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Prof. Earl H. Dowell
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA

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0 Acoustics
0 Aeroelasticity
0 Nonlinear Dynamics
0 Structural Dynamics
0 Unsteady Aerodynamics

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Aeroelasticity
Unsteady Aerodynamics
Nonlinear Dynamics
Structural Dynamics

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Journal article
Published: 31 December 2020 in Journal of Sound and Vibration
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This paper studies the dynamic behaviors of a magnetically coupled oscillator with two-degrees-of-freedom. For the certain parameter combinations, the target component (TC), which is excited by a base movement, enters the saturated steady-state responses. Another component, which is called as the spatially constrained system (SCS), is considered as an energy absorber pumping out of the energy from the TC under 1:3 internal resonance. The governing equations of motion are derived using a magnetic dipole model and then are solved with the method of multiple scales. The energy distributions between the TC and SCS can vary with the base movement amplitude and excitation frequency. The saturation behavior is found and used for constraining the moving amplitude of an excited system. The bifurcation diagrams reveal the complex and interesting responses when the excitation frequency and amplitude change. The results include the comparisons among the analytical predictions, numerical simulations, and experimental tests. For the purpose of suppressing the primary resonance, the present system effectively transfer the energy from the excited component. The jumping and saturation phenomena are found in the experiments and the changes in the spectrum of two steady-state responses are also observed.

ACS Style

J. Zhou; W. Zhang; X.S. Wang; B.P. Mann; E.H. Dowell. Primary resonance suppression of a base excited oscillator using a spatially constrained system: Theory and experiment. Journal of Sound and Vibration 2020, 496, 115928 .

AMA Style

J. Zhou, W. Zhang, X.S. Wang, B.P. Mann, E.H. Dowell. Primary resonance suppression of a base excited oscillator using a spatially constrained system: Theory and experiment. Journal of Sound and Vibration. 2020; 496 ():115928.

Chicago/Turabian Style

J. Zhou; W. Zhang; X.S. Wang; B.P. Mann; E.H. Dowell. 2020. "Primary resonance suppression of a base excited oscillator using a spatially constrained system: Theory and experiment." Journal of Sound and Vibration 496, no. : 115928.

Journal article
Published: 26 May 2020 in Journal of Fluids and Structures
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Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.

ACS Style

Larissa Drews Wayhs Lopes; Earl H. Dowell; Douglas D. Bueno. Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration. Journal of Fluids and Structures 2020, 96, 103054 .

AMA Style

Larissa Drews Wayhs Lopes, Earl H. Dowell, Douglas D. Bueno. Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration. Journal of Fluids and Structures. 2020; 96 ():103054.

Chicago/Turabian Style

Larissa Drews Wayhs Lopes; Earl H. Dowell; Douglas D. Bueno. 2020. "Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration." Journal of Fluids and Structures 96, no. : 103054.

Journal article
Published: 21 February 2020 in Energies
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Nowadays, actuator line method (ALM) has become the most potential method in wind turbine simulations, especially in wind farm simulations and fluid-structure interaction simulations. The regularization kernel, which was originally introduced to ALM to avoid numerical singularity, has been found to have great influence on rotor torque predictions and wake simulations. This study focuses on the effect of each parameter used in the standard kernel and the anisotropic kernel. To validate the simulation, the torque and the wake characteristics of a model wind turbine were measured. The result shows that the Gaussian width ϵ (for standard kernel) and the parameter in chord length direction ϵc (for anisotropic kernel) mainly affect the normal velocity of each blade element when using ALM but have little effect on the tangential velocity calculation. Therefore, these parameters have great influence on the attack angle and rotor torque prediction. The thickness parameter ϵt is the main difference between the standard kernel and the anisotropic kernel and it has a strong effect on the wind turbine wakes simulation. When using the anisotropic kernel, the wake structure is clearer and less likely to disperse, which is more consistent with the experimental results. Based on the studies above, a non-uniform mesh is recommended when using the anisotropic regularization kernel. Using a mesh refined in the main flow direction, ALM with anisotropic kernel can predict torque and wake characteristics better while maintaining low computational costs.

