Random Excitation of Dynamic Systems with Multiple Internal Resonances

本研究项目的目的是开发一种方法， 用于分析一般多自由度的动态行为， 具有多重内共振的自由度非线性系统 在外部随机激励下。这项研究将采取的形式 结合分析、数值和实验 调查事务所多重内部共振经常存在于 连续和离散的多自由度系统， 如电缆系统、板、耦合梁、航空航天结构， 和机制。多重内共振系统 在实验上表现出危险和复杂的反应 谐波激励下的特性，如在 实验室在随机激励下，我们将发展两种模式 随机分叉这些模式将用于检查 灾难性行为出现的条件 根据系统参数空间和激发光谱 密度水平。分析方法基于以下方法： 响应能量包络的随机平均， 创新。这种方法的优点是它提供了 关于能源之间的转移的有用信息 相互作用模态及其随机分岔 多个内共振条件的邻域的 分析方法的有效性将通过Monte 随机振动的Carlo数值模拟和实验检验 激发非线性模型所有方法都有一个共同的目标， 提高我们对潜在机制的理解 危险的非线性现象。这项研究的结果将 为参与设计的工程师提供新的指导方针， 工业机械部件、电缆结构、飞机 结构、液体推进剂火箭和高架水塔。

The purpose of this research project is to develop an approach for analyzing the dynamic behavior of general multi-degree-of- freedom nonlinear systems possessing multiple internal resonances under external random excitation. The research will take the form of combined analytical, numerical and experimental investigations. Multiple internal resonances frequently exist in both continuous and discrete multi-degree-of-freedom systems such as cable systems, plates, coupled beams, aerospace structures, and mechanisms. Systems with multiple internal resonances experimentally exhibit dangerous and complex response characteristics under harmonic excitation, as observed in the laboratory. Under random excitation, we will develop two modes for stochastic bifurcation. These modes will be used to examine the conditions under which catastrophic behavior can be presented in terms of system parameters space and excitation spectral density level. The analytical approach is based on the method of stochastic averaging of the response energy envelope, with some innovations. The advantage of this approach is that it provides useful information pertaining to energy transfer among the interacting modes and their stochastic bifurcation in the neighborhood of multiple internal resonance conditions. The validity of the analytical approach will be verified by Monte Carlo numerical simulations and experimental tests of random excited nonlinear models. All approaches have the common goal of improving our understanding of the mechanisms underlying dangerous nonlinear phenomena. The results of this research will lead to new guidelines for engineers involved in the design of industrial machine components, cable structures, aircraft structures, liquid propellant rockets, and elevated water towers.