Repair of a cracked Timoshenko beam subjected to a moving mass using piezoelectric patches

This paper presents an analytical method for the application of piezoelectric patches for the repair of cracked beams subjected to a moving mass. The beam equations of motion are obtained based on the Timoshenko beam theory by including the dynamic effect of a moving mass traveling along a vibrating path. The criterion used for the repair is altering the first natural frequency of the cracked beam towards that of the healthy beam using a piezoelectric patch. Conceptually, an external voltage is applied to actuate a piezoelectric patch bonded on the beam. This affects the closure of the crack so that the singularity induced by the crack tip will be decreased. The equations of motion are discretized by using the assumed modes method. The cracked beam is modeled as number of segments connected by two massless springs at the crack locations (one, extensional and the other, rotational). The relationships between any two spans can be obtained by considering the compatibility requirements on the crack section and on the ends of the piezoelectric patch. Using the analytical transfer matrix method, eigensolutions of the system can be calculated explicitly. Finally, numerical simulations are performed with respect to different conditions such as the moving load velocity. It is seen that when the piezoelectric patch is used, the maximum deflection of the cracked beam approaches maximum deflection of the healthy beam.     

悬臂压电叠层复合梁的弯曲振动固有频率

压电叠层复合梁是一种三叠片对称结构。这里以压电陶瓷-金属-压电陶瓷复合结构为研究对象,给出了悬臂式对称压电复合结构的压电振子弯曲振动共振频率表达式,并建立了相应的有限元模型;计算分析了压电陶瓷-金属复合梁弯曲振动的固有频率值与几何尺寸之间的关系,并与相应的有限元模态分析结果进行了比较。结果表明,两种分析方法得到的压电振子的固有频率值基本符合,计算公式和模型是精确有效的;压电叠层复合梁愈细长则表达式的计算结果愈准确。     

联合载荷作用下悬臂梁大变形分析的打靶法

利用微积分基本知识，这里导出了集中力和任意横向分布载荷作用下悬臂梁的挠曲线微分方程。基于两点边值问题的打靶法，分别计算了两种联合载荷作用下悬臂粱的大变形。所得微分方程不仅具有普遍性，而且本文的计算方法对类似问题的解决具有一定的借鉴意义。     

冲击载荷下小模数齿轮动态应力研究

以冲击电钻小模数变速齿轮为研究对象,采用有限元方法研究,冲击电钻在堵转时所引起的不同的冲击载荷和冲击时间,对小模数齿轮齿根动态应力的影响,并分析比较在相同的静载荷作用下的静应力状态,以及不同的齿根过渡曲线对齿轮强度的影响。     

Large deflection of constant curvature cantilever beam under follower load

This paper describes a method to analyze for the large deflections of curved prismatic cantilever beams with uniform curvature subjected to a follower load at the tip. The large deflection, the deflection dependent follower load and the initial curved geometry are the important features of the beam considered in this work. Shear force formulation proposed by Lee [Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-Linear Mech 2002;37(3)] is used for deriving the governing equations. Using this approach, the resulting two point boundary value problem (TPBVP) can be reduced to an initial value problem (IVP). Fourth order Runge-Kutta method along with one parameter reverse shooting method is applied to the numerical solution to the problem. A novel approach presented in this paper of integrating from the free end to the fixed end of the cantilever beam simply replaces the two parameter shooting with a single parameter shooting yielding several advantages. This solution technique is demonstrated for various types of follower tip loads on curved and straight cantilever beams and is validated with existing solutions in the literature.     

平行梁型称重传感器的力学特性

平行梁型称重传感器以其准确度、刚度和灵敏度较高、便于调整四角误差等特点,广泛应用于商业、家用等各种电子秤,但在其结构特性和实际应用中有些问题常常被误解。为此,本文介绍了平行梁型称重传感器的力学特性、结构类型与特点、弹性元件的受力分析与理论计算、产生偏载误差的因素及修正方法等方面内容。     

组合式货架横梁承载的计算

针对组合式货架横梁的实际使用和受力特点,提出了新的横梁承载计算模型和方法,该方法简单、实用、精确度高,为企业进行横梁系列化设计、横梁承载计算提供了一种实用的计算方法。     

平行梁型称重传感器的力学特性

平行梁型称重传感器以其准确度高、刚度和灵敏度较大、便于调整四角误差等特点,广泛应用于商业和家用各种电子秤,但在其结构特性和实际应用中有些问题常常被误解。为此,介绍了平行梁型称重传感器的力学特性、结构类型与特点、弹性元件的受力分析与理论计算、产生偏载误差的因素及修正方法。     

Stability of tri-taper journal bearings under dynamic load using a non-linear transient method

Stability of a tri-taper journal bearing which is subjected to steady, periodic and variable rotating loads is studied theoretically using a non-linear transient approach. The hydrodynamic forces are initially obtained by solving the Reynolds equation, satisfying the Reynolds boundary conditions. Further, the transient behavior of rotor bearing system is predicted by substituting these hydrodynamic forces in the equations of motion and then solving them by fourth order Runge Kutta method. Stability of the rotor bearing system is determined from the journal locus. Comparative studies predict that the dynamic performance is superior for a bearing with high ramp size and aspect ratio.     

两自由度悬臂梁压电发电装置的宽频发电性能

研究一种两自由度悬臂梁压电发电装置,以提高悬臂梁式压电发电装置在环境振源振动频率波动情况下的发电能力。建立了两自由度悬臂梁压电发电装置的频率特性理论模型,并对该理论模型进行了有限元仿真验证,结果显示理论计算与有限元仿真结果基本一致。对两自由度悬臂梁压电发电装置的频率特性模型进行了数值模拟,模拟显示:装置的前两阶模态频率比随着长度比、宽度比、厚度比及质量块的质量比的增大均出现一个最小值,且在长度比为0.8,宽度比为2.0,厚度比为1.0,质量块的质量比为0.5时,装置的前两阶模态频率比最小,结果表明通过合理设计两自由度悬臂梁压电发电装置的结构参数,可以使得装置的前两阶模态频率最接近。最后,实例设计了两自由度悬臂梁压电发电装置,并进行了试验测试,证实了优化后的两自由度悬臂梁压电发电装置具有宽频带发电能力。     

双剪梁型称重传感器的有限元分析

利用有限单元法,在多处建立接触单元,对双剪梁型称重传感器弹性体及其关联部件进行了分析,建立了弹性体及其关联部件的既简化又符合实际的有限元模型;研究了弹性体的结构参数、载荷等各种因素对贴片区应变的影响,为优化设计提供了依据。     

复杂载荷变刚度静不定梁通用力学模型及变形方程

对复杂载荷下变刚度静不定梁建立了一种通用力学模型,得出梁任一截面的变矩方程。通过对变矩方程的积分和积分后方程的递推,推导出梁任意截面的转角和挠度变形的一般方程,并给出工程计算实例。该方程易于采用计算机处理,为复杂载荷下变刚度静不定梁程序化求解提供基础。     

一种调整悬臂剪切梁传感器误差的方法

本文从电阻应变式悬臂剪切梁传感器结构对非线性误差进行分析,采用有限元方法计算贴片孔位置对传感器的非线性误差影响,再通过试验对计算结果进行验证。结果表明悬臂剪切梁的承载孔位置对传感器的非线性误差影响可通过有限元方法定量计算。设计应用悬臂剪切梁式传感器时,对非线性误差应与传感器的其他误差综合考虑能有效提高传感器的精度。     

Parametric instability of a Leipholz beam due to distributed frictional axial load

In this paper, the parametric instability of a beam subjected to a moving distributed contact load that also oscillates in the transverse direction of the beam is studied. Due to the presence of friction between the beam and the moving contact surface, the beam is excited by a pulsating, distributed, follower-type axial load, which results in the problem of a Leipholz column subjected to parametric excitation. The study of this prototypical one-dimensional model is intended to provide further understanding of the instability of systems that have similar loading conditions such as automotive disc brake pads rubbed by the oscillatory rotor or beam-like structures. Effects of several parameters such as boundary conditions, coefficient of friction, intermediate supports, and waviness of the contact load on the instability are examined. Results show that the combination resonance of both the sum and difference types exists for the boundary conditions considered in this study. It is also found that the shearing motion of the friction material plays an important role in determining the stability of the Leipholz beam model. Analogous behavior of instability between the present model and the disc brake pad system is also discussed.     