ACS Style

Zhe Ma; Liping Lei; Earl Dowell; Pan Zeng. An Experimental Study on the Actuator Line Method with Anisotropic Regularization Kernel. Energies 2020, 13, 977 .

AMA Style

Zhe Ma, Liping Lei, Earl Dowell, Pan Zeng. An Experimental Study on the Actuator Line Method with Anisotropic Regularization Kernel. Energies. 2020; 13 (4):977.

Chicago/Turabian Style

Zhe Ma; Liping Lei; Earl Dowell; Pan Zeng. 2020. "An Experimental Study on the Actuator Line Method with Anisotropic Regularization Kernel." Energies 13, no. 4: 977.

Journal article
Published: 31 January 2020 in Journal of Fluids and Structures
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A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.

ACS Style

Maxim Freydin; Earl H. Dowell; Thomas J. Whalen; Stuart J. Laurence. A theoretical computational model of a plate in hypersonic flow. Journal of Fluids and Structures 2020, 93, 102858 .

AMA Style

Maxim Freydin, Earl H. Dowell, Thomas J. Whalen, Stuart J. Laurence. A theoretical computational model of a plate in hypersonic flow. Journal of Fluids and Structures. 2020; 93 ():102858.

Chicago/Turabian Style

Maxim Freydin; Earl H. Dowell; Thomas J. Whalen; Stuart J. Laurence. 2020. "A theoretical computational model of a plate in hypersonic flow." Journal of Fluids and Structures 93, no. : 102858.

Journal article
Published: 11 December 2019 in Journal of Computational and Nonlinear Dynamics
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A free-free beam with a compressive follower force applied to one end exhibits interesting flutter and limit cycle oscillation responses. Here, the derivation from Lagrange's Equations is given for the nonlinear inextensible beam with such a force applied. The inextensibility constraint is met with a Lagrange Multiplier added to the Lagrangian, and the beam is allowed three rigid body modes in planar motion in addition to its elastic deformation. The Rayleigh-Ritz modal expansion method and the Runge-Kutta method are used to calculate time histories of the forced beam response. This new model is validated against classical results for the stability boundary and new limit cycle oscillation (LCO) bifurcation diagrams are computed.

ACS Style

Kevin A McHugh; Earl Dowell. Nonlinear Response of an Inextensible, Free-free Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics 2019, 15, 1 .

AMA Style

Kevin A McHugh, Earl Dowell. Nonlinear Response of an Inextensible, Free-free Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics. 2019; 15 (2):1.

Chicago/Turabian Style

Kevin A McHugh; Earl Dowell. 2019. "Nonlinear Response of an Inextensible, Free-free Beam Subjected to a Nonconservative Follower Force." Journal of Computational and Nonlinear Dynamics 15, no. 2: 1.

Journal article
Published: 23 October 2019 in Aerospace Science and Technology
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Wind tunnel walls may significantly affect the aerodynamic characteristics of an airfoil if the distance between walls is not large enough and the experimental data may be influenced by the confinement effect. The purpose of this paper is to investigate the wall effects on a NACA 0012 airfoil at high angle of attack (the flow over the airfoil is assumed to be fully separated). The effects on both a static airfoil and also an oscillating airfoil (pitching motion) are studied. Reynolds number varies from 105 to 3×105. For a static airfoil, there is a dominant frequency of the flow oscillations called the Strouhal or buffet frequency. Strouhal number of an airfoil in confined flow is affected by blockage ratio and angle of attack. A new wall correction formula for the Strouhal number has been determined. For an oscillating airfoil, lock-in is determined by a combination of excitation frequency and amplitude of the oscillating airfoil. The reason of difference between computational and experimental lock-in regions are explained. Lock-in region decreases with increase of blockage ratio. Reynolds number has slight impact on lock-in region, both in unconfined flow and confined flow.

ACS Style

Tong Zhou; Earl Dowell; Shun-Shan Feng. Computational investigation of wind tunnel wall effects on buffeting flow and lock-in for an airfoil at high angle of attack. Aerospace Science and Technology 2019, 95, 105492 .

