U.S.-France Cooperative Research: Shape Analysis of DampingProcesses for Elastic Systems in Structural Modelling

这项为期三年的奖项支持美法在应用数学方面的合作研究。调查人员是弗吉尼亚大学的Irena Lasiecka和Roberto Triggiani，以及尼斯大学的J.P.Zolsio和M.Souli。研究人员将利用偏微分方程组、双曲型方程和数值分析来解决结构力学中的一些问题。该项目的重点是弹性结构，其动力行为受到内部振动阻尼的影响。其目的是通过确定弹性结构的最佳形状或设计来增强稳定性，从而减少不需要的振动。美国研究人员将他们在结构阻尼的数学建模、最优控制和相关问题以及利用弹性偏微分方程来确定可控性和稳定性方面的专业知识带到了这次合作中。这与法国在形状分析和优化方面的专业知识相辅相成。这项研究在空间力学和控制领域具有重要的应用。

This three-year award supports U.S.-France cooperative research in applied mathematics. The investigators are Irena Lasiecka and Roberto Triggiani from the University of Virginia and J.P. Zolesio and M. Souli from the University of Nice. The investigators will utilize partial differential equations, hyperbolic equations and numerical analysis in approaching a number of problems in structural mechanics. The project focuses on elastic structures whose dynamical behavior is effected by internal damping of vibrations. The objectives are to enhance stability properties by determining the optimal shape or design of the elastic structure so that undesirable vibrations are reduced. The U.S. investigators bring to this collaboration their expertise in mathematical modelling of structural damping, optimum control and related questions and the utilization of elastic partial differential equations for determining controllability and stabilization properties. This is complemented by French expertise in shape analysis and optimization. The research has important applications in the areas of space mechanics and control.