Frequency determination and non-dimensionalization for composite cantilever plates
TL;DR: In this paper, a method for estimating the natural frequencies of composite cantilever plates and for non-dimensionalizing frequency data is developed and demonstrated based on a partial Ritz (Kantorovich) analysis, which reduces the problem to a set of uncoupled ordinary differential equations.
About: This article is published in Journal of Sound and Vibration.The article was published on 1980-09-08. It has received 74 citations till now. The article focuses on the topics: Ritz method & Finite element method.
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TL;DR: Aeroelastic tailoring technology is reviewed with reference to the historical background, underlying theory, current trends, and specific applications as mentioned in this paper, and the future of aero-linear tailoring and the development of an automated strength-aero-elastic design tool under the Automated Strength-AeroELastic Design program are examined.
Abstract: Aeroelastic tailoring technology is reviewed with reference to the historical background, the underlying theory, current trends, and specific applications. The specific application discussed include the Transonic Aircraft Technology program, an Advanced Design Composite Aircraft, the Wing/Inlet Advanced Development program, and the forward-swept wing. Finally, the future of aeroelastic tailoring and the development of an aeroelastic tailoring analysis and design tool under the Automated Strength-Aeroelastic Design program are examined.
364 citations
TL;DR: In this article, an analytical and experimental investigation was conducted to determine the aeroelastic flutter and divergence behavior of unswept, rectangular wings simulated by graphite/epox y, cantilevered plates with various amounts of bending-torsi on stiffness coupling.
Abstract: An analytical and experimental investigation was conducted to determine the aeroelastic flutter and divergence behavior of unswept, rectangular wings simulated by graphite/epox y, cantilevered plates with various amounts of bending-torsi on stiffness coupling. The analytical approach incorporated a Rayleigh-Ritz energy formulation and unsteady, incompressible two-dimensional aerodynamic theory. Flutter and divergence velocities were obtained using the \ -g method and compared to results of low-speed wind tunnel tests. Stall flutter behavior was also examined experimentally. There was good agreement between analytical and experimental results. Wings with negative stiffness coupling exhibited divergence, while positive coupling delayed the onset of stall flutter.
137 citations
TL;DR: In this article, a nonlinear, stalled, aeroelastic behavior of rectangular, graphite/epoxy, cantilevered wings with varying amount of bending-torsi on stiffness coupling is investigated.
Abstract: The nonlinear, stalled, aeroelastic behavior of rectangular, graphite/epoxy, cantilevered wings with varying amount of bending-torsi on stiffness coupling is investigated. A nonlinear aeroelastic analysis is developed using the nonlinear, stalled ONERA aerodynamic model initially presented by Tran and Petot. Nonlinear flutter calculations are carried out using Fourier analysis to extract the harmonics from the ONERA aerodynamics, then a harmonic balance method and a Newton-Raphson solver are applied to the resulting nonlinear, Rayleigh-Ritz aeroelastic formulation. Test wings were constructed and subjected to wind-tunnel tests for comparison against the developed analysis. Wind-tunnel tests show reasonable agreement between theory and experiment for static deflections, for linear flutter and divergence, and for nonlinear, torsional stall flutter and bending stall flutter limit cycles. The current nonlinear analysis shows a transition from divergence to bending stall flutter, which linear analyses are unable to predict.
108 citations
TL;DR: In this article, the authors performed a systematic computational study of the hypersonic aeroelastic and aerothermoelastic behavior of a three-dimensional configuration of a low-aspect-ratio wing.
Abstract: The testing of aeroelastically and aerothermoelastically scaled wind-tunnel models in hypersonic flow is not feasible; thus, computational aeroelasticity and aerothermoelasticity are essential to the development of hypersonic vehicles. Several fundamental issues in this area are examined by performing a systematic computational study of the hypersonic aeroelastic and aerothermoelastic behavior of a three-dimensional configuration. Specifically, the flutter boundary of a low-aspect-ratio wing, representative of a fin or control surface on a hypersonic vehicle, is studied over a range of altitudes using third-order piston theory and Euler and Navier-Stokes aerodynamics. The sensitivity of the computational-fluid-dynamics-based aeroelastic analysis to grid resolution and parameters governing temporal accuracy are considered. In general, good agreement at moderate-to-high altitudes was observed for the three aerodynamic models. However, the wing flutters at unrealistic Mach numbers in the absence of aerodynamic heating. Therefore, because aerodynamic heating is an inherent feature of hypersonic flight and the aeroelastic behavior of a vehicle is sensitive to structural variations caused by heating, an aerothermoelastic methodology is developed that incorporates the heat transfer between the fluid and structure based on computational-fluid-dynamics-generated aerodynamic heating. The aerothermoelastic solution procedure is then applied to the low-aspect-ratio wing operating on a representative hypersonic trajectory. In the latter study, the sensitivity of the flutter margin to perturbations in trajectory angle of attack and Mach number is considered. Significant reductions in the flutter boundary of the heated wing are observed. The wing is also found to be susceptible to thermal buckling.