AMA Style

Tong Zhou, Earl Dowell, Shun-Shan Feng. Computational investigation of wind tunnel wall effects on buffeting flow and lock-in for an airfoil at high angle of attack. Aerospace Science and Technology. 2019; 95 ():105492.

Chicago/Turabian Style

Tong Zhou; Earl Dowell; Shun-Shan Feng. 2019. "Computational investigation of wind tunnel wall effects on buffeting flow and lock-in for an airfoil at high angle of attack." Aerospace Science and Technology 95, no. : 105492.

Journal article
Published: 14 September 2019 in Mechanical Systems and Signal Processing
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Equations of motion for beams assuming only longitudinal, normal stress are derived for large-amplitude beam deflection. The formulation includes various physical extensibility conditions without expansion or truncation of their nonlinear nature. The Lagrange multiplier for an inextensible beam model is explicitly written. The limits of the applicability of various beams models with purely longitudinal, normal stress are explored, and the validity of a pure transverse displacement for a beam with fixed ends is quantified.

ACS Style

Dean Culver; Kevin McHugh; Earl Dowell. An assessment and extension of geometrically nonlinear beam theories. Mechanical Systems and Signal Processing 2019, 134, 106340 .

AMA Style

Dean Culver, Kevin McHugh, Earl Dowell. An assessment and extension of geometrically nonlinear beam theories. Mechanical Systems and Signal Processing. 2019; 134 ():106340.

Chicago/Turabian Style

Dean Culver; Kevin McHugh; Earl Dowell. 2019. "An assessment and extension of geometrically nonlinear beam theories." Mechanical Systems and Signal Processing 134, no. : 106340.

Journal article
Published: 01 August 2019 in AIAA Journal
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This work studies the instability (flutter) and poststability oscillations of an elastic shallow shell in a supersonic gas flow. The only available experimental results for flutter of a shallow shell with clamped edges are provided by Anderson. A comparison between theory and experiment is a novel and important contribution of this work. The nonlinear vibrations of a rectangular isotropic thin curved shell in supersonic airflow are studied to find the flutter speed and the limit cycle oscillations beyond the flutter boundary. Using the Galerkin method and the piston theory aerodynamic model for supersonic flow, the flutter and postflutter characteristics of the panel have been analyzed. Panel vibration frequencies and flutter dynamic pressure have been determined and compared with experimental results.

ACS Style

Sadegh Amirzadegan; Earl Dowell. Correlation of Experimental and Computational Results for Flutter of Streamwise Curved Plate. AIAA Journal 2019, 57, 3556 -3561.

AMA Style

Sadegh Amirzadegan, Earl Dowell. Correlation of Experimental and Computational Results for Flutter of Streamwise Curved Plate. AIAA Journal. 2019; 57 (8):3556-3561.

Chicago/Turabian Style

Sadegh Amirzadegan; Earl Dowell. 2019. "Correlation of Experimental and Computational Results for Flutter of Streamwise Curved Plate." AIAA Journal 57, no. 8: 3556-3561.

Journal article
Published: 01 July 2019 in Journal of Aerospace Information Systems
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Modern computational fluid dynamic simulations of flows about naval vessels produce an enormous amount of flow-field data. The computations are performed in order to model details of the erratic unsteady flows that can occur about naval superstructures. The flow-field data can then be used in flight simulators for naval pilot training purposes. Often, however, far too much data are generated for the flight simulators to process in real-time. This paper demonstrates the use of both proper orthogonal decomposition and Fourier series decomposition approaches for airwake dataset compression. The proper orthogonal decomposition method is used for compressing airwake data in the time domain, and Fourier series decomposition is used for compressing airwake data in the spatial coordinates. The approaches are applied to airwake data for a simplified frigate vessel model. A separate aircraft tanker configuration is also examined in order to demonstrate that the level of numerical precision can have an effect on the dataset compression results. Both approaches are effective at reducing airwake dataset size while preserving the dominant flow-field features, and both approaches are inexpensive and straightforward to implement. The level of dataset compression ultimately depends on the level of accuracy required by the user.

