Free vibration analysis of linear particle chain impact damper

Impact dampers have gained much research interest over the past decades that resulted in several analytical and experimental studies being conducted in that area. The main emphasis of such research was on developing and enhancing these popular passive control devices with an objective of decreasing the three parameters of contact forces, accelerations, and noise levels. To that end, the authors of this paper have developed a novel impact damper, called the Linear Particle Chain (LPC) impact damper, which mainly consists of a linear chain of spherical balls of varying sizes. The LPC impact damper was designed utilizing the kinetic energy of the primary system through placing, in the chain arrangement, a small-sized ball between each two large-sized balls. The concept of the LPC impact damper revolves around causing the small-sized ball to collide multiple times with the larger ones upon exciting the primary system. This action is believed to lead to the dissipation of part of the kinetic energy at each collision with the large balls.     

The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.     

计算机辅助受迫振动实验

在Matlab平台下编写了图形用户界面程序，该程序利用计算机的声卡采集音叉上的压电换能器信号，精确地计算出频率值和平均振幅，通过多组数据采集及插值计算，可自动绘制出不同阻尼下的共振曲线．     

Performance analysis of nonlinear vibration isolator with magneto-rheological damper

A nonlinear vibration isolator is considered to study effectiveness of isolation against harmonic force and displacement excitations. Nonlinearity in the magneto-rheological (MR) fluid based damper as well as in the elastic member is taken into account. The MR-damper has been modeled including Bouc–Wen hysteretic element and the spring is taken to have cubic nonlinearity. Analytical expression for the energy dissipation characteristics of the damper has been derived. Near resonant response of the isolated mass is obtained by a modified averaging technique suitable for hysteretic type nonlinearity present in the system. The performance of the isolators is estimated for various nonlinear stiffness values, both hardening and softening types. Different performance measures are also proposed to judge the performance of the nonlinear isolator.     

光学系统受迫振动的激光测量方法

将激光信号与高帧频CCD结合,解决了光学系统中振动信号和激光信号之间的转换问题,不仅能够测量振动对系统光束指向稳定性的影响,而且能够得到振动信号本身的频率特性。利用该方法对振源为150 Hz和200 Hz两种条件下的光学系统受迫振动进行测量,得到了与输入信号相吻合的振动信号属性。通过实验与分析得知:时域振幅测量精度为6.25 m,频域分辨力为2 Hz,方法简便高效,测量结果准确,已应用于角多路准分子激光主振荡功率放大器系统打靶试验平台光束指向稳定性的研究中。     

受迫振动与共振实验的创新设计

利用变频器、同步电动机和磁性书写板来改进受迫振动与共振演示实验装置.本装置可以用来定量演示受迫振动,还可以用来研究共振的发生条件及描绘共振曲线.     

关于受迫振动、共振的实验研究

简要分析了现行中学物理课本中关于受迫振动和共振的演示实验中存在的缺点,并针对其不足加以改进.改进后的实验装置演示效果更好,便于学生理解和掌握相应的物理规律.     

Corner bifurcations in non-smoothly forced impact oscillators

We consider an impacting mechanical system in which a particle at position u(t) impacts with a periodically moving obstacle at position z(t), the motion of which is non-smooth. In particular we look at corner events when u impacts with z very close to a point where z loses smoothness. We show that this leads, through a corner bifurcation, to complex dynamics in u which can include periodic orbits of arbitrary period and period-adding cascades. By analysing associated maps close to the corner event, we show that this dynamics can be understood in terms of the iterations of a two-dimensional, piecewise linear, discontinuous map. We also show some links between this analysis and the difficult problem of understanding the motion of three objects which may have simultaneous impacts.     

"受迫振动、共振"演示实验的研究与改进

对现有受迫振动、共振演示实验装置的不足进行了剖析,改进了原有的实验装置,制作了受迫振动、共振演示仪器. 阐述了改进后的实验装置的具体制作、教学使用及特点.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,...     