97 citations
Cites background from "Frequency determination and non-dim..."
...Furthermore, it was shown that the warping stiffness of a cantilever plate is a function of both aspect ratio and the ratio of bending/torsion stiffness [12,73]....
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...More recently, this effect has been studied in the context of composites [73,74]....
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TL;DR: In this paper, the free-vibration characteristics of directionally stiffened, laminated composite beam-like structures such as high-aspect-ratio lifting surfaces are discussed.
Abstract: This paper discusses the free-vibration characteristics of directionally stiffened, laminated composite beamlike structures such as high-aspect-ratio lifting surfaces. A bounded nondimensional parameter, , is defined to describe the degree of elastic coupling between bending curvature and twist rate for a laminated beam. In addition, three different stiffness models commonly used to model laminated beam/tube deformation are described and compared. Using one of these models, the ability of the laminate design to control mode shape or node line characteristics is illustrated for a cross-coupled laminated cantilever beam. Finally, the effect of the nondimensional cross-coupling parameter, i/s on cantilever beam free-vibration node line positions and frequencies is illustrated, independent of a specific laminate design.
92 citations
References
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01 Jan 1976
TL;DR: Numerical methods in finite element analysis, Numerical techniques in finite elements analysis, and so on.
Abstract: Numerical methods in finite element analysis , Numerical methods in finite element analysis , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
2,085 citations
TL;DR: In this article, mixed formulations are introduced as a means for reducing severe constraints in finite-element derivations for plate bending elements to include transverse shear effect and to be applicable also to thin plates.
Abstract: Mixed formulations are introduced as a means for reducing severe constraints in finite-element derivations. For plate bending elements to include transverse shear effect and to be applicable also to thin plates, the method can reduce the conditions of constraints of zero transverse shear strain energy. For shell elements, the constraints of rigid-body modes can be lessened similarly. Certain mixed formulations have been shown to be equivalent to displacement models with reduced integration scheme. But the present approach provides a general and rational method for the finite-element development. Illustrative examples include plate, circular arch, and shell elements.
229 citations
TL;DR: The natural frequencies and mode shapes of a number of Graphite/Epoxy and Graphite-Epoxy-Aluminum plates and shells were determined in this article, and the results were compared with those calculated by a finite element analysis.
Abstract: The natural frequencies and mode shapes of a number of Graphite/ Epoxy and Graphite/Epoxy-Aluminum plates and shells were experimen tally determined. The samples tested include 8 ply Graphite/Epoxy plates, cyclindrical shell sections, and Graphite/Epoxy-Aluminum hybrid plates of various laminates and aspect ratio. Fabrication and test procedures are described. Natural frequency and mode shape results are compared with those calculated by a finite element analysis. Agreement between calcu lated and observed mode shapes is excellent; while reasonable agreement is found for frequencies. Among the sources of this discrepancy in frequency results is the possibility of a difference between dynamic-flexural moduli and static in-plane moduli.
124 citations
01 Jun 1951
TL;DR: In this article, the authors considered the problem of combined bending and torsion of cantilever plates of variable thickness, such as might be considered for solid thin high-speed airplane or missile wings.
Abstract: The problem of combined bending and torsion of cantilever plates of variable thickness, such as might be considered for solid thin high-speed airplane or missile wings, is considered in this paper. The deflections of the plate are assumed to vary linearly across the chord; minimization of the potential energy by means of the calculus of variations then leads to two ordinary linear differential equations for the bending deflections and the twist of the plate. Because the cantilever is analyzed as a plate rather than as a beam, the effect of constraint against axial warping in torsion is inherently included. The application of this method to specific problems involving static deflection, vibration, and buckling of cantilever plates is presented. In the static-deflection problems, taper and sweep are considered.
63 citations