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In this paper two nonlinear effects are investigated. One is the effect of the static stiffness nonlinearity in changing the linear dynamic natural frequency and the other is the combination of nonlinear stiffness and nonlinear inertia effects in changing the nonlinear dynamic transient response due to a change in the initial release state of the system. A theoretical model has been developed for a cantilevered thin plate with a range of length to width ratio using beam theory and considering both stiffness and inertial nonlinearities in the model. Lagrange’s equation was used to deduce nonlinear inertia and stiffness matrices for a modal representation. Some insights into how these nonlinear components influence the beam response are presented. Measurements with both a hammer test and also a release test of cantilevered thin plates were done using different configurations and tip mass values. Results from static and dynamic analysis using the linear and the nonlinear theoretical model show good agreement between theory and experiment for natural frequencies and the amplitude displacements versus time. 

A cantilevered plate at an angle of attack in axial high speed flow represents a prototypical control surface. Using a computationally efficient modal structural model cou- pled with a novel enhanced piston theory aerodynamic method, a nonlinear aeroelastic model is developed. Results presented include pre-flutter stable steady state solutions, flutter points, and post-flutter limit cycle oscillations. Because of the computationally efficient methodology, many simulations can be run to define sensitivities to mathematical modeling, model parame- ters, and numerical methods. 

The large deflections of panels in subsonic flow are considered, specifically a fully clamped von Karman plate accounting for both rotational inertia in plate filaments and (mild) structural damping. The panel is taken to be embedded in the boundary of the positive half-space in ℝ3 containing a linear, subsonic potential flow. Solutions are constructed via a semigroup approach despite the lack of natural dissipativity associated with the generator of the linear dynamics. The flow–plate dynamics are then reduced—via an explicit Neumann-to-Dirichlet (downwash-to-pressure) solver for the flow—to a memory-type dynamical system for the plate. For the non-conservative plate dynamics, a global attractor is explicitly constructed via Lyapunov and recent quasi-stability methods. Finally, it is shown that, via the compactness of the attractor and finiteness of the dissipation integral, all trajectories converge strongly to the set of stationary states. 

The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers consider a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and the agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear postcritical limit cycle oscillations (LCO) are studied including a concentration on the force which enforces the inextensibility constraint.