A New Approach to Vibration Mitigation of Moving-load Problems

在分析和实验上，移动载荷的动态问题比传统的固定（但动态）载荷的问题更难解决。然而，它们是非常常见的，发生在桥梁、道路和铁路轨道上的交通流、输送流体的管道、诸如离合器、制动器和滑块的机器部件、涉及金属去除的机加工操作、锯木机和起重机中。据信，移动负载问题在许多现代机器应用中可能是极其重要的，特别是在需要低质量和非常高的操作速度的情况下，例如计算机磁盘驱动器和高速加工。人行桥（例如千禧桥）和轻质大跨度楼板特别容易受到人们行走（以及跳舞或跳跃）的激励，现在已成为土木和结构工程师特别关注的问题。近年来高速列车的发展也带来了严峻的新技术挑战。由移动载荷引起的典型问题包括产生不必要的噪声、颤振、非线性和自激振动，从而导致不稳定和/或大幅值极限环。必须认识到，移动荷载不可避免地会激发振动。因此，中心研究问题不是完全抑制由移动载荷激发的振动，因为这是不可能实现的，而是减轻由此引起的振动。由移动载荷激发的振动通常不是静止的，并且具有宽频率范围和高振幅的特征，因此很难减少和控制。本文的目的是系统地研究移动荷载动力问题的减振问题，移动荷载问题的非平稳特性造成了两方面的困难：（1）当移动结构穿越空间域时，随时间变化的频率形成频带;（2）频率也随移动结构的速度变化。因此，以前建立的方法，如分配频率固定值和瞬时最佳控制，将不能很好地工作，或可能根本不工作。结构振动控制可以采用几种控制策略：（1）经典线性最优控制，（2）极点和零点配置，（3）瞬时最优控制，（4）独立模态空间控制，（5）有界状态控制。虽然许多结构振动控制的工作是基于一阶状态空间公式，直接处理的二阶运动方程是振动工程师的自然框架。此外，基于接收的逆方法（Ram和Mottershead在2007年首先针对对称系统提出，然后由本申请人在2009年扩展到非对称系统）具有特别的吸引力，因为接收易于测量并且仅在少量自由度下需要;不需要知道质量、刚度或阻尼矩阵，从而可以避免数值建模误差（有限元模型虽然有用，但不需要）。振动主动控制一直是一个主要的研究课题，并已显示出相当大的希望，在解决实际的工程应用，在最近几年，但相对非常少的例外情况下，移动负载问题的主动解决方案很少被研究。非移动荷载主动控制理论和方法的丰富性在移动荷载问题中被忽略了。这种明显的缺失提供了一个不容错过的机会，可以创建一个新的知识体系并将其应用于新的应用程序。申请人旨在为解决长期存在但不断扩展的移动负载动态问题领域带来新的想法，并使用主动和被动控制实现移动负载动态中的振动缓解。

Dynamic problems with moving loads are analytically and experimentally more difficult to solve than problems with conventional stationary (but dynamic) loads. They are however very commonplace, occurring in traffic flows on bridges, roads and rail tracks, pipelines carrying fluids, machine parts such as clutches, brakes and sliders, machining operations involving metal removal, wood saws and cranes. It is believed that moving-load problems are likely to be extremely important in many modern machine applications, especially where low mass and very high speeds of operation are required, such as computer disk drives and high speed machining. Foot bridges (for example, the Millennium Bridge) and light-weight long-span floors are particularly susceptible to excitation by people walking (and also dancing or jumping for the latter) and have now become of particular concern to civil and structural engineers. The development of high speed trains in recent years has also posed serious and new technological challenges. Typical problems caused by moving loads include generation of unwanted noise, chatter, nonlinear and self-excited vibrations leading to instability and/or large-amplitude limit cycles. It must be recognised that it is inevitable that moving loads excite vibration. So the central research issue is not to completely suppress vibration excited by moving loads, because that is impossible to achieve, but rather to mitigate vibration thus caused. Vibrations excited by moving loads are not stationary in general and are characterised by a wide frequency range and high-amplitude, hence it is very difficult to reduce and control. The purpose of this new proposal is to study vibration mitigation of moving-load dynamic problems in a systematic way.The non-stationary nature of moving-load problems creates a two-fold difficulty: (1) time-varying frequencies form bands as the moving structure traverses the spatial domain and (2) the frequencies also vary with the speed of the moving structure. Therefore previously established methodologies, such as assigning frequencies to fixed values and instantaneous optimal control, would not work well or possibly not at all. New control concepts have to be explored, which is the major motivation of this new project.Structural vibration control may be based on several strategies: (1) classical linear optimal control, (2) pole and zero assignment, (3) instantaneous optimal control, (4) independent modal space control, and (5) bounded state control. While many works on structural vibration control are based on the first-order state-space formulation, direct treatment of the second-order equation of motion is the natural framework to vibration engineers. In addition, receptance-based inverse methods, first put forward for symmetric systems by Ram and Mottershead in 2007 and then extended to asymmetric systems by this applicant in 2009, have a particular appeal in that receptances are easy to measure and are required at only a small number of degrees-of-freedom; there is no need to know mass, stiffness or damping matrices so that numerical modelling errors can be avoided (a finite element model, though useful, is not required). Active vibration control has been a major research topic and has shown considerable promise in solving practical engineering applications in recent years, but with a relatively very small number of exceptions, active solutions of moving-load problems have rarely been studied. The abundant wealth of active control methods and theories used in non-moving-load problems have largely been left out of moving-load problems. This glaring absence presents a not-to-be-missed opportunity to create a new body of knowledge and apply it to novel applications. The applicant aims to bring fresh ideas into solving the long-standing but continuously expanding field of moving-load dynamic problems and achieve vibration mitigation in moving-load dynamics using active and passive control.