Non-Gaussian Probability Densities for Nonlinear Systems Under Random Parametric Excitations: Experimental Investi- gation

随机参数激励下非线性系统的非高斯概率密度：实验研究

• 批准号: 8611335
• 负责人: Raouf Ibrahim
• 金额: $ 0.2万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1986
• 资助国家: 美国
• 起止时间: 1986-12-01 至 1987-09-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8611335&HistoricalAwards=false
• 关键词: Non; Gaussian; Probability; Densities; Nonlinear

In the discipline of nonlinear mechanics, much is known about the theory of deterministic systems. Phenomena such as internal resonance and catastrophic deformation of elastic systems have been demonstrated both theoretically and experimentally. However, the existence and mechanism of these phenomena in random vibration have not yet been verified experimentally. This project conducts a series of experimental investigations to measure the random response statistics and stability boundaries of a number of dynamical models. In a previous grant, the PI has developed a non-Gaussian closure scheme for nonlinear systems under random parametric excitations. In this project, the theoretically predicted results (from the aforementioned theory) will be compared to the measured results in order to verify the theory. The models selected for experiment are a liquid sloshing in a tank, a cantilever beam, and an autoparametric vibration absorber. These models have received extensive experimental and analytical investigations under harmonic excitations and are appropriate models for this project. The proposed experimental work will be very valuable in providing more insight ot the random behavior of non-linear systems. The Principal Investigator has been a major contributor to nonlinear dynamics for several years. He is well-qualified to implement this project. An award is recommended.

在非线性力学这门学科中，关于确定性系统的理论我们知道很多。从理论上和实验上证明了弹性系统的内部共振和突变变形等现象。然而，这些现象在随机振动中的存在及其机理尚未得到实验验证。本项目进行了一系列的实验研究，测量了一些动力模型的随机响应统计量和稳定性边界。在之前的拨款中，PI已经开发了随机参数激励下非线性系统的非高斯闭包格式。在这个项目中，将理论预测结果（来自上述理论）与测量结果进行比较，以验证理论。实验选择的模型有：罐内液体晃动模型、悬臂梁模型和自参数减振器模型。这些模型在谐波激励下得到了广泛的实验和分析研究，是本项目的合适模型。所提出的实验工作对于提供对非线性系统的随机行为的更多见解将是非常有价值的。首席研究员多年来一直是非线性动力学的主要贡献者。他完全有资格实施这个项目。建议颁发奖项。