Dynamics Of A Two-dimensional Flexible Plate Immersed In Inviscid Flow And Effects Of The Material Viscoelasticity

Complex interactions of plates with ambient fluid are common in nature, e.g. tree leaf falling in the air, fish swimming in the water. The phenomena are also common in daily lives, e.g. flag flapping in a wind, aerofoil oscillating in a flow. During the interaction, the plate has complex nonlinear dynamics, e.g. chaos, and as a result, the study of this topic is of practical and theoretical significance. This dissertation focuses on the interaction between a plate and the ambient fluid. The objectives of this dissertation include:(1) to explore the nonlinear dynamics of the plate;(2) to investigate energy exchange between the plate and fluid;(3) the further study on the dynamics of a plate with external excitation. The main results of this dissertation are as follows:1. A two-dimensional model was developed to study the interaction between a flexible plate and the ambient inviscid fluid. The model was validated by comparing predicted responses with available experimental results.2. For a system with a flag immersed in an inviscid flow, a route from a steady state to a chaotic state was investigated with the increase of the dimensionless fluid velocity. Five distinct periodic oscillating states and three chaotic states are identified along the route. For the periodic symmetrical oscillating states, the frequency of the system increases with the increase of the dimensionless fluid velocity, and the drag force on the flag scales with the Strouhal number. The system transitions from one periodic state to another via period-doubling bifurcations or quasi-periodic bifurcations, and it transitions from a periodic state to a chaotic state via quasi-periodic bifurcations.3. Viscoelastic properties of the fins of Crucian carp (Carassius auratus) were measured with relaxation experiments. A fractional Zener model was used to fit the relaxation force, and results show that the model could describe the viscoelastic properties of the fins of Crucian carp well.4. Effects of the material viscoelasticity on flag flutter were studied based on three models, i.e. the classic Kelvin-Voigt model, the fractional element and the fractional Kelvin-Voigt model. Results show that with the increase of the material damping, the flutter frequency decreases, and the dissipation rate initially increases and then decreases. The increase of the material damping causes the transition of the system from a higher frequency oscillating state to a lower frequency oscillating state, and from a chaotic state to a periodic state.5. The dynamics of a flag in a two-dimensional inviscid flow pitched periodically at the leading edge was studied. For most pitching frequencies, the flag flaps with the nature frequency of the system and the pitching frequency; when the pitching frequency is in certain ranges, the flag flaps with only one frequency, which is either the nature frequency or the pitching frequency. When the pitching frequency is around the natural frequency of the system, the resonance phenomenon is observed.6. A formulation of fish swimming was presented. In the model, the fish body in inviscid fluid swims freely with the activation of muscle contraction. The fish body is simplified as a non-uniform beam and the muscle contraction is simplified as bending moments along the fish body.