ACS Style

Jeffrey P. Thomas; Earl Dowell; Michael Anderson; Gregory Z. McGowan. Progress Toward Efficient Compression Algorithms for Application in Flight Simulation Environments. Journal of Aerospace Information Systems 2019, 16, 278 -288.

AMA Style

Jeffrey P. Thomas, Earl Dowell, Michael Anderson, Gregory Z. McGowan. Progress Toward Efficient Compression Algorithms for Application in Flight Simulation Environments. Journal of Aerospace Information Systems. 2019; 16 (7):278-288.

Chicago/Turabian Style

Jeffrey P. Thomas; Earl Dowell; Michael Anderson; Gregory Z. McGowan. 2019. "Progress Toward Efficient Compression Algorithms for Application in Flight Simulation Environments." Journal of Aerospace Information Systems 16, no. 7: 278-288.

Journal article
Published: 01 July 2019 in AIAA Journal
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This paper presents a study of the shock buffet phenomenon on the RA16SC1 supercritical airfoil using the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) modal approaches. The computational fluid dynamics simulation is validated, and the full buffet envelope of the RA16SC1 airfoil is mapped. POD and DMD techniques are then applied to compute a set of flow modes and corresponding dynamical data (for the DMD method). A dominant buffet mode is identified at the buffet frequency. The corresponding mode shape represents the interaction between the shock wave and boundary-layer. Higher modes, at multiples of the buffet frequency, show smaller coherent flow structures at the shock travel area. Further higher modes, of mixed frequencies, are associated with flow structures mainly in the boundary-layer area. Only a few modes are required for accurate reconstruction of the buffet flow field. Finally, it is shown that similar modes are present in all buffet angles of attack. The modal approach used in this study enables straightforward extraction of the underlying flow structures and dynamic properties of buffet flows.

ACS Style

Lior Poplingher; Daniella E. Raveh; Earl Dowell. Modal Analysis of Transonic Shock Buffet on 2D Airfoil. AIAA Journal 2019, 57, 2851 -2866.

AMA Style

Lior Poplingher, Daniella E. Raveh, Earl Dowell. Modal Analysis of Transonic Shock Buffet on 2D Airfoil. AIAA Journal. 2019; 57 (7):2851-2866.

Chicago/Turabian Style

Lior Poplingher; Daniella E. Raveh; Earl Dowell. 2019. "Modal Analysis of Transonic Shock Buffet on 2D Airfoil." AIAA Journal 57, no. 7: 2851-2866.

Conference paper
Published: 08 June 2019 in Lecture Notes in Electrical Engineering
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By modeling an aero-refueling hose as a flexible pipe, an experimental research is performed on measuring the sectional bending stiffness of a flexible pipe withstanding a internal-pressurized fluid. A Revised Midpoint-Concentrate-Force-Loading Methodology (RMCFLM) with its valid range is developed to measure the sectional bending stiffness of a flexible pipe. The total system measurement error would be controlled within 7%. Three test specimens of a silica gel pipe, a polyvinyl chloride pipe and a rubber hose with fabric insert are conducted to measure their sectional-bending-stiffness in variable internal-pressurized fluid. The sectional-bending-stiffness increases with an incremental fluid pressure in a flexible pipe. Furthermore, the equivalent elastic modulus of a pipe is smaller and a incremental rate of the sectional-bending-stiffness is larger.

ACS Style

Hao Wen; Aiming Shi; Earl Dowell; Xiang Li. Measuring the Aero-Refueling Hose Model’s Sectional-Bending-Stiffness in the RMCFLM Experimental System. Lecture Notes in Electrical Engineering 2019, 2974 -2991.

AMA Style

Hao Wen, Aiming Shi, Earl Dowell, Xiang Li. Measuring the Aero-Refueling Hose Model’s Sectional-Bending-Stiffness in the RMCFLM Experimental System. Lecture Notes in Electrical Engineering. 2019; ():2974-2991.

Chicago/Turabian Style

Hao Wen; Aiming Shi; Earl Dowell; Xiang Li. 2019. "Measuring the Aero-Refueling Hose Model’s Sectional-Bending-Stiffness in the RMCFLM Experimental System." Lecture Notes in Electrical Engineering , no. : 2974-2991.

