Asymptotic analysis of boundary value problems for strongly inhomogeneous multi-layered elastic plates

民用、航空航天和汽车工程如今正面临着令人兴奋的工业发展，激发了新的多功能和可持续材料在结构部件中的应用。经历重大技术变革的一个关键领域涉及多层结构的设计，这些结构的特征通常是层的机械和几何特性的高对比度。各种各样的这种复合材料出现在许多应用中，包括在汽车工程中广泛开发的轻质结构部件，其目前强烈关注绿色汽车生产。此外，现代航空航天工业受益于使用多层结构，该多层结构包含新型轻质多功能材料，例如气凝胶，在飞行器中提供隔热和隔音。尽管快速增长的工业需求，一个一致的数学方法建模的薄弹性层压板与一个强大的垂直不均匀性尚未开发。其主要原因是机械和几何特性的对比，导致许多额外的问题参数。另一个基本问题是，高对比度层压板的最实际重要的低频振动表现出以前没有观察到的均匀或弱不均匀结构的新功能。一个复杂的低频响应显着复杂的数值和实验数据的解释，旨在结构优化和非破坏性evaluation.This项目将提供一个相当普遍的近似模型，高对比度的多层薄板，涵盖了广泛的问题参数，并涉及数学上一致的方程的低频运动和边界条件沿沿着的边缘。边界条件的推导传统上是薄弹性结构的严格理论中的主要挑战，并且仅在均匀框架内进行了尝试。

Civil, aerospace and automotive engineering are nowadays facing exciting industrial developments, inspiring new multifunctional and sustainable materials to be implemented within structural components. A key area, experiencing major technological changes, is concerned with design of multi-layered structures which are often characterised by a high contrast in mechanical and geometric properties of the layers. A diverse variety of such composites arises in numerous applications, including lightweight structural components widely exploited in automotive engineering which is currently strongly focused on green car production. In addition, the modern aerospace industry benefits from making use of multi-layered structures incorporating new lightweight multifunctional materials, such as aerogels, providing both thermal and acoustical insulation in aircrafts. In spite of rapidly growing industrial demands, a consistent mathematical approach for modelling of thin elastic laminates with a strong vertical inhomogeneity has not yet been developed. The main reason for this is presence of the contrast in mechanical and geometrical characteristics, resulting in numerous extra problem parameters. Another fundamental problem is that the most practically important low-frequency vibrations of high-contrast laminates manifest novel features which has not been previously observed for homogeneous or weakly inhomogeneous structures. A sophisticated low-frequency response significantly complicates interpretation of numerical and experimental data aimed at structural optimisation and non-destructive evaluation.This project will provide a fairly universal approximate model for high-contrast multi-layered thin plates covering a broad range of problem parameters and involving the mathematically consistent equations of the low-frequency motion and the boundary conditions along the edges. The derivation of the boundary conditions is traditionally the main challenge in the rigorous theories for thin elastic structures and have been attempted only within the homogeneous framework.