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NASA NTRS1967

Integrating Matrix Method for Determining the Natural Vibrations of a Rotating, Unsymmetrical Beam with Application to Twisted Propeller Blades

A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.

Hunter, William F.↗

NASA NTRS2005

Torsion of Noncircular Composite Cylinders

The paper presents a brief overview of the predicted deformation and failure characteristics of noncircular composite cylinders subjected to torsion. Using a numerical analysis, elliptical cylinders with a minor-to-major diameter ratio of 0.7 are considered. Counterpart circular cylinders with the same circumference as the elliptical cylinders are included for comparison. The cylinders are constructed of a medium-modulus graphite-epoxy material in a quasi-isotropic lay-up. Imperfections generated from the buckling mode shapes are included in the initial cross-sectional geometry of the cylinders. Deformations until first fiber failure, as predicted using the maximum stress failure criterion and a material degradation scheme, are presented. For increasing levels of torsion, the deformations of the elliptical cylinders, in the form of wrinkling of the cylinder wall, occur primarily in the flatter regions of the cross section. By comparison the wrinkling deformations of the circular cylinders are more uniformly distributed around the circumference. Differences in the initial failure and damage progression and the overall torque vs. twist relationship between the elliptical and circular cylinders are presented. Despite differences in the response as the cylinders are being loaded, at first fiber failure the torque and twist for the elliptical and circular cylinders nearly coincide.

Rouse, Marshall↗

NASA NTRSDate not supplied

Structural Design and Aeromechanical Analysis of Unconventional Blades for Future Mars Rotorcraft

The structural design for rotor blades with thin, unconventional airfoils for Earth-based testing is obtained using three-Dimensional (3D) aeromechanical analysis. This analysis is in support of the NASA ROAMX project. The outer mold was provided by NASA, but the internal structural design was developed at the University of Maryland and is presented here, along with a thorough aeromechanical analysis. The main objectives are to verify the structural integrity of the design and understand the unique aeroelastic behavior of the non-conventional airfoils designed for low-Reynolds number and high-Mach number flow. Six different blade models are considered, with the pitch axis varied from quarter-chord to mid-chord to determine the effect of C.G. offset on natural frequencies, blade deformations, root loads, and 3D stresses. All six blade designs are first studied under rotation in pure vacuum, and significant reductions in root loads and 3D stresses are achieved by moving the pitch axis closer to mid-chord to reduce the C.G. offset. Based on the vacuum analysis, the blade design with the pitch axis at 40% chord is selected for aerodynamic analysis. The blade control load, airloads, deformations, and 3D stresses are studied for steady hover. Dynamic control load and dynamic 3D stresses are studied for unsteady hover achieved using cyclic. Significant elastic twist is observed due to the trapeze effect and propeller moment, affecting the spanwise distribution of aerodynamic loads on the blades. However, the effect of aerodynamic loads on 3D stresses and the blade control load is found to be minimum. The dynamic control load is found to increase significantly due to inertial coupling from the C.G. offset. The dynamic stresses also increase, although still have factors of safety greater than two for both tensile and compressive stress.

Structural Design↗

NASA NTRS2023

Structural Design and Aeromechanical Analysis of Unconventional Blades for Future Mars Rotorcraft

The structural design for rotor blades with thin, unconventional airfoils for Earth-based testing is obtained using three-Dimensional (3D) aeromechanical analysis in support of the NASA ROAMX project. The outer mold line was provided by NASA, but the internal structural design was developed at the University of Maryland and is presented here along with a thorough aeromechanical analysis. The main objectives are to verify the structural integrity of the design and understand the unique aeroelastic behavior of the non-conventional airfoils designed for low-Reynolds number and high subsonic Mach number. Four different blade models are considered, with the pitch axis varied from quarter-chord to mid-chord to determine the effect of C.G. offset on natural frequencies, blade deformations, root loads, and 3D stresses. First, torsional stability is calculated for each of the designs – especially important due to the low Lock number on Mars. All four blade designs are studied under rotation in vacuum, and significant reductions in root loads and 3D stresses are achieved by moving the pitch axis closer to mid-chord to reduce the C.G. offset. Based on the vacuum analysis, the blade design with the pitch axis at 40% chord is selected for aeromechanical analysis. The blade control load, airloads, deformations, and 3D stresses are studied for steady hover. Dynamic control load and dynamic 3D stresses are studied for unsteady hover achieved using cyclic. Significant elastic twist is observed due to the trapeze effect and propeller moment, affecting the spanwise distribution of aerodynamic loads on the blades. The dynamic control load is found to increase significantly due to inertial coupling from the C.G. offset. The dynamic stresses also increase, although still have factors of safety greater than two for both tensile and compressive stress.

Structural Design↗

NASA NTRS1998

Test of a flexible spacecraft dynamics simulator

There are a number of approaches one can take to modeling the dynamics of a flexible body. While one can attempt to capture the full dynamical behavior subject to disturbances from actuators and environmental torques, such a detailed description often is unnecessary. Simplification is possible either by limiting the amplitude of motion to permit linearization of the dynamics equations or by restricting the types of allowed motion. In this work, we study the nonlinear dynamics of bending deformations of wire booms on spinning spacecraft. The theory allows for large amplitude excursions from equilibrium while enforcing constraints on the dynamics to prohibit those modes that are physically less relevant or are expected to damp out fast. These constraints explicitly remove the acoustic modes (i.e., longitudinal sound waves and shear waves) while allowing for arbitrary bending and twisting, motions which typically are of lower frequency. As a test case, a spin axis reorientation maneuver by the Polar Plasma Laboratory (POLAR) spacecraft has been simulated. POLAR was chosen as a representative spacecraft because it has flexible wire antennas that extend to a length of 65 meters. Bending deformations in these antennas could be quite large and have a significant effect on the attitude dynamics of the spacecraft body. Summary results from the simulation are presented along, with a comparison with POLAR flight data.

Dichmann, Donald↗

DOE OSTI2020

Solid Cylinder Torsion for Large Shear Deformation and Failure of Engineering Materials

Using a thin-walled tube torsion test to characterize a material’s shear response is a well-known technique; however, the thin walled specimen tends to buckle before reaching large shear deformation and failure. An alternative technique is the surface stress method (Nadai 1950; Wu et al. J Test Eval 20:396–402, 1992), which derives a shear stress-strain curve from the torque-angular displacement relationship of a solid cylindrical bar. The solid bar torsion test uniquely stabilizes the deformation which allows us to control and explore very large shear deformation up to failure. However, this method has rarely been considered in the literature, possibly due to the complexity of the analysis and experimental issues such as twist measurement and specimen uniformity.

42 ENGINEERING↗

NASA NTRS2019

Structure Deformation Calculation Program Based on Displacement Theory for Shape Predictions

Separated programs were written in C/C++ to validate the Displacement Transfer Functions. The Structure Deformation Calculation Program was written to combine all of the programs to calculate deformed shapes of a structure using surface strain data and structural geometrical parameters. Users do not need to know the material properties, nor the complex internal structures geometry because the Displacement Theory is purely geometrical in nature. Users only need to know the structure types as defined in this report and information such as the structure length, depth factors, number of strain sensors, and the surface strains measured at the strain-sensing stations installed on the structures. Depending on the structure type, an applicable Displacement Transfer Function will be used. This program requires two input files created by users; the recorded strain data file in comma-separated values format and the structure geometry data file in text format. The program will output the out-of-plane deflections, slopes, cross-sectional twist angles, and depth factors if applicable. All output files are created in comma-separated values format. A section in this report describes step-by-step procedures on how to use the Structure Deformation Calculation Program for structure deformed shape calculations.

Displacement theory↗

DOE OSTI2022

More Powerful Twistron Carbon Nanotube Yarn Mechanical Energy Harvesters

We report that stretching a coiled carbon nanotube (CNT) yarn can provide large, reversible electrochemical capacitance changes, which convert mechanical energy to electricity. Here, it is shown that the performance of these “twistron” harvesters can be increased by optimizing the alignment of precursor CNT forests, plastically stretching the precursor twisted yarn, applying much higher tensile loads during precoiling twist than for coiling, using electrothermal pulse annealing under tension, and incorporating reduced graphene oxide nanoplates. The peak output power for a 1 and a 30 Hz sinusoidal deformation are 0.73 and 3.19 kW kg -1 , respectively, which are 24- and 13-fold that of previous twistron harvesters at these respective frequencies. This performance at 30 Hz is over 12-fold that of other prior-art mechanical energy harvesters for frequencies between 0.1 and 600 Hz. The maximum energy conversion efficiency is 7.2-fold that for previous twistrons. Twistron anode and cathode yarn arrays are stretched 180° out-of-phase by locating them in the negative and positive compressibility directions of hinged wine-rack frames, thereby doubling the output voltage and reducing the input mechanical energy.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Effect of Composite Stiffened Panel Design on Skin-Stringer Separation in Postbuckling

