Large Deflection Inextensible Beams and Plates and their Responses to Nonconservative Forces: Theory and Computations
There is a growing interest among aeroelasticity researchers for insight into large deflection oscillations of aerospace structures. Here, a new beam and plate model is derived using Hamilton's Principle to lay the structural framework for a nonlinear, large deflection aeroelastic model. Two boundary conditions of the beam are explored: cantilevered and free-free. For a plate, the cantilevered boundary condition is considered. In these conditions, the nonlinearity stems from the structure's large curvature rather than from stretching. Therefore, this model makes use of the simplifying assumption that the the structure has no strain along the midplane; thus the model is ``inextensible." Insight into the nonlinearity of this system is gained by applying harmonic loads to the structure, and stability conditions are also investigated by applying nonconservative follower loads.
Upon validating the structural model, the model is then coupled with aerodynamic models to form new, nonlinear aeroelastic models. Using classical aeroelasticity tools such as Piston Theory to model aerodynamic forces on the largely deflected cantilever, new insights are gained into the stability behavior of the system, the post-flutter behavior of the system, and the utility of these classic techniques with these novel configurations. With the large deflection cases, several novel nonlinearities are introduced, and it is shown that the systems are highly sensitive to the inclusion of these nonlinearities. Of course these classical aerodynamic theories are derived assuming small deflections, so attention is given to ensure that the Classical Piston Thoery is applicable in the current configurations. Also a new aerodynamic theory is proposed for pressures on structures undergoing large deflections. In total, this document proposes and explores new methodologies for modeling aeroelastic structures which tend to undergo large elastic deformations.
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