Localized vibration modes in free anisotropic wedges

Propagation of flexural localized vibration modes along edges of anisotropic wedges is considered in the framework of the geometrical-acoustics approach. Its application allows for straightforward evaluation of the wedge-mode velocities in the general case of arbitrary elastic anisotropy. The velocities depend on the wedge apex angle and on the mode number in the same way as in the isotropic case, but there appears to be additional dependence on elastic coefficients. The velocities in tetragonal wedges (with the midplane orthogonal to the four-fold axis) and in "weakly" monoclinic wedges are explicitly calculated and analyzed. Bounds of the wedge-wave velocity variation in tetragonal materials are established.     

矩形薄膜受迫横振动问题的求解及可视化

膜的横振动分析在乐器膜、耳膜以及植物细胞膜中有着广泛的应用价值.相比自由振动,受迫膜振动问题的研究更符合应用实际.本文采用数学物理定解问题的傅里叶级数法与冲量定理法,对四周固定的均匀矩形薄膜振动问题进行了研究,得到了此类问题在受迫振动下的解析解,并对其振动状态进行了可视化分析.研究发现：一维弦振动解法同样可为二维有界膜振动问题提供简便的求解途径,且膜振动将呈现更加丰富的特点.本文的二维非齐次振动问题的冲量定理解法还可推广到二维有源(汇)输运问题中去.     

The free and forced waves on a fluid-loaded elastic plate

The often-studied problem of the response of a fluid-loaded thin elastic plate to external forcing is considered again, with the aim of determining those “free waves” of the coupled system which can actually be excited. General properties of the quintic equation whose roots yield the free wavenumbers can be used to establish the character of those roots, and a generalized “coincidence condition” can be given at which the nature of the roots changes. It is argued, however, and demonstrated, that in general no significance can be attached to this condition or to any of the roots except that relating to the undamped subsonic surface wave. The far field contributions associated with all other waves, including the so-called “leaky waves”, may be altered merely by change of integration path from the stationary phase contour to the steepest descent contour in the complex wavenumber plane, and thus these contributions, which are exponentially small with distance, do not represent physically meaningful free modes. It is shown, however, that if a second limit process, associated with small fluid loading, is considered simultaneously with the far field limit, then the leaky waves can be unambiguously identified over a large, but not too large, range of distances, and that for such distances these waves generate a conical or plane beam (in three or two dimensions, respectively).     

Suppression of maglev vehicle-girder self-excited vibration using a virtual tuned mass damper

The self-excited vibration that occurs between a stationary Electromagnetic Suspension (EMS) maglev vehicle and a girder is a practical problem that greatly degrades the performance of a maglev system. As of today, this problem has not been fully solved. In this article, the principle underlying the self-excited vibration problem is explored, and it is found that the fundamental resonance frequency of the maglev girder plays a vital role in the initiation of the self-excited vibration. To suppress the self-excited vibration, a scheme applying a tuned mass damper (TMD) to the maglev girder is proposed, and the stability of the combined system is analyzed. Furthermore, a novel concept of a virtual TMD is introduced, which uses an electromagnetic force to emulate the force of a real TMD acting on the girder. However, in the presence of the time delay caused by the inductance of the electromagnets, the stability analysis of the levitation system combined with the virtual TMD becomes complex. Analysis of the stability shows that there exist some repeated time delay zones within which the overall system is stable. Based on this rule, time delay control is introduced to stabilize the system with a virtual TMD, and a procedure to determine the optimal time delay and gain is proposed. Numerical simulation indicates that the proposed virtual TMD scheme can significantly suppress the self-excited vibration caused by one unstable vibration mode, and is suitable for application to EMS maglev systems.     

Extended field method free vibration solutions

An apparent paradox involving the relation between the plate bending natural frequencies of two elastic plates when one plate encloses the other is examined and dispelled. Specifically it is shown (1) that the extended field method of analysis can exactly, or with excellent numerical convergence, calculate plate bending eigenvalues, and (2) that the extended field method forced vibration solutions are not compromised by the singularities at the eigenvalues of the extended plate.