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

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的壳体的非线性动力学和流体-结构相互作用。飞机、航天火箭和生物医学应用的壳体结构之间有相似之处。然而，这些应用的材料特性非常不同。由传统、复合和功能梯度材料制成的壳体和板可以建模为线性弹性材料，而软生物材料需要建模为超弹性和粘弹性。 振动研究将采用数值方法，根据使用自然模式进行离散化的降阶模型开发创新性数值代码，并采用先进的三维激光多普勒测振仪等先进测量系统和程序进行实验，以获取振动期间的位移和速度。 有五个主要的科学主题连接申请人的研究在未来五年。第一个目标是壳结构的非线性动力学的数值模拟，使用一个新的一致的非线性高阶剪切变形理论，保留旋转惯性和厚度变形与应用程序的夹层结构，功能梯度和软生物材料。第二个目标是实验测试，目的是通过在存在流体-结构相互作用的情况下对复合材料和软材料结构进行测试，充分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识别和建模。第四个目标是一个新的非线性壳理论，考虑到厚度变化，血液脉动流，材料和耗散的非线性的基础上，人体主动脉的稳定性和动态分析。第五个目标是解决2D材料中纳米器件的动力学问题，如石墨烯纳米板。特别是，由于2D材料非常薄，因此非常容易激发非线性和参数振动。在这种尺度下，制造缺陷的影响（如毛刺）尤其重要，它们对动力学的影响是一个悬而未决的问题。 拟议研究的影响将横向于从心血管生物力学到纳米器件的几个学科。研究结果有可能激发新一代主动脉假体的设计，并揭示目前缺失的导致主动脉夹层和破裂的病理过程背后的生物力学解释。深入了解2D材料中纳米器件的动力学将可能定义新的设计方法，以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.