The Dynamics Of Plates In Axial Flow With Fluid-Structure Interaction

The interactions between fluids and plates widely exist in nature. The research on this subject, which has great theoretical value and practical significance, not only reveals the mechanism of flow-induced vibration of plates, but also helps us to improve engineering design and application performance, prevent the vibration of structures induced by fluid flow, enhance the system stability and reliability, and fabricate new energy-harvesting devices to utilize the energy from nature.Fluid-structure interaction (FSI) is a cross-discipline which involves fluid mechanics, solid mechanics, dynamics and computational mechanics. In this dissertation, stress has been placed on the study of the dynamics of cantilevered plates subjected to axial flow, which is based on linear model, nonlinear model and finite element model, coupled with wind tunnel testing. The main contributions of this dissertation can be summarized as follows:1. A linear partial differential equation of motion based on the Euler-Bernoulli beam theory are derived for the two-dimensional plate with different boundary conditions, The plates are clamped at the leading edge and free at the trailing edge (cantilevered), or either clamped or pinned at both ends. The Galerkin method is used to discretize the partial differential equations, and the complex modal analysis is adopted to analyze the instability characteristics of the plates. The non-dimensional critical flow velocities are predicted, the relationship between damping, frequency and flow velocity were also discussed. It is shown that for low flow velocities below the critical point, the plates remains in the stable flat state; for high flow velocities beyond the critical point, the plates may be subject to buckling and flutter. Typically, cantilevered plates flutter in their second and third modes, clamped-clamped and pinned-pinned plates are subject to buckling in their first mode, and flutter in their higher modes, furthermore, second mode buckling occurs in pinned-pinned plates.2. Finite element equations of fluid and structure are developed, and finite element model of fluid-structure interaction for plates in axial flow is established. The dynamics of the two-dimensional cantilevered plate subjected to axial flow is investigated using COMSOL Multiphysics software. The dynamical behaviour and vibration responses of the cantilevered plate at corresponding flow velocity are presented.3. A nonlinear partial differential equation of motion of the two-dimensional plate in axial How based on the inextensibility assumption are derived from Hamilton's principle, and nondimensionalization of the nonlinear equation of motion is carried out. The pressure difference between the two sides of the plate is calculated with a panel method. The partial differential equation of motion is discretized involving the use of the Galerkin method, and the resulting set of nonlinear ordinary differential equations is solved by Houbolt's finite difference method. The convergence of simulation results with respect to four numerical parameters, i.e., the number of Galerkin modes, the number of panels, the time step and the length of truncated wake street, is examined, and the optimum values of these four parameters are obtained. The developed nonlinear model of the cantilevered plate is validated by comparing with published research findings.4. Critical flow velocities and flutter characteristics of two typical cantilevered plates with different mass ratio are predicted by means of the nonlinear model. The influence of four factors on the dynamics of the system are discussed, including the length of the upstream rigid segment, the material damping, the viscous drag and the longitudinal displacement. A hysteresis caused by vortex street is obtained by changing the initial deformation of the plate, finally the flutter boundary of the system is predicted. It is shown that the cantilevered plates lose stability at a critical flow velocity via a Hopf bifurcation, and limit-cycle oscillations are observed at higher flow velocities. With increasing the flow velocity, the flutter amplitude and frequency of the cantilevered plate increase monotonically, the transient time of the system decreases, the vibration modes of the plate change from a second-beam-mode shape to a complex shape with the appearance of a third-beam-mode component. With the consideration of the longitudinal displacement, the model predicts a larger flutter amplitude and a same critical flow velocity. The flutter amplitude increases as the length of the upstream rigid segment increases. With increasing the material damping coefficient and the viscous drag coefficient, the critical flow velocity increases, and the transverse displacement decreases monotonically. For short plates, the dependence of the critical flow velocity on the plate length is strong, the critical flow velocity decreases precipitously with increasing the plate length; for long plates, the critical flow velocity is not sensitive to the plate length, the critical flow velocity decreases gradually as the plate length increases, when the plate is sufficiently long, the critical flow velocity converges to a nearly constant value; for a medium length plate, the critical flow velocity jumps up and then down rapidly as the plate length increases.5. Experimental investigations of cantilevered plates are conducted in a wind tunnel. In the experiments, time traces, power spectral densities (PSDs), phase-plane plots, Poincare maps, probability density functions (PDFs) and autocorrelations are used to characterize the motions of the system. It is shown that the experimental critical flow velocity and flutter frequency increase as material damping coefficient is increased. The plates undergo periodic limit-cycle oscillations, quasiperiodic oscillation, and then chaotic motions with increasing flow velocity. For large aspect ratio plates, the cantilevered plates lose stability by a subcritical Hopf bifurcation, and the hysteresis phenomenon is obvious, which is considered to be due to three-dimensional spanwise deformation. Furthermore, in the hysteresis loop, the stable plate subjected to a relatively small external disturbance will flutter with the same amplitude as the self-excited oscillation at the same flow velocity. For small aspect ratio plates, they do not suffer three-dimensional deformation, the cantilevered plates lose stability by a supercritical Hopf bifurcation, and the hysteresis phenomenon disappears. The experimental flutter boundary is in good agreement with the current nonlinear theoretical prediction, which shows that the nonlinear model with structural stiffness nonlinearity and mass inertia nonlinearity developed here can be used to investigate this fluid-structure interaction problems excellently.