Nonlinear oscillations of a fluttering functionally graded plate

Haddadpour, H.; Navazi, H.M.; Shadmehri, Farjad

doi:10.1016/j.compstruct.2006.01.006

Cited by 69 publications

(16 citation statements)

References 18 publications

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“…Another research area in which aerothermoelasticity in high-speed flows has been studied widely is the area of functionally graded panels. [19][20][21][22][23][24] These works include aerothermoelastic effects to varying extents and are motivated largely by the need to assess the response of the structure as well as its aerothermoelastic stability. Praveen and Reddy 19 include thermal effects by imposing temperatures at the ceramic-rich and metal-rich surfaces and solving a simple steady state heat transfer problem to obtain the through-thickness temperature distribution of the plate.…”

Section: Ia Previous Work On Aerothermoelastic Modelingmentioning

confidence: 99%

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Falkiewicz

Cesnik

Crowell

et al. 2010

AIAA Atmospheric Flight Mechanics Conference

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Hypersonic vehicle control system design and simulation requires models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics in the hypersonic regime. Though there exist techniques for analyzing the effects of each of the various disciplines, these methods often require solution of large systems of equations which is infeasible within a control design and evaluation environment. This work therefore presents an aerothermoelastic framework with reduced-order aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles. The problem is outlined and aerothermoelastic coupling mechanisms are described. Details of the reduced-order models are given and a representative hypersonic vehicle control surface to be used for the study is described. The error between the reduced-order models is characterized by comparison with high-fidelity models. The effect of aerothermoelasticity on total lift and drag is studied and is found to result in up to 8% change in lift and 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the necessary angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants. Application of the routine to different cruise trajectories shows a maximum departure from the initial angle of attack of 7%.

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Section: Ia Previous Work On Aerothermoelastic Modelingmentioning

confidence: 99%

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Falkiewicz

Cesnik

Crowell

et al. 2010

AIAA Atmospheric Flight Mechanics Conference

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“…The equations of motion were formulated using Lagrange's equations, and eigenvalue solutions were used to assess the critical aerodynamic pressure for flutter. A later work [15] extended the study of [16] by using piston theory to incorporate quasi-steady aerodynamic loads; however, this study did not include thermal effects. In a related work [14], thermal effects were incorporated along with the quasi-steady piston theory formulation.…”

Section: Aerodynamicmentioning

confidence: 98%

“…Another research area in which aerothermoelasticity in high-speed flows has been studied widely is the area of functionally graded panels [11][12][13][14][15][16]. These works include aerothermoelastic effects to varying extents and are motivated largely by the need to assess the response of the structure as well as its aerothermoelastic stability.…”

Section: Aerodynamicmentioning

confidence: 99%

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Falkiewicz¹,

Cesnik²,

Crowell³

et al. 2011

AIAA Journal

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Hypersonic vehicle control system design and simulation require models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics. Although there exist techniques for analyzing the effects of each of the various disciplines, these methods often require solution of large systems of equations, which is infeasible within a control design and evaluation environment. This work presents an aerothermoelastic framework with reducedorder aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles. Details of the reduced-order models are given, and a representative hypersonic vehicle control surface used for the study is described. The methodology is applied to a representative structure to provide insight into the importance of aerothermoelastic effects on vehicle performance. The effect of aerothermoelasticity on total lift and drag is found to result in up to an 8% change in lift and a 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants. Application of the routine to different cruise trajectories shows a maximum departure from the initial angle of attack of 8%.corresponding to ith column of A C = correlation matrix c = modal coordinate of thermal proper orthogonal decomposition basis vector Cx = correlation model for kriging c p = specific heat at constant pressure d = structural modal coordinates, kriging sample point E = modulus of elasticity F = thermal load vector of full system in physical space f = generalized thermal load vector of reduced system in modal space F s = structural load vector of full system in physical space f s = generalized structural load vector of reduced system in modal space H i = coefficient matrices for integration of equations of motion h i = thickness of ith layer of thermal protection system K = thermal conductivity matrix of full system in physical space k = generalized thermal conductivity matrix of reduced system in modal space K G = geometric stiffness matrix K s = structural stiffness matrix k s = generalized stiffness matrix of reduced system in modal space k T = thermal conductivity of material K s = modified structural stiffness matrix L = aerodynamic lift, length M = thermal capacitance matrix of full system in physical space, Mach number m = generalized thermal capacitance matrix of reduced system in modal space M s = structural mass matrix of full system in physical space m s = generalized mass matrix of reduced system in modal space n = number of proper orthogonal decomposition snapshots n e = number of snapshots for kriging evaluation cases n k = number of kriging snapshots n s = number of structural parameters in reduced-order aerothermodynamic model n t = number of thermal parameters...

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“…Singha and Ganapathi [43] investigated the effect of the system parameters on supersonic panel flutter behaviors of laminated composite plates. Haddadpour et al [44] investigated the nonlinear aeroelastic behaviors of FGM. Singha and Mandal [45] used a 16-node isoparametric degenerated shell element to study the supersonic panel flutter behaviors of laminated composite plates and cylindrical panels.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Liu

Zhang

2020

Mathematical Problems in Engineering

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The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.

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Nonlinear oscillations of a fluttering functionally graded plate

Cited by 69 publications

References 18 publications

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

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