Nonlinear vibrations and stability of shells and panels in presence of fluid and flow

材料科学与工程的不断进步，沿着对改进设计、安全和能源效率要求的不断提高，需要建立和验证新的非线性理论来描述薄壁结构与周围流体之间的相互作用。本文研究薄壁结构在流固耦合作用下的非线性振动和动力稳定性。传统的层压复合材料和功能梯度材料的薄壳、板和弯曲面板（具有单曲率或双曲率）可以在许多工程应用中找到，例如在飞行器、航天器、火箭、汽车、计算机磁盘（CD）、DVD、硬盘、潜艇、船、储罐和建筑物的屋顶中。壳结构也是许多生物系统的一部分，例如在人体中发现的肺通道和静脉。研究的目标是双重的：（一）开发一个研究接近开放的问题，在实验，理论和数值研究的突破性创新，和（二）使用统一的方法来合并分支研究，在过去已经单独进行，但目前有许多共同的问题。本研究还旨在改进现有的壳体非线性力学理论模型，例如通过构建一个新的一致的非线性壳体理论，包括三阶剪切变形和转动惯量，这对先进材料特别重要。非线性分析将（i）通过开发基于降阶模型的创新数字代码进行数字分析，（ii）通过开发复杂的测量系统和程序进行实验分析，包括用于放置在水洞和风洞中的样品的激光多普勒振动计，以验证数字代码，研究复杂的动力学并评估几何缺陷的影响。具体而言，实验程序还将涉及（a）利用突发随机或冲击激励的实验模态分析;以及（B）利用反馈控制的步进正弦激励识别非线性响应，改变激励频率以引起滞后和跳跃。

The continuous advancement of material science and engineering along with the increasing demand for improved design, safety and energy efficiency requirements necessitates the establishment and verification of new nonlinear theories to describe the interaction between thin-walled structures and the surrounding fluid. The proposed research considers the study of nonlinear vibrations and dynamic stability of thin-walled structures with fluid-structure interaction. Thin shells, plates and curved panels (with single or double curvature) of traditional, laminated composite and functionally graded materials can be found in many engineering applications e.g. in aircraft, spacecraft, rockets, cars, computer disks (CD), DVD, hard-disks, submarines, boats, storage tanks and roof of buildings. Shell structures are also part of many biological systems such as the pulmonary passage and veins found in the human body. The objective of the research is twofold: (i) to develop a study approaching open problems with ground-breaking innovations in experimental, theoretical and numerical investigation, and (ii) to use an unifying approach to merge branches of research that have proceeded separately in the past but that present many common problems. This research also aims to improve existing theoretical models for the nonlinear mechanics of shells, e.g. by constructing a new consistent nonlinear shell theory including third-order shear deformation and rotary inertia, which is particularly important for advanced materials. The nonlinear analysis will be (i) performed numerically, by developing innovative numerical codes based on reduced-order models and, (ii) experimentally, by developing a sophisticated measuring system and procedure, including a laser Doppler vibrometer used on specimens placed in water and wind tunnels, in order to validate the numerical codes, study the complex dynamics and evaluate the effect of geometric imperfections. Specifically, the experimental procedure will also involve (a) experimental modal analysis with burst random or impact excitation; and (b) identification of the nonlinear response using feedback controlled step-sine excitation, altering the excitation frequency to induce hysteresis and jumps.