Parametric Resonance and Stochastic Dynamic Stability of Structures: Theory, Experiments, and Applications

结构的参数共振和随机动态稳定性：理论、实验和应用

• 批准号: RGPIN-2019-06069
• 负责人: Deng, Jian
• 金额: $ 1.89万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714832
• 关键词: Parametric; Resonance; Stochastic; Dynamic; Stability

One of the most important tasks in civil engineering is assessing structural safety and reliability under dynamic loads (e.g., buildings during earthquake, bridges excited by turbulent winds, and underground mine pillars subjected to rock blasting). These loadings are often random forces and would appear as one of the coefficients in the governing equations of motion. Such systems are said to be parametrically excited and the associated instability is called parametric resonance. With the construction of more and more high-rise buildings, long bridges and underground structures, investigations of dynamic stability of structures under stochastic excitation are increasingly important. Parametric resonance is more dangerous than ordinary resonance because it is characterized by exponential growth of the response amplitudeeven in the presence of dampingwhereas ordinary resonance is characterized by linear growth of the response amplitude. Parametric resonance occurs over a region of parameter space and the excitation frequencies may be higher or lower than the natural frequency. Moreover, parametric resonance may interact with ordinary resonance in unexpected ways. Over the last 18 years, the applicant and collaborators have made significant progress in the study of stochastic dynamics. In particular, approximate algorithms were developed and applied to linear single degree-of-freedom systems, and preliminary lab experiments were conducted at Lakehead University. The knowledge, expertise, and experimental skills acquired by my research team will benefit the proposed NSERC program for stochastic stability of structures. In order to apply the developed methods to real structural systems, it is imperative to extend the study to higher-dimensional systems. The objective of the proposed research program is to theoretically and experimentally study parametric resonance and dynamic stability of fractional viscoelastic non-linear structures subjected to stochastic loads, with applications to civil and mining engineering. We will develop efficient analytical and numerical methods to determine the dynamic stability of various systems with both strong and weak non-linearity, such as coupled systems with commensurable and non-commensurable frequencies, gyroscopic systems, time-delay systems, and multiple degree-of-freedom systems excited by both multiplicative and additive loads. The proposed research will contribute significantly to the advancement of knowledge and technologies associated with dynamic stability of structures. Enhanced understanding of stochastic parametric resonance will inform protocols and measures, by adjusting structural parameters or blasting variables, to avoid or alleviate dynamic disasters due to seismic, wind, or stress wave loadings. This research program will provide unique and leading-edge opportunities to train HQP in these related subjects. Thus, this program will benefit the construction and excavation industries in Canada.

土木工程中最重要的任务之一是评估动态载荷下的结构安全性和可靠性（例如，地震期间的建筑物，湍流风格的桥梁以及受岩石爆炸的地下矿山支柱）。这些载荷通常是随机的力，并且会作为管理方程式中的系数之一。这种系统被称为参数激发，相关的不稳定性称为参数共振。随着越来越高层建筑，长桥和地下结构的建造，随机激发下结构的动态稳定性的研究越来越重要。 参数共振比普通共振更为危险，因为它的特征在于在阻尼温度存在普通共振的情况下响应幅度的指数增长的特征是响应振幅的线性生长。参数共振发生在参数空间区域，激发频率可能高于或低于固有频率。此外，参数共振可能会以意想不到的方式与普通共振相互作用。 在过去的18年中，申请人和合作者在随机动力学的研究中取得了重大进展。特别是，开发了近似算法并应用于线性单一自由度系统，并在莱克黑德大学进行了初步实验实验。我的研究团队获得的知识，专业知识和实验技能将使拟议的NSERC计划受益于结构的随机稳定性。为了将开发的方法应用于实际结构系统，必须将研究扩展到高维系统。 拟议的研究计划的目的是在理论上和实验研究参数共振和动态稳定性的分数粘弹性非线性结构的动态稳定性，该结构承受了随机载荷，并应用于民用和采矿工程。我们将开发有效的分析和数值方法，以确定具有强和弱无线性的各种系统的动态稳定性，例如具有相应和不可固定的频率的耦合系统，陀螺仪系统，时间 - 播放系统，时间 - 时间层系统以及多个程度的程度 - 通过乘法和加性载荷激发的自由系统。 拟议的研究将有助于与结构动态稳定性相关的知识和技术的发展。加强对随机参数共振的理解将通过调整结构参数或爆破变量来为方案和度量提供信息，以避免或减轻由于地震，风或应力波负载而引起的动态灾害。该研究计划将为培训HQP在这些相关主题中培训HQP的独特和领先的机会。因此，该计划将使加拿大的建设和发掘行业受益。