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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738688
• 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 amplitude-even in the presence of damping-whereas 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、狂风激发的桥梁以及遭受岩石爆破的地下矿柱）。这些载荷通常是随机力，并且会出现。作为运动控制方程中的系数之一，此类系统被称为参数激励，相关的不稳定性称为参数共振。随机激励下结构的稳定性变得越来越重要。参数共振比普通共振更危险，因为它的特点是响应幅度呈指数增长——即使存在阻尼——而普通共振的特点是响应幅度呈线性增长。参数共振发生在参数空间区域，并且激发频率可能高于或低于固有频率，而且，参数共振可能以意想不到的方式与普通共振相互作用。在过去的 18 年里，申请人和合作者取得了重大进展。在研究中特别是，我们开发了近似算法并将其应用于线性单自由度系统，并且在湖首大学进行了初步实验室实验，我的研究团队获得的知识、专业知识和实验技能将有利于拟议的 NSERC。为了将所开发的方法应用于实际结构系统，必须将研究扩展到更高维的系统，该研究计划的目标是从理论上和实验上研究参数共振和动态稳定性。分数粘弹性承受随机载荷的非线性结构，并应用于土木和采矿工程，我们将开发有效的分析和数值方法来确定具有强非线性和弱非线性的各种系统的动态稳定性，例如具有可通约和非线性的耦合系统。 -可通约频率、陀螺系统、时滞系统以及由乘法和加法载荷激发的多自由度系统。所提出的研究将极大地促进与结构动态稳定性相关的知识和技术的进步。随机参数共振的研究将为协议和措施提供信息，通过调整结构参数或爆破变量，以避免或减轻由地震、风或应力波载荷引起的动态灾害。​该研究计划将为培训 HQP 提供独特且前沿的机会因此，该计划将使加拿大的建筑和挖掘行业受益。