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DOE OSTI2025

Slender-body approach for computing second-order wave loads in the frequency domain

This work presents a slender-body approach to evaluate the second-order wave loads acting on a floating structure in the frequency domain. The approach is in the same spirit as the common use of Morison’s equation to approximate the wave loads without solving the radiation/diffraction problem. To do so, we employ Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear effects. We introduce modifications to Rainey’s formulation in order to evaluate wave kinematics at the mean body position instead of the original approach of considering instantaneous displacements. We also propose a simple approximation to partially account for wave scattering effects on the second-order loads based on the analytical solution of a surface-piercing bottom-mounted vertical circular cylinder. Though limited to structures composed of cylinders, this slender-body approach is orders of magnitude faster than computing second-order wave coefficients with a radiation/diffraction code. We implemented this approach for difference-frequency (slow drift) loads in an open-source frequency-domain floating wind turbine model. We present comparisons against results obtained with radiation/diffraction theory for three reference floating wind turbine designs: the OC3-Hywind spar, the OC4-DeepCwind semisubmersible, and the VolturnUS-S semisubmersible. In general, the results show that the proposed slender-body approach with the correction to approximate wave scattering effects provides useful estimations of the difference-frