纳米表面相互作用及振动测头模型

如何实现高精度的测量是现代制造业及微电子技术领域的热点问题之一. 基于微纳米测头的三坐标测量机是当前实现高精度测量的重要手段. 随着测量尺寸的减小, 常用的纳米/微纳尺度的测头与待测表面之间形成静态接触, 其表面相互作用成为了影响其测量精度和可靠性的关键因素之一. 本文基于一种触发式振动测头, 研究了其动力学模型, 并通过对测头纳米尺度表面相互作用的理论分析及数值模拟, 确立了测头振动参数与表面相互作用之间的关联. 实验研究表明, 参数优化后的谐振微纳测头能有效抑制表面作用带来的干扰, 提高测量精度.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms

Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations, especially in aerospace, mechanical, and architectural engineering, etc. Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously, which limits further engineering application, especially in the low-frequency range. In recent twenty years, the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities. One of the most widely studied objects is the “three-spring” configured quasi-zero-stiffness (QZS) vibration isolator, which can realize the negative stiffness and high-static-low-dynamic stiffness (HSLDS) characteristics. The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance. Due to the characteristics of fast response, strong stroke, nonlinearities, easy control, and low-cost, the nonlinear vibration with electromagnetic mechanisms has attracted attention. In this review, we focus on the basic theory, design methodology, nonlinear damping mechanism, and active control of electromagnetic QZS vibration isolators. Furthermore, we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity. The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle. The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode. Only the shear strain gradient through the thickness is considered in the present model. With geometric nonlinearity, the governing equations are converted into differential equations as the function of time by the Galerkin method. The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation. Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent, and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates. The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly. The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.     

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency, ranging from 2 Hz to 5 Hz. Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity. In this paper, inspired by the human spine, we propose a novel bionic human spine inspired quasi-zero stiffness (QZS) vibration isolator which consists of a cascaded multi-stage negative stiffness structure. The force and stiffness characteristics are investigated first, the dynamic model is established by Newton’s second law, and the isolation performance is analyzed by the harmonic balance method (HBM). Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages, and reducing the damping values and external force values can obtain better low-frequency isolation performance. In comparison with the linear structure and existing traditional QZS isolator, the bionic spine isolator has better vibration isolation performance in low-frequency regions. It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．     

集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。     

船舶轴系振动教学演示实验台架设计与实验分析

通过船舶轴系振动理论和实践特点的分析,设计和制作了船舶轴系振动教学演示实验台架.同时,在教学演示实验台架与实船之间开展了比对实验,在船舶轴系振动信号、轴系扭振频谱、横振频谱、纵振频谱等关键实验环节进行了比对分析和讨论,得出了船舶轴系振动教学演示实验台架的可用性和可比性.     

Chatter mitigation using the nonlinear tuned vibration absorber

A passive vibration absorber, termed the nonlinear tuned vibration absorber (NLTVA), is designed for the suppression of chatter vibrations. Unlike most passive vibration absorbers proposed in the literature for suppressing machine tool vibrations, the NLTVA comprises both a linear and a nonlinear restoring force. Its linear characteristics are tuned in order to optimize the stability properties of the machining operation, while its nonlinear properties are chosen in order to control the bifurcation behavior of the system and guarantee robustness of stable operation. In this study, the NLTVA is applied to turning machining.