Nonlinear dynamics of shell and plate structures, multi-dimensional and multi-field applications

这项拟议的研究将提出一种统一的方法来研究机械、航空航天、核、纳米和生物医学应用中的壳的非线性动力学和流固耦合。飞行器、航天火箭的外壳结构与生物医学应用的外壳结构有相似之处。然而，这些应用的材料特性非常不同。由传统、复合材料和功能梯度材料制成的壳和板可以被建模为线弹性材料，而软生物材料则需要被建模为超弹性和粘弹性。 对振动的研究将以数字方式进行，方法是开发基于使用自然模式进行离散化的降阶模型的创新数字代码，并在试验中使用复杂的测量系统和程序，包括先进的三维激光多普勒振动仪，以获取振动过程中的位移和速度。 有五个主要科学主题将申请者未来五年的研究联系在一起。第一个目标是利用一种新的一致非线性高阶剪切变形理论对壳结构的非线性动力学进行数值模拟，该理论保留了旋转惯性和厚度变形，并应用于夹层结构、功能梯度和软生物材料。第二个目标是实验测试，目的是通过对存在流固相互作用的复合材料和软材料结构进行测试，全面了解物理行为并验证非线性结构模型。第三个目标是大振幅振动的非线性阻尼辨识和建模。第四个目标是基于一种新的考虑厚度变化、血液脉动流动、材料和耗散非线性的非线性壳理论，对人体主动脉的稳定性和动力学进行分析。第五个目标是解决二维材料中纳米器件的动力学公开问题，如石墨烯纳米板。特别是，由于2D材料非常薄，非线性和参数振动非常容易被激发。在这个尺度上，制造缺陷(如起皱)的影响尤其重要，它们对动力学的影响是一个悬而未决的问题。 这项拟议的研究的影响将横跨从心血管生物力学到纳米设备的几个学科。研究结果有可能启发新一代主动脉假体的设计，并揭示导致主动脉夹层和破裂的病理过程背后目前缺乏的生物力学解释。深入了解2D材料中纳米器件的动力学，可能会定义新的设计方法来指导这种新一代材料的产品开发。

The proposed research will propose a unifying approach to investigate nonlinear dynamics and fluid-structure interaction of shells for mechanical, aerospace, nuclear, nano and biomedical applications. There are similarities between the shell structures of aircraft, space rockets and those for biomedical applications. However, material properties for these applications are very different. Shells and plates made of traditional, composite and functionally graded materials can be modelled as linear elastic material, while soft biomaterials need to be modelled as hyperelastic and viscoelastic. The study of vibrations will be performed numerically, by developing innovative numerical codes based on reduced-order models that use natural modes for discretization and, experimentally with sophisticated measuring systems and procedures, including an advanced three-dimensional laser Doppler vibrometer to acquire displacements and velocities during vibrations. There are five major scientific themes linking the applicant's research over the next five years. The first goal is the numerical simulation of the nonlinear dynamics of shell structures using a new consistent nonlinear higher-order shear deformation theory that retains rotary inertia and thickness deformation with applications to sandwich structures, functionally graded and soft biological materials. The second goal is experimental testing with the aim of fully understanding the physical behaviour and validating the nonlinear structural models by performing tests on composite and soft material structures in presence of fluid-structure interaction. The third goal is the nonlinear damping identification and modelling in large-amplitude vibrations. The fourth goal is the stability and dynamic analysis of human aorta based on a new nonlinear shell theory that takes into account thickness variation, blood pulsatile flow, material and dissipation nonlinearities. The fifth goal is to address open problems of dynamics of nano-devices in 2D materials, as graphene nano-plates. In particular, nonlinear and parametric vibrations are extremely easily excited since the 2D materials are extremely thin. The effect of manufacturing imperfections, like wrinkling, is particularly important at this scale and their influence on the dynamics is an open problem. The impact of the proposed research will be transversal to several disciplines from cardiovascular biomechanics to nano-devices. Research findings have the potential to inspire the design of a new generation aortic prosthesis and reveal the currently missing biomechanical explanation behind the pathological process leading to aortic dissection and rupture. Providing a deep insight into the dynamics of nano-devices in 2D materials will potentially define novel design methods to guide product development of this new generation material.