Random Vibrations with Impacts

本研究项目涉及预测振动冲击系统对随机激励响应的方法和程序的发展。典型的应用领域包括工程（系泊体对海浪的响应）和动力工程，特别是核能（导流管内燃料束的流动引起的振动；以及热交换器管对支撑板的冲击）。其他潜在的应用包括铁路机械（具有冲击型轮轨相互作用的车辆动力学）和旋转机械（具有反向运动的齿轮箱）。准保守随机平均方法与傅立叶级数展开在一个响应周期内的“快速”时间内一起使用。此外，基于碰撞对轻阻尼系统响应加速度总谱密度的主要贡献，提出了一种新的近似方法，并对其进行了评价。采用随机相位调制的周期激励模型，预测了海洋系泊平台对海浪的亚谐波响应，并预测了换热器管道在平面和旋转流激振动之间的过渡。在此研究过程中发展的新的分析方法和程序以及（强非线性）系统的一些新的具体解将有利于非线性振动和控制的基础理论。此外，这项研究将有助于响应预测和控制，以及预测和/或测试可靠性，并为海上和电力工程系统制定设计指南。

This research project deals with the development of methods and procedures for predicting response of vibroimpact systems to random excitation. Typical fields of applications include Engineering (response of moored bodies to ocean waves) and Power Engineering, particularly Nuclear (flow- induced vibrations of fuel bundles within channelling tubes; and of heat exchanger tubes impacting against support plates). Other potential applications include Railway Machinery (vehicle dynamics with impact-type wheel/rail interactions) and Rotating Machinery (gearboxes with reversals of motion). A quasiconservative stochastic averaging method is used together with a Fourier series expansion in a `rapid` time, within a response cycle. In addition, a new approximation procedure is developed and evaluated which is based on the dominating contribution of the impacts into overall spectral density of response acceleration for lightly damped systems. The model of a periodic excitation with random phase modulation is used to predict subharmonic response of moored offshore platforms to ocean waves, and to predict transitions between planar and whirling flow-induced vibrations of tubes in heat exchangers. Fundamental theory of nonlinear vibration and control would benefit through new analytical methods and procedures developed during the course of this research and some new specific solutions obtained for (strongly nonlinear) systems. Also, this research will assist in response prediction and control, as well as predicting and/or testing reliability and developing design guidelines for systems in offshore and power engineering.