Vibration and Buckling of Viscoelastic Structures with Geometric and Material Uncertainties - Conves Modelling

具有几何和材料不确定性的粘弹性结构的振动和屈曲 - Conves 建模

• 批准号: 9215698
• 负责人: Isaac Elishakoff
• 金额: $ 10.1万
• 依托单位: Florida Atlantic University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-01-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9215698&HistoricalAwards=false
• 关键词: Vibration; Buckling; Viscoelastic; Structures; Geometric

Fundamental issues of the methodology, convex modelling of uncertainty, dedicated to unified treatment of geometric and material characteristics, are put forward in this research. Instead of classical probabilistic methods, no probabilistic treatment is utilized, but the new set-theoretical description of the uncertain variables and functions is presented. In addition, instead of usual optimization problems, where the minimum possible responses or least favorable shapes of the structures are sought, here an uncertainty modelling is developed as an anti-optimization problem of finding the least favorable responses due to shape or material uncertainty. Special emphases are placed on vibration and dynamic buckling of viscoelastic structures. The novel dynamic stability criterion based on Lyapunov exponents is introduced for viscoelastic structures. New treatment of uncertainty is especially attractive from the design point of view-since extrenal responses can be used for valid design of structures, with scant experimental data needed for their substantiation.

本研究提出了方法论的基本问题，即不确定性凸建模，致力于统一处理几何特征和材料特征。本文不采用传统的概率方法，而是采用一种新的集论方法来描述不确定变量和函数。此外，在通常的优化问题中，寻求最小可能的响应或最不利的结构形状，而不是通常的优化问题，在这里，不确定性模型被发展为寻找由于形状或材料不确定性而产生的最不利响应的反优化问题。特别强调粘弹性结构的振动和动力屈曲。提出了一种基于李雅普诺夫指数的粘弹性结构动力稳定性判据。从设计的角度来看，对不确定性的新处理特别有吸引力，因为外部响应可以用于有效的结构设计，而需要很少的实验数据来证实它们。