Mathematical Sciences: Modeling, Analysis and Control Of Multilayer Plates

点击翻译按钮获取中文摘要

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. ***