Article
Published: 02 April 2019 in Science China Technological Sciences
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In this paper, the effects of the nonlinear vibration on stress distribution and fatigue life of the axially moving beam are studied. The parametric excitation of the flexible material is created by the pulsating moving speed. Three-to-one internal resonance condition is satisfied. The three-parameter model is adopted in the viscoelastic constitutive relation. The nonlinear vibration of the axially moving beam with parametric and internal resonance are studied by using the direct multiple scales method (MSM) with numerical simulation confirmation. Based on the approximate analytical solution, the distribution of tensile stress and bending stress on the axially moving beam is presented by adopting a V-belt as the prototype. Based on the maximum stable cyclic stress, the limit cycle response of the V-belt is utilized to evaluate the effect of the resonance on the fatigue life. Also, the influences of the internal resonance on the steady-state responses and the fatigue life of the V-belt are revealed. Numerical examples illustrate that large unwanted resonances occur and the second-order mode receives vibration energy from to the first-order mode. The numerical results demonstrate that the nonlinear vibration significantly reduces the fatigue life of the V-belt. The fatigue life analysis method in this paper can be applied to the excited vibration of other axially moving systems and even static continuum.

ACS Style

Hu Ding; Ling-Lu Huang; Earl Dowell; Li-Qun Chen. Stress distribution and fatigue life of nonlinear vibration of an axially moving beam. Science China Technological Sciences 2019, 62, 1123 -1133.

AMA Style

Hu Ding, Ling-Lu Huang, Earl Dowell, Li-Qun Chen. Stress distribution and fatigue life of nonlinear vibration of an axially moving beam. Science China Technological Sciences. 2019; 62 (7):1123-1133.

Chicago/Turabian Style

Hu Ding; Ling-Lu Huang; Earl Dowell; Li-Qun Chen. 2019. "Stress distribution and fatigue life of nonlinear vibration of an axially moving beam." Science China Technological Sciences 62, no. 7: 1123-1133.

Journal article
Published: 26 March 2019 in International Journal of Turbo and Jet Engines
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The clearance has an obvious influence on the rotordynamic characteristics of brush seals. In order to better know the influence of brush seal on the stability of the rotor bearing system, the rotordynamic coefficients of labyrinth brush seal under different clearance cases and operating conditions are numerically analyzed using CFD RANS solutions coupling with a non-Darcian porous medium model. The results show that at the same geometry parameter the radial force and tangential force will increase when the pressure ratio rises. And when the clearance increases, the direct stiffness decreases sharply at first and then rises slightly. The variation of cross-coupled stiffness is complex. Moreover, at the same operating condition the value of direct damping coefficients increases when clearance increases, which add a stable factor to the rotor.

ACS Style

Yuan Wei; Earl Dowell; Zhaobo Chen. Numerical Prediction of Impact of Clearance on Rotordynamic Coefficients for Labyrinth Brush Seal. International Journal of Turbo and Jet Engines 2019, 36, 31 -43.

AMA Style

Yuan Wei, Earl Dowell, Zhaobo Chen. Numerical Prediction of Impact of Clearance on Rotordynamic Coefficients for Labyrinth Brush Seal. International Journal of Turbo and Jet Engines. 2019; 36 (1):31-43.

Chicago/Turabian Style

Yuan Wei; Earl Dowell; Zhaobo Chen. 2019. "Numerical Prediction of Impact of Clearance on Rotordynamic Coefficients for Labyrinth Brush Seal." International Journal of Turbo and Jet Engines 36, no. 1: 31-43.

Journal article
Published: 07 March 2019 in Journal of Fluids and Structures
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Two experimental models are constructed, i.e. partially covered and fully covered, cantilevered plates with piezoelectric piezo patches and film sensors. Two different experimental methods are used to obtain large flapping vibrations, a mechanically forced vibration and a limit cycle oscillation from an aeroelastic responses. AC voltage outputs from the piezo patch or film sensors and a DC power extraction through a AC/DC converter circuit are obtained. These experiments are used to evaluate a new computational model and code for a piezoelectric-aeroelastic system.

