Theoretical Approaches to the Dynamics of Fluid-Structure Interactions in Various Applications

Fluid-structure interactions have received a vast interest from the engineering community for decades with primarily experimental and numerical approaches utilized to tackle arising practical problems. More recently (at least in the last two decades), the field has started to attract applied mathematicians. It can be partially explained by the fact that mathematical modeling of fluid and structural components has advanced significantly, and the point has reached where its coupling is considered to be feasible and promising with all the mathematical apparatus developed up-to-date. Along these lines, current study is intended to build a bridge between mechanical engineering and applied mathematics communities to establish practical but rigorous approaches to adequately respond to today challenges the scientific community has been faced to. In this context, an ultimate goal is to end up with the methods and approaches to be general enough to admit applications in a widest scale and materials properties ranges. To make the ultimate goal more achievable, it is reasonable to reach it in step-by-step fashion. In this study I consider theoretically three distinct problems united by the same solving approach namely, spatial-temporal separation analysis. More specifically, the case of the moving structure for fluid-structure interactions in application to prediction and optimization of the 3D printing process (constrained-surface stereolithography) is considered in Chapter 2. The proposed approach was verified numerically and showed an excellent agreement between theoretical model and numerical simulations. In Chapters 3 and 4 the case of deformable structure for fluid-structure interactions in linearized elasticity approximation is addressed. In particular, Chapter 3 covers the dynamics of a single bubble and coupled bubble pair trapped in circular cavity (modeled as a clamped thin plate). The model developed has been verified experimentally for a single bubble and identical bubble pair and showed an excellent agreement. Chapter 4 is devoted to the behavior of thin cantilever beams subjected to spatially-distributed loads with homogeneous boundary conditions. Theoretical predictions for transverse beam displacements along with normal and tensile stresses have been verified with the available experimental data from other studies.