     

Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

An analytical approach for crack identification procedure in uniform beams with an open edge crack, based on bending vibration measurements, is developed in this research. The cracked beam is modeled as two segments connected by a rotational mass-less linear elastic spring with sectional flexibility, and each segment of the continuous beam is assumed to obey Timoshenko beam theory. The method is based on the assumption that the equivalent spring stiffness does not depend on the frequency of vibration, and may be obtained from fracture mechanics. Six various boundary conditions (i.e., simply supported, simple–clamped, clamped–clamped, simple–free shear, clamped–free shear, and cantilever beam) are considered in this research. Considering appropriate compatibility requirements at the cracked section and the corresponding boundary conditions, closed-form expressions for the characteristic equation of each of the six cracked beams are reached. The results provide simple expressions for the characteristic equations, which are functions of circular natural frequencies, crack location, and crack depth. Methods for solving forward solutions (i.e., determination of natural frequencies of beams knowing the crack parameters) are discussed and verified through a large number of finite-element analyses. By knowing the natural frequencies in bending vibrations, it is possible to study the inverse problem in which the crack location and the sectional flexibility may be determined using the characteristic equation. The crack depth is then computed using the relationship between the sectional flexibility and the crack depth. The proposed analytical method is also validated using numerical studies on cracked beam examples with different boundary conditions. There is quite encouraging agreement between the results of the present study and those numerically obtained by the finite-element method.     

广义边界下含双相流水平井钻柱频率特性分析

钻柱在内流作用和旋转因素的影响下容易产生耦合振动,发生疲劳失效。本文基于微分求积法（DQM）对含双相流水平井钻柱耦合动力学特性进行了研究。利用扩展的Hamilton变分原理建立了计入内流、轴向压力及旋转等因素影响的水平井钻柱动力学方程。在振动问题中考虑了广义边界条件,通过改变边界等效弹簧刚度将模型简化为简支、悬臂等简单边界条件模型进行研究。通过分析旋转角速度、轴向压力、液相流速、气体体积分数等因素对模型频率特性的影响,得到了无量纲固有频率随不同参数变化的特征曲线。分析结果表明：不同边界条件下模型的频率特性曲线有很大的差别;气体体积分数对临界流速的影响在悬臂管系统中表现的更为明显;在简支管模型中,随着轴力的增大会产生模态耦合颤振。此外,通过液相流速和旋转角速度的频率云图展示了两种因素对钻柱频率特性的影响。     

Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

Vibration responses were investigated for a viscoelastic Single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations were derived. The Transfer function method (TFM) was then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters were obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases were discussed. Substantial nonlocal effects, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation were observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system.     

Flow-induced vibration and stability analysis of multi-wall carbon nanotubes

The free vibration and flow-induced flutter instability of cantilever multi-wall carbon nanotubes conveying fluid are investigated and the nanotubes are modeled as thin-walled beams. The non-classical effects of the transverse shear, rotary inertia, warping inhibition, and van der Waals forces between two walls are incorporated into the structural model. The governing equations and associated boundary conditions are derived using Hamilton’s principle. A numerical analysis is carried out by using the extended Galerkin method, which enables us to obtain more accurate solutions compared to the conventional Galerkin method. Cantilevered carbon nanotubes are damped with decaying amplitude for a flow velocity below a certain critical value. However, beyond this critical flow velocity, flutter instability may occur. The variations in the critical flow velocity with respect to both the radius ratio and length of the carbon nanotubes are investigated and pertinent conclusions are outlined. The differences in the vibration and instability characteristics between the Timoshenko beam theory and Euler beam theory are revealed. A comparative analysis of the natural frequencies and flutter characteristics of MWCNTs and SWCNTs is also performed.     

Kinetostatic model of spring constant ratios for an AFM cantilever with end extended mass

In previous work we showed that the kinetostatic method is very effective in computing the increase in value of the spring constants of an AFM free (with or without added mass) and supported rectangular cantilever for higher mode oscillations relative to their values for natural vibration. We have considered in all previous cases that added mass is a concentrated one. However, the additional mass may be an extended one particularly in the case of a V-shaped cantilever. In this article we consider the influence of the constituent beam’s (leg’s) mutual skew and the altered position of the nodal points in the case when the attached extended triangular (trapezoid) mass of the V-shaped cantilever has a significant moment of rotational inertia and a center of this mass gravity located beyond the constituent beam end. We show that considering these effects in using the kinetostatic model yields results for the ratios of the spring constants at higher modes of oscillation and their values at the first frequency natural vibration for a V-shaped cantilever which are in good agreement with the thermomechanical noise amplitudes obtained by other researchers. This should prove helpful for the proper calibration of V-shaped cantilevers whose application with higher modes oscillation provides increased measurement sensitivity.     

