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  1. Issue 14 , September | Onera Aerospacelab Journal
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  3. Nonlinear Aeroelasticity
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  5. Studies in Nonlinear Aeroelasticity

In the past 20 years, the Duke aeroelastic group has designed many aeroelastic models and conducted wind tunnel tests to evaluate new theoretical aeroelastic theories and new computational methods. He has served on the boards of visitors of several universities and is a consultant to government, industry and universities in science and technology policy and engineering education as well as on the topics of his research. Dowell research ranges over the topics of aeroelasticity, nonsteady aerodynamics, nonlinear dynamics and structures. In addition to being author of over three hundred research articles, Dr.

His teaching spans the disciplines of acoustics, aerodynamics, dynamics and structures. Dowell received his B.

Issue 14 , September | Onera Aerospacelab Journal

In , Arthur Roderick Collar defined aeroelasticity as "the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an airstream, and the influence of this study on design. In an aeroplane, two significant static aeroelastic effects may occur.

Perturbation methods for nonlinear PDEs (Lecture - 02) by Vishal Vasan

Divergence is a phenomenon in which the elastic twist of the wing suddenly becomes theoretically infinite, typically causing the wing to fail spectacularly. Control reversal is a phenomenon occurring only in wings with ailerons or other control surfaces, in which these control surfaces reverse their usual functionality e.

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Divergence occurs when a lifting surface deflects under aerodynamic load so as to increase the applied load, or move the load so that the twisting effect on the structure is increased. The increased load deflects the structure further, which eventually brings the structure to the point of divergence. Divergence can be understood as a simple property of the differential equation s governing the wing deflection. For example, modelling the airplane wing as an isotropic Euler—Bernoulli beam , the uncoupled torsional equation of motion is:.

Under a simple lift forcing theory the aerodynamic moment is of the form:. This yields an ordinary differential equation of the form:. For given structural parameters, this will correspond to a single value of free-stream velocity U. This is the torsional divergence speed.

Nonlinear Aeroelasticity

Note that for some special boundary conditions that may be implemented in a wind tunnel test of an airfoil e. Control surface reversal is the loss or reversal of the expected response of a control surface, due to deformation of the main lifting surface. For simple models e. Control reversal can be used to aerodynamic advantage, and forms part of the Kaman servo-flap rotor design.

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Dynamic aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:.

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Flutter is a dynamic instability of an elastic structure in a fluid flow, caused by positive feedback between the body's deflection and the force exerted by the fluid flow. In a linear system , 'flutter point' is the point at which the structure is undergoing simple harmonic motion —zero net damping —and so any further decrease in net damping will result in a self-oscillation and eventual failure.

Flutter can be classified into two types: hard flutter , in which the net damping decreases very suddenly, very close to the flutter point; and soft flutter , in which the net damping decreases gradually.

For nonlinear systems , flutter is usually interpreted as a limit cycle oscillation LCO , and methods from the study of dynamical systems can be used to determine the speed at which flutter will occur. Structures exposed to aerodynamic forces—including wings and aerofoils, but also chimneys and bridges—are designed carefully within known parameters to avoid flutter.

In complex structures where both the aerodynamics and the mechanical properties of the structure are not fully understood, flutter can be discounted only through detailed testing. Even changing the mass distribution of an aircraft or the stiffness of one component can induce flutter in an apparently unrelated aerodynamic component. At its mildest this can appear as a "buzz" in the aircraft structure, but at its most violent it can develop uncontrollably with great speed and cause serious damage to or lead to the destruction of the aircraft, [13] as in Braniff Flight , or the prototypes for the VL Myrsky fighter aircraft.

Famously, the original Tacoma Narrows Bridge was destroyed as a result of aeroelastic fluttering. In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.

Studies in Nonlinear Aeroelasticity

Buffeting is a high-frequency instability, caused by airflow separation or shock wave oscillations from one object striking another. It is caused by a sudden impulse of load increasing. It is a random forced vibration. Generally it affects the tail unit of the aircraft structure due to air flow downstream of the wing.