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NASA NTRS1940

The frequencies of cantilever wings in beam and torsional vibrations

Methods are described for calculating the period and frequency of vibration of cantilever wings and similar structures in which the weight and moment of inertia vary along the span. Both the beam and torsional frequencies may be calculated by these methods. The procedure is illustrated by examples. It is shown that a surprisingly close approximation to the beam frequency may be obtained by a very brief calculation in which the curvature of the wing in vibration is assumed to be constant. A somewhat longer computation permits taking account of the true curvature of the beam by a series of successive approximations which are shown to be strongly convergent. Analogous methods are applied to calculations of the torsional frequency. For the first approximation it is assumed that the angle of twist varies linearly alone the semispan. True variation of the twist is computed by successive approximations which are strongly convergent, as in the case of beam vibrations.

Burgess, C P↗

NASA NTRS1936

Analysis of 2-spar cantilever wings with special reference to torsion and load transference

This report deals with the analysis of 2-spar cantilever wings in torsion, taking cognizance of the fact that the spars are not independent, but are interconnected by ribs and other structural members. The principles of interaction are briefly explained, showing that the mutual relief action occurring depends on the "pure torsional stiffness" of the wing cross section. Various practical methods of analysis are outlined. The "Friedrichs-Von Karman equations" are shown to require the least amount of labor. Numerical examples by the several methods of analysis are given and the agreement between the calculation and experiment is shown.

Kuhn, Paul↗

NASA NTRS1929

Cantilever Wings for Modern Aircraft: Some Aspects of Cantilever Wing Construction with Special Reference to Weight and Torsional Stiffness

In the foregoing remarks I have made an attempt to touch on some of the structural problems met with in cantilever wings, and dealt rather fully with a certain type of single-spar construction. The experimental test wing was a first attempt to demonstrate the principles of this departure from orthodox methods. The result was a wing both torsionally stiff and of light weight - lighter than a corresponding biplane construction.

WINGS - STRUCTURE↗

NASA NTRS1992

Flexure-torsion behavior of sheat-deformable beams with applications to aircraft wing sections

The flexure-torsion behavior of a tip-loaded cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross-sections, the calculated coefficients represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shear centers (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.

Kosmatka, J. B.↗

NASA NTRS2015

Novel Control Effectors for Truss Braced Wing

At cruise flight conditions very high aspect ratio/low sweep truss braced wings (TBW) may be subject to design requirements that distinguish them from more highly swept cantilevered wings. High aspect ratio, short chord length and relative thinness of the airfoil sections all contribute to relatively low wing torsional stiffness. This may lead to aeroelastic issues such as aileron reversal and low flutter margins. In order to counteract these issues, high aspect ratio/low sweep wings may need to carry additional high speed control effectors to operate when outboard ailerons are in reversal and/or must carry additional structural weight to enhance torsional stiffness. The novel control effector evaluated in this study is a variable sweep raked wing tip with an aileron control surface. Forward sweep of the tip allows the aileron to align closely with the torsional axis of the wing and operate in a conventional fashion. Aft sweep of the tip creates a large moment arm from the aileron to the wing torsional axis greatly enhancing aileron reversal. The novelty comes from using this enhanced and controllable aileron reversal effect to provide roll control authority by acting as a servo tab and providing roll control through intentional twist of the wing. In this case the reduced torsional stiffness of the wing becomes an advantage to be exploited. The study results show that the novel control effector concept does provide roll control as described, but only for a restricted class of TBW aircraft configurations. For the configuration studied (long range, dual aisle, Mach 0.85 cruise) the novel control effector provides significant benefits including up to 12% reduction in fuel burn.

White, Edward V.↗

NASA NTRS1995

Interactive flutter analysis and parametric study for conceptual wing design

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed on MathCad (trademark) platform for Macintosh, with integrated documentation, graphics, database and symbolic mathematics. The analysis method was based on nondimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The plots were compiled in a Vaught Corporation report from a vast database of past experiments and wind tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended Wing Body concept, proposed by McDonnell Douglas Corporation. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

NASA NTRS1996

An Interactive Software for Conceptual Wing Flutter Analysis and Parametric Study

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well-defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed for Macintosh or IBM compatible personal computers, on MathCad application software with integrated documentation, graphics, data base and symbolic mathematics. The analysis method was based on non-dimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, taper ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The parametric plots were compiled in a Vought Corporation report from a vast data base of past experiments and wind-tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended-Wing-Body concept, proposed by McDonnell Douglas Corp. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

NASA NTRS1955

Behavior of a Cantilever Plate Under Rapid-heating Conditions

The temperature distributions encountered in thin solid wings subjected to aerodynamic heating induce thermal stresses that may effectively reduce the stiffness of the wing. The effects of this reduction in stiffness were investigated experimentally by rapidly heating the edges of a cantilever plate. The midplane thermal stresses imposed by the nonuniform temperature distribution caused the plate to buckle torsionally, increased the deformations of the plate under a constant applied torque, and reduced the frequency of the first two natural modes of vibration. By using small-deflection theory and employing energy methods, the effect of nonuniform heating on the plate stiffness was calculated. The theory predicts the general effects of the thermal stresses, but becomes inadequate as the temperature difference increases and plate deflections become large.

Vosteen, Louis F↗

NASA NTRS1990

Effects of spoiler surfaces on the aeroelastic behavior of a low-aspect-ratio rectangular wing

An experimental research study to determine the effectiveness of spoiler surfaces in suppressing flutter onset for a low-aspect-ratio, rectangular wing was conducted in the Langley Transonic Dynamics Tunnel (TDT). The wing model used in this flutter test consisted of a rigid wing mounted to the wind-tunnel wall by a flexible, rectangular beam. The flexible beam was connected to the wing root and cantilever mounted to the wind-tunnel wall. The wing had a 1.5 aspect ratio based on wing semispan and a NACA 64A010 airfoil shape. The spoiler surfaces consisted of thin, rectangular aluminum plates that were vertically mounted to the wing surface. The spoiler surface geometry and location on the wing surface were varied to determine the effects of these parameters on the classical flutter of the wing model. Subsonically, the experiment showed that spoiler surfaces increased the flutter dynamic pressure with each successive increase in spoiler height or width. This subsonic increase in flutter dynamic pressure was approximately 15 percent for the maximum height spoiler configuration and for the maximum width spoiler configuration. At transonic Mach numbers, the flutter dynamic pressure conditions were increased even more substantially than at subsonic Mach numbers for some of the smaller spoiler surfaces. But greater than a certain spoiler size (in terms of either height or width) the spoilers forced a torsional instability in the transonic regime that was highly Mach number dependent. This detrimental torsional instability was found at dynamic pressures well below the expected flutter conditions. Variations in the spanwise location of the spoiler surfaces on the wing showed little effect on flutter. Flutter analysis was conducted for the basic configuration (clean wing with all spoiler surface mass properties included). The analysis correlated well with the clean wing experimental flutter results.

Cole, Stanley R.↗