Research on parallel load sharing principle of piezoelectric six-dimensional heavy force/torque sensor

In working process of huge heavy-load manipulators, such as the free forging machine, hydraulic die-forging press, forging manipulator, heavy grasping manipulator, large displacement manipulator, measurement of six-dimensional heavy force/torque and real-time force feedback of the operation interface are basis to realize coordinate operation control and force compliance control. It is also an effective way to raise the control accuracy and achieve highly efficient manufacturing. Facing to solve dynamic measurement problem on six-dimensional time-varying heavy load in extremely manufacturing process, the novel principle of parallel load sharing on six-dimensional heavy force/torque is put forward. The measuring principle of six-dimensional force sensor is analyzed, and the spatial model is built and decoupled. The load sharing ratios are analyzed and calculated in vertical and horizontal directions. The mapping relationship between six-dimensional heavy force/torque value to be measured and output force value is built. The finite element model of parallel piezoelectric six-dimensional heavy force/torque sensor is set up, and its static characteristics are analyzed by ANSYS software. The main parameters, which affect load sharing ratio, are analyzed. The experiments for load sharing with different diameters of parallel axis are designed. The results show that the six-dimensional heavy force/torque sensor has good linearity. Non-linearity errors are less than 1%. The parallel axis makes good effect of load sharing. The larger the diameter is, the better the load sharing effect is. The results of experiments are in accordance with the FEM analysis. The sensor has advantages of large measuring range, good linearity, high inherent frequency, and high rigidity. It can be widely used in extreme environments for real-time accurate measurement of six-dimensional time-varying huge loads on manipulators.     

基于Mindlin模型的悬臂梁传感器接触滞后误差分析

基于摩擦学方法对悬臂梁安装结构建立物理模型,采用有限元方法计算接触面的应力状态进行求解,然后根据接触力学中的Mindlin方法得出接触面耗散的能量,从而得出接触面产生的滞后误差。通过试验对计算结果进行验证,结果表明悬臂梁的滞后误差与加载额度和最大载荷有关。但最大载荷一定时,相对滞后误差趋近于常数。设计应用悬臂梁式传感器时,要根据载荷确定安装面的结构能够在一定范围内提高悬臂梁传感器的精度。     

高速重载齿轮传动动载系数计算方法

从动力学的角度研究齿轮传动的动载荷和动载系数,首次定量考虑到冲击激励对动态特性的影响,提出一个新的动载系数计算公式。通过算例与ISO标准的动载系数计算B法进行比较分析,二者结果十分吻合,证明该法的正确性和可靠性。     

Research on the parallel load sharing principle of a novel self-decoupled piezoelectric six-dimensional force sensor

This paper presents a novel integrated piezoelectric six-dimensional force sensor which can realize dynamic measurement of multi-dimensional space load. Firstly, the composition of the sensor, the spatial layout of force-sensitive components, and measurement principle are analyzed and designed. There is no interference of piezoelectric six-dimensional force sensor in theoretical analysis. Based on the principle of actual work and deformation compatibility coherence, this paper deduces the parallel load sharing principle of the piezoelectric six-dimensional force sensor. The main effect factors which affect the load sharing ratio are obtained. The finite element model of the piezoelectric six-dimensional force sensor is established. In order to verify the load sharing principle of the sensor, a load sharing test device of piezoelectric force sensor is designed and fabricated. The load sharing experimental platform is set up. The experimental results are in accordance with the theoretical analysis and simulation results. The experiments show that the multi-dimensional and heavy force measurement can be realized by the parallel arrangement of the load sharing ring and the force sensitive element in the novel integrated piezoelectric six-dimensional force sensor. The ideal load sharing effect of the sensor can be achieved by appropriate size parameters. This paper has an important guide for the design of the force measuring device according to the load sharing mode.     

Anomalous dynamic elastic-plastic response of a galerkin beam model

A study of the anomalous motion of an elastic—plastic beam under short pulse loading is presented. The geometric nonlinearity due to axial end constraints is taken into account. We apply the Galerkin method to the governing partial differential equation of the transverse motion to obtain a general model of n degrees of freedom (nDoF). The results of elastic—plastic deformation analysis and dynamic response for the 2DoF model of a pin-ended beam are presented. The regular and irregular motions of the 2DoF model for the pin-ended beam are examined by various methods including time history, phase diagram, Lyapunov characteristic exponent and power spectral density.     

柱塞式液压泵曲轴载荷特性及力学性能分析

建立了柱塞式液压泵曲轴连杆机构的力学模型,并用MATLAB对曲轴的受力情况进行了模拟仿真,研究了曲轴所受动态载荷的变化规律,确定了其工作循环中的危险点.用有限元方法分析了曲轴在危险工况的静态强度和刚度特性,采用多步载荷积累的方法计算了其疲劳使用系数.研究结果对曲轴部件的优化设计具有较高的实用价值.