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

在非线性力学的学科中， 确定性系统理论 现象，如内部 弹性系统的共振和灾难性变形 在理论和实验上都得到了证实。 然而，这些现象的存在和机制在随机 振动尚未得到实验验证。 这 项目进行了一系列的实验研究， 测量随机响应统计和稳定边界 一系列的动力学模型。 在以前的补助金中，PI已经 发展了一种非高斯封闭方案的非线性系统 在随机参数激励下 本工程 理论预测结果（来自上述理论） 将与测量结果进行比较，以验证 理论 实验选用的模型为液体晃动 在坦克，悬臂梁，和自参数振动 吸收器 这些模型已经得到了广泛的实验和 谐波激励下的分析研究， 适合这个项目的模式。 拟议的实验 工作将是非常有价值的，在提供更多的洞察力， 非线性系统的随机行为。 主要研究者一直是主要贡献者， 非线性动力学研究多年。 他很有资格 实施这个项目。 建议给予奖励。

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.