To design aeronautical composite multi-stringer panels that can safely operate in a postbuckled state, it is important to identify the parameters that can influence the different modes in which skin-stringer separation might occur. A methodology is under development to study the interaction between the skin-stringer separation and the postbuckling deformation using the building block approach and single-stringer specimens. In particular, the methodology can identify whether the skin-stringer separation occurs due to bending or twisting, so that these two possible modes can be studied separately. For bending, a simple criterion that can predict the location of initiation is presented. This procedure has the potential to reduce the overall development cost and allows the investigation of the design parameters that influence the skin-stringer separation.

Lucas J. Koote↗

NASA NTRS1939

Experimental Study of Deformation and of Effective Width in Axially Loaded Sheet-stringer Panels

The deformation of two sheet-stringer panels subjected to end compression under carefully controlled end conditions was measured at a number of points and at a number of loads, most of which were above the load at which the sheet had begun to buckle. The two panels were identical except for the sheet, which was 0.70-inch 24st alclad for specimen 1 and 0.025-inch 24st aluminum alloy for specimen 6. A technique was developed for attaching Tuckerman optical strain gauges to the sheet without disturbing the strain distribution in the sheet by the method of attachment. This technique was used to explore the strain distribution in the sheet at various loads. The twisting and the bending of the stringers was measured by means of pointers attached to the stringers. The shape of the buckles in the sheet of specimen 6 was recorded at two loads by means of plaster casts. The sheet and the stringer loads at failure are compared with the corresponding loads for five similar panels tested at the Navy Model Basin. A detailed comparison is made between the measured deformation of the buckled sheet and the deformation calculated from approximate theories for the deformation in a rectangular sheet with freely supported edges buckling under end compression advanced by Timoshenko, Frankland, and Marguerre. The measured effective width for the specimens is compared with the effective width given by nine different relations for effective width as a function of the edge stress divided by the buckling stress of the sheet. The analysis of the measured stringer deformation is confined to an application of Southwell's method of plotting deformation against deformation over load. It was concluded that the stringer failure in both specimens were due to an instability in which the stringer was simultaneously twisted and bent as a column.

FORMULAS - BUCKLING - KARMAN↗

NASA NTRS2001

Summary Report of the Orbital X-34 Wing Static Aeroelastic Study

This report documents the results of a computational study conducted on the Orbital Sciences X-34 vehicle to compute its inviscid aerodynamic characteristics taking into account the wing structural flexibility. This was a joint exercise between LaRC and SDRC of California. SDRC modeled the structural details of the wing, and provided the structural deformation for a given pressure distribution on its surfaces. This study was done for a Mach number of 1.35 and an angle of attack of 9 deg.; the freestream dynamic pressure was assumed to be 607 lb/sq ft. Only the wing and the body were simulated in the CFD computations. Two wing configurations were examined. The first had the elevons in the undeflected position and the second had the elevons deflected 20 deg. up. The results indicated that with elevon undeflected, the wing twists by about 1.5 deg. resulting in a reduction in the angle of attack at the wing tip to by 1.5 deg. The maximum vertical deflection of the wing is about 3.71 inches at the wing tip. For the wing with the undeflected elevons, the effect of this wing deformation is to reduce the normal force coefficient (C(sub N)) by 0.012 and introduce a noise up pitching moment coefficient (C(sub m)) of 0.042.

Prabhn, Ramadas K.↗

DOE OSTI2020

Design of Chiral Domains by Surface Confinement of Liquid Crystals

Chirality, or absence of mirror symmetry, is a fascinating attribute of inanimate and living objects, which inspires artists and fascinates scientists in various disciplines, from physics to mathematics, biology to chemistry and crystallography. Producing and controlling the sense of handedness in systems formed by mirror-symmetric elements or containing an equal amount of left- and right-twisted elements is usually a nontrivial task. In this issue of ACS Central Science, Geonhyeong Park et al [1] demonstrate that a slab of a lyotropic chromonic liquid crystal (LCLC), formed by achiral molecules dispersed in water, can produce a periodic array of domains with left- and right-handed twists of the orientation of molecular aggregates. The twist develops over macroscopic regions of tens of microns in size and is caused by a balance of two facets of the orientational order pertinent to liquid crystals: the elastic response to deformations of orientation and anisotropy of surface interactions at confining boundaries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1975