Dynamic spring constants for higher flexural modes of cantilever plates with applications to atomic force microscopy

In atomic force microscopy (AFM) a sharp tip fixed close to the free end of a cantilever beam interacts with a surface. The interaction can be described by a point-mass model of an equivalent oscillator with a single spring located at the position of the tip. However, other spring constants have to be used to describe the oscillation behavior correctly if forces are acting on the cantilever over an extended lateral range. A point-mass model is then no longer valid. In the present study we derive expressions for the spring constants of cantilevers that can interact with any part of their plan view area along the beam and for all flexural modes. The equations describe the oscillation behavior in the corresponding mass model and are based on the eigenfrequencies and modal shapes of the free cantilever. The results are of high practical relevance, for example if an AFM is operated in a higher flexural mode, if the tip is not located at the free end of the cantilever beam, or if the external conservative forces affecting cantilever movement are not restricted to a single point. The limitations of the approach are discussed.     

Dynamic behaviors of an elastically restrained beam carrying a moving mass

Dynamic responses of a simply supported beam with a translational spring carrying a moving mass are studied. Governing equations of motion including all the inertia effects of a moving mass are derived by employing the Galerkin’s mode summation method, and solved by using the Runge-Kutta integral method. Numerical solutions for dynamic responses of a beam are obtained for various cases by changing parameters of the spring stiffness, the spring position, the mass ratio and the velocity ratio of a moving mass. Some experiments are conducted to verify the numerical results obtained. Experimental results for the dynamic responses of the test beam have a good agreement with numerical ones.     

基于曲率模态与柔度曲率的损伤识别

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。     

Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory

Nonlinear free vibration and instability of fluid-conveying double-walled boron nitride nanotubes (DWBNNTs) embedded in viscoelastic medium are studied in this paper. The effects of the transverse shear deformation and rotary inertia are considered by utilizing the Timoshenko beam theory. The size effect is applied by the modified couple stress theory and considering a material length scale parameter for beam model. The nonlinear effect is considered by the Von Kármán type geometric nonlinearity. The electromechanical coupling and charge equation are employed to consider the piezoelectric effect. The surrounding viscoelastic medium is described as the linear visco-Pasternak foundation model characterized by the spring and damper. Hamilton’s principle is used to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is employed to discretize the nonlinear higher-order governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequency and critical fluid velocity of fluid-conveying DWBNNTs with clamped-clamped (C-C) boundary conditions. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, spring and damping constants of surrounding viscoelastic medium and fluid velocity on the nonlinear free vibration, instability and electric potential distribution of DWBNNTs. This study might be useful for the design and smart control of nano devices.     

Optimization of a quasi-zero-stiffness isolator

The frequency range over which a mount can isolate a mass from a vibrating base (or vice versa) is often limited by the mount stiffness required to support the weight of the mass. This compromise can be made more favourable by employing non-linear mounts with a softening spring characteristic such that small excursions about the static equilibrium position result in small dynamic spring forces and a correspondingly low natural frequency. This paper concerns the force-displacement characteristic of a so-called quasi-zero-stiffness (QZS) mechanism which is characterised by an appreciable static stiffness but very small (theoretically zero) dynamic stiffness. The mechanism studied comprises a vertical spring acting in parallel with two further springs which, when inclined at an appropriate angle to the vertical, produce a cancelling negative stiffness effect. Analysis of the system shows that a QZS characteristic can be obtained if the system’s parameters (angle of inclination and ratio of spring stiffnesses) are opportunely chosen. By introducing the additional criterion that the displacement of the system be largest without exceeding a desired (low) value of stiffness an optimal set of parameter values is derived. Under sufficiently large displacements the stiffness of the QZS mechanism can eventually exceed that of the simple mass-spring system and criteria for this detrimental scenario to arise are presented.