# Investigating the Route to Flutter in a Pitch–Plunge Airfoil Subjected to Combined Flow Fluctuations

01 Jan 2021-pp 369-378

TL;DR: In this article, a pitch-plunge airfoil with cubic hardening nonlinearity in the pitch degree of freedom is modeled as a long time-scale random process and the role of noisy flow fluctuations in the same is analyzed by examining the dependency on noise intensity.

Abstract: The dynamics and response a pitch–plunge airfoil with cubic hardening nonlinearity in the pitch degree of freedom are investigated numerically. The aerodynamics is assumed to be linear and modeled using the unsteady aero-dynamical formulation. The flow is fluctuating in both the longitudinal and vertical directions. The fluctuating flow is mathematically modeled as a long time-scale random process. The mean flow speed is used as the bifurcation parameter, and response analysis is carried out by systematically varying the bifurcation parameter. The route to flutter is presented, and the role of noisy flow fluctuations in the same is analyzed by examining the dependency on noise intensity.

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TL;DR: An introduction to the theory of aeroelasticity, An Introduction to the Theory of Aero-Elasticity as mentioned in this paper, An introduction to aero-elasticities,

Abstract: An introduction to the theory of aeroelasticity , An introduction to the theory of aeroelasticity , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

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TL;DR: In this paper, a presentation of the determination of gust loads on airplanes, especially continuous turbulence gust loads, is presented, emphasizing the basic concepts involved and covers relationships, definitions of terminology and nomenclature, historical perspective and explanations of calculations.

Abstract: This is a presentation of the determination of gust loads on airplanes, especially continuous turbulence gust loads. It emphasizes the basic concepts involved and covers relationships, definitions of terminology and nomenclature, historical perspective and explanations of calculations.

446 citations

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01 Jan 1940

TL;DR: In this paper, the aerodynamic inertia and the angle of attack of the infinite wing of a fixed aspect ratio plane were corrected by correcting the aerodynamics inertia and angle of attacks of the plane.

Abstract: Unsteady-lift functions for wings of finite aspect ratio have been calculated by correcting the aerodynamic inertia and the angle of attack of the infinite wing. The calculations are based on the operational method.

397 citations

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TL;DR: In this paper, the effect of a cubic structural restoring force on the flutter characteristics of a two-dimensional airfoil placed in an incompressible flow is investigated, and the results for soft and hard springs are presented for a pitch degree-of-freedom nonlinearity.

Abstract: In this paper, the effect of a cubic structural restoring force on the flutter characteristics of a two-dimensional airfoil placed in an incompressible flow is investigated. The aeroelastic equations of motion are written as a system of eight first-order ordinary differential equations. Given the initial values of plunge and pitch displacements and their velocities, the system of equations is integrated numerically using a fourth order Runge-Kutta scheme. Results for soft and hard springs are presented for a pitch degree-of-freedom nonlinearity. The study shows the dependence of the divergence flutter boundary on initial conditions for a soft spring. For a hard spring, the nonlinear flutter boundary is independent of initial conditions for the spring constants considered. The flutter speed is identical to that for a linear spring. Divergent flutter is not encountered, but instead limit-cycle oscillation occurs for velocities greater than the flutter speed. The behaviour of the airfoil is also analysed using analytical techniques developed for nonlinear dynamical systems. The Hopf bifurcation point is determined analytically and the amplitude of the limit-cycle oscillation in post-Hopf bifurcation for a hard spring is predicted using an asymptotic theory. The frequency of the limit-cycle oscillation is estimated from an approximate method. Comparisons with numerical simulations are carried out and the accuracy of the approximate method is discussed. The analysis can readily be extended to study limit-cycle oscillation of airfoils with nonlinear polynomial spring forces in both plunge and pitch degrees of freedom.

108 citations

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TL;DR: In this article, the dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow are investigated numerically using a Monte Carlo approach, and the results are examined in terms of the probability structure of the response and the largest Lyapunov exponent.

Abstract: The dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow is investigated numerically using a Monte Carlo approach. Both the longitudinal and vertical components of turbulence, corresponding to parametric (multiplicative) and external (additive) excitation, respectively, are modelled. The properties of the airfoil are chosen such that the underlying non-excited, deterministic system exhibits binary flutter; the loss of stability of the equilibrium point due to flutter then leads to a limit cycle oscillation (LCO) via a supercritical Hopf bifurcation. For the random system, the results are examined in terms of the probability structure of the response and the largest Lyapunov exponent. The airfoil response is interpreted from the point of view of the concepts of D- and P-bifurcations, as defined in random bifurcation theory. It is found that the bifurcation is characterized by a change in shape of the response probability structure, while no discontinuity in the variation of the largest Lyapunov exponent with airspeed is observed. In this sense, the trivial bifurcation obtained for the deterministic airfoil, where the D- and P-bifurcations coincide, appears only as a P-bifurcation for the random case. At low levels of turbulence intensity, the Gaussian-like bell-shaped bi-dimensional PDF bifurcates into a crater shape; this is interpreted as a random fixed point bifurcating into a random LCO. At higher levels of turbulence intensity, the post-bifurcation PDF loses its underlying deterministic LCO structure. The crater is transformed into a two-peaked shape, with a saddle at the origin. From a more universal point of view, the robustness of the random bifurcation scenario is critiqued in light of the relative importance of the two components of turbulent excitation.

49 citations