Unsteady vortex lattice techniques applied to wake formation and performance of the statically thrusting propeller

The application is considered of vortex lattice techniques to the problem of describing the aerodynamics and performance of statically thrusting propellers. A numerical lifting surface theory to predict the aerodynamic forces and power is performed. The chordwise and spanwise loading is modelled by bound vortices fixed to a twisted flat plate surface. In order to eliminate any apriori assumptions regarding the wake shape, it is assumed the propeller starts from rest. The wake is generated in time and allowed to deform under its own self-induced velocity field as the motion of the propeller progresses. The bound circulation distribution is then determined with time by applying the flow tangency boundary condition at certain selected control points on the blades. The aerodynamics of the infinite wing and finite wing are also considered. The details of wake formation and roll-up are investigated, particularly the localized induction effect. It is concluded that proper wake roll-up and roll-up rates can be established by considering the details of motion at the instant of start.

Hall, G. F.↗

NASA NTRS1987

Comparison of composite rotor blade models: A coupled-beam analysis and an MSC/NASTRAN finite-element model

A methodology was developed for the structural analysis of composite rotor blades. This coupled-beam analysis is relatively simple to use compared with alternative analysis techniques. The beam analysis was developed for thin-wall single-cell rotor structures and includes the effects of elastic coupling. This paper demonstrates the effectiveness of the new composite-beam analysis method through comparison of its results with those of an established baseline analysis technique. The baseline analysis is an MSC/NASTRAN finite-element model built up from anisotropic shell elements. Deformations are compared for three linear static load cases of centrifugal force at design rotor speed, applied torque, and lift for an ideal rotor in hover. A D-spar designed to twist under axial loading is the subject of the analysis. Results indicate the coupled-beam analysis is well within engineering accuracy.

Hodges, Robert V.↗

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 NTRS1999

Pressure-Sensitive Paint and Video Model Deformation Systems at the NASA Langley Unitary Plan Wind Tunnel

Pressure-sensitive paint (PSP) and video model deformation (VMD) systems have been installed in the Unitary Plan Wind Tunnel at the NASA Langley Research Center to support the supersonic wind tunnel testing requirements of the High Speed Research (HSR) program. The PSP and VMD systems have been operational since early 1996 and provide the capabilities of measuring global surface static pressures and wing local twist angles and deflections (bending). These techniques have been successfully applied to several HSR wind tunnel models for wide ranges of the Mach number, Reynolds number, and angle of attack. A review of the UPWT PSP and VMD systems is provided, and representative results obtained on selected HSR models are shown. A promising technique to streamline the wind tunnel testing process, Modern Experimental Design, is also discussed in conjunction with recently-completed wing deformation measurements at UPWT.

Erickson, G. E.↗

NASA NTRS1999

Pressure-Sensitive Paint and Video Model Deformation Systems at the NASA Langley Unitary Plan Wind Tunnel

Erickson, G. E.↗

DOE OSTI2021

Design, modeling and experimental validation of a micro cantilever beam with an electro-controllable twisting ability

The structure design of micro cantilever beams (MCBs), which has a significant effect on MCBs' controllable actuation range, is usually restricted by the establishment of the inner electric circuit. This paper proposes the design of a micro electro-controllable twisting cantilever beam (METCB). The architecture and the fabrication diagram of the proposed METCB are presented before its features are theoretically and experimentally validated. In detail, the analytical validation includes a sequence of two models: electro-thermal and thermo-mechanical. Through these two models, the thermal distribution along the METCB and the deformation brought by the thermal distribution are investigated, respectively. On the basis of the design and equations, the METCB samples have been manufactured using a planar deposition technique with an e-beam evaporator. Two in-site experiments are then conducted to sequentially figure out the upper voltage limit of the inner electric circuit and the maximum temperature limit of the METCB. Finally, another experiment is carried out to explore the relation between the applied voltage and the relative twisting angle of the METCB sample. Here, the theoretical prediction and the observed experiment result both prove the feasibility of the proposed METCB and its electro-controllable twisting ability.

36 MATERIALS SCIENCE↗