ACS Style

D.M. Tang; Dani Levin; E.H. Dowell. Experimental and theoretical correlations for energy harvesting from a large flapping flag response. Journal of Fluids and Structures 2019, 86, 290 -315.

AMA Style

D.M. Tang, Dani Levin, E.H. Dowell. Experimental and theoretical correlations for energy harvesting from a large flapping flag response. Journal of Fluids and Structures. 2019; 86 ():290-315.

Chicago/Turabian Style

D.M. Tang; Dani Levin; E.H. Dowell. 2019. "Experimental and theoretical correlations for energy harvesting from a large flapping flag response." Journal of Fluids and Structures 86, no. : 290-315.

Journal article
Published: 25 January 2019 in Journal of Fluids and Structures
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Linear and nonlinear aeroelastic analyses and results for a cantilevered beam subjected to an unsteady subsonic airflow are presented as a model of a high aspect ratio wing. A third-order nonlinear beam model is used as the structural model. This model includes nonlinear inertial and damping terms as well as nonlinear stiffness terms. To model aerodynamic loads a Wagner model based on a state-space model along with 2D and 3D Peters’ aerodynamic models are used and the results are compared. The Galerkin method is used to transform partial differential equations to ordinary differential equations. For aeroelastic analysis of a high aspect ratio wing, using a state-space Wagner model reduces the number of degrees of freedom. The distribution of the lift and inflow derived using 2D and 3D Peters aerodynamic models are compared and the range of aspect ratios has been determined for which a 2D aerodynamic model is sufficient. There is a good agreement between the flutter speed obtained in this study and those reported in the literature. Beside nonlinear stiffness terms, the effects of nonlinear inertial and damping terms may be significant for flow velocities above the flutter speed. As the flow velocity increases further the oscillations lose their periodicity and become chaotic. Using the different number of structural modes, the convergence of the results is shown.

ACS Style

Amir Hossein Modaress-Aval; Firooz Bakhtiari-Nejad; Earl H. Dowell; David A. Peters; Hossein Shahverdi. A comparative study of nonlinear aeroelastic models for high aspect ratio wings. Journal of Fluids and Structures 2019, 85, 249 -274.

AMA Style

Amir Hossein Modaress-Aval, Firooz Bakhtiari-Nejad, Earl H. Dowell, David A. Peters, Hossein Shahverdi. A comparative study of nonlinear aeroelastic models for high aspect ratio wings. Journal of Fluids and Structures. 2019; 85 ():249-274.

Chicago/Turabian Style

Amir Hossein Modaress-Aval; Firooz Bakhtiari-Nejad; Earl H. Dowell; David A. Peters; Hossein Shahverdi. 2019. "A comparative study of nonlinear aeroelastic models for high aspect ratio wings." Journal of Fluids and Structures 85, no. : 249-274.

Journal article
Published: 11 January 2019 in Journal of Computational and Nonlinear Dynamics
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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.

ACS Style

Kevin A. McHugh; Earl H. Dowell. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics 2019, 14, 1 .

AMA Style

Kevin A. McHugh, Earl H. Dowell. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Journal of Computational and Nonlinear Dynamics. 2019; 14 (3):1.

Chicago/Turabian Style

Kevin A. McHugh; Earl H. Dowell. 2019. "Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force." Journal of Computational and Nonlinear Dynamics 14, no. 3: 1.

Proceedings article
Published: 06 January 2019 in AIAA Scitech 2019 Forum
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ACS Style

Earl Dowell; Jalen Doherty; Mahendra Joshi; Mayank Sharma; Robert Kielb; Marco Rauseo. Investigation of the Nonlinear Interaction of a Flutter/Limit Cycle Oscillation of a Cantilevered Wing with a Gust Excitation. AIAA Scitech 2019 Forum 2019, 1 .

AMA Style

Earl Dowell, Jalen Doherty, Mahendra Joshi, Mayank Sharma, Robert Kielb, Marco Rauseo. Investigation of the Nonlinear Interaction of a Flutter/Limit Cycle Oscillation of a Cantilevered Wing with a Gust Excitation. AIAA Scitech 2019 Forum. 2019; ():1.

Chicago/Turabian Style

Earl Dowell; Jalen Doherty; Mahendra Joshi; Mayank Sharma; Robert Kielb; Marco Rauseo. 2019. "Investigation of the Nonlinear Interaction of a Flutter/Limit Cycle Oscillation of a Cantilevered Wing with a Gust Excitation." AIAA Scitech 2019 Forum , no. : 1.

Journal article
Published: 17 November 2018 in Communications in Nonlinear Science and Numerical Simulation
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Computational simulations of a two-dimensional incompressible regularized lid-driven cavity flow were performed and analyzed to identify the dynamic behavior of the flow through multiple bifurcations which ultimately result in Eulerian chaotic flow. Semi-implicit, pseudo-spectral numerical simulations were performed at Reynolds numbers from 1,000 to 25,000. Poincaré maps were used to identify transitions as the Reynolds number increased from stable-laminar flow to periodic flow, periodic flow to quasi-periodic flow, quasi-periodic flow to chaotic flow, and a sudden, brief return from chaotic flow to periodic flow. The first critical Reynolds number, near 10,250, is found in agreement with existing literature. An additional bifurcation is observed near a Reynolds number of 15,500. A power spectrum analysis, in which the novel concepts of frequency shredding and power capacity are introduced, was performed with the conclusion that no further bifurcations occurred at Reynolds numbers above 15,500 even though Eulerian chaos was not formally observed until Reynolds numbers above 18,000. While qualitative changes in the fluid flow’s attractor were apparent from trajectories in the phase space, mechanisms by which such changes can occur were apparent from power spectra of flow time histories. The novel power spectrum analysis may also serve as a new approach for characterizing multi-scale nonlinear dynamical systems.

ACS Style

Michael W. Lee; Earl Dowell; Maciej J. Balajewicz. A study of the regularized lid-driven cavity’s progression to chaos. Communications in Nonlinear Science and Numerical Simulation 2018, 71, 50 -72.

AMA Style

Michael W. Lee, Earl Dowell, Maciej J. Balajewicz. A study of the regularized lid-driven cavity’s progression to chaos. Communications in Nonlinear Science and Numerical Simulation. 2018; 71 ():50-72.

Chicago/Turabian Style

Michael W. Lee; Earl Dowell; Maciej J. Balajewicz. 2018. "A study of the regularized lid-driven cavity’s progression to chaos." Communications in Nonlinear Science and Numerical Simulation 71, no. : 50-72.

Conference paper
Published: 26 August 2018 in Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
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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 considers 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 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 post-critical limit cycle oscillations are studied including a concentration on the force which enforces the inextensibility constraint.

ACS Style

Kevin A. McHugh; Earl Dowell. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control 2018, 1 .

AMA Style

Kevin A. McHugh, Earl Dowell. Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force. Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. 2018; ():1.

Chicago/Turabian Style

Kevin A. McHugh; Earl Dowell. 2018. "Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force." Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control , no. : 1.

Article
Published: 18 July 2018 in Journal of Mechanical Science and Technology
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In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled equations of motion are solved using Runge-Kutta algorithm with adaptive time step and the instability boundary is determined using the Floquet theory. Numerical results present effects of some parameters such as fluid flow fluctuation, bending-to-torsional rigidity ratio, nozzle inclination angle, nozzle mass and viscoelastic material on the stability margin of the system and some conclusions are drawn.

ACS Style

A. R. Askarian; H. Abtahi; R. D. Firouz-Abadi; H. Haddadpour; Earl Dowell. Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle. Journal of Mechanical Science and Technology 2018, 32, 2999 -3008.

AMA Style

A. R. Askarian, H. Abtahi, R. D. Firouz-Abadi, H. Haddadpour, Earl Dowell. Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle. Journal of Mechanical Science and Technology. 2018; 32 (7):2999-3008.

Chicago/Turabian Style

A. R. Askarian; H. Abtahi; R. D. Firouz-Abadi; H. Haddadpour; Earl Dowell. 2018. "Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle." Journal of Mechanical Science and Technology 32, no. 7: 2999-3008.