Mathematical Sciences: Modeling, Analysis and Control Of Multilayer Plates

9623144汉森本研究涉及多层板的建模和分析，其中层内剪切变形的影响可能很重要。 具体实例包括层压板、约束层板和具有表面安装致动器的板。 该项目将（i）开发新的动态多层板模型并改进现有模型;（ii）确定各种模型在模型设计参数方面的有效性范围;（iii）确定如何设计控制和稳定反馈，使其在模型参数不确定性方面具有鲁棒性。 剪切变形板的Reissner-Mindlin理论被用来获得一个初始模型，允许独立的剪切变形中的每一层。 较低阶的近似模型，更适合于计算和模拟，然后将获得微扰技术。 各种模型的有效性范围将通过分析初始模型的解相对于适当的扰动参数的连续性来研究。 一旦开发的各种系统的解决方案的连续性，鲁棒性和灵敏度方面的参数和不确定性的问题将进行分析。 本研究涉及多层板的建模和分析，其中层内剪切变形的影响可能很重要。 具体实例包括层压板、约束层板和具有表面安装致动器的板。 该研究适用于多层复合材料的设计和控制中出现的一大类建模问题。 这种材料用于从体育用品到船体的广泛应用中，并且通常需要构造成满足各种设计标准，例如最佳强度质量比，或者具有某些最佳阻尼特性。 在许多应用中，主动反馈控制将被用于增强材料在其预期应用中的性能。 这项研究将提供一个统一的，严格的，数学基础的建模等材料及其动态特性，并将开发各种控制理论的模型的属性。 为了跟上传感器快速增长的速度，需要这样的理论基础 和执行器，并充分利用现代制造能力。 ***

9623144 Hansen This research involves the modeling and analysis of multilayer plates in which the effects of shear deformation within layers may be important. Specific examples include laminated plates, constrained layer plates and plates with surface-mounted actuators. The project will (i) develop new dynamic multilayer plate models and refine existing ones; (ii) determine the range of validity of the various models with respect to design parameters in the models; and (iii) determine how to design controls and stabilizing feedbacks that are robust with respect to parameter uncertainties in the models. The Reissner-Mindlin theory of shear-deformable plates is used to obtain an initial model that allows independent shear deformations in each layer. Lower order approximate models which are more amenable to computations and simulations will then be obtained by perturbation techniques. The range of validity of the various models will be investigated by analyzing the continuity properties of the solutions of the initial model with respect to the appropriate perturbation parameters. Once the continuity properties of the solutions of the various systems are developed, issues of robustness and sensitivity with regard to parameters and uncertainties will be analyzed. %%% This research involves the modeling and analysis of multilayer plates in which the effects of shear deformation within layers may be important. Specific examples include laminated plates, constrained layer plates and plates with surface-mounted actuators. The research is applicable to a large class of modeling problems that arise in the design and control of multilayer composite materials. Such materials are used in a wide range of applications, from sporting goods to ship hulls, and often need to be constructed to meet various design criteria, such as optimal strength-to-mass ratio, or to have certain optimal damping properties. In many applications, active feedback control will be utilized to enhance the performance of the material in its intended application. This research will provide a unified, rigorous, mathematical foundation for the modeling of such materials and their dynamic properties, and will develop various control-theoretic properties of the models. Such a theoretical foundation is needed in order to keep pace with the rapidly increasing speed of sensors and actuators and to take full advantage of modern manufacturing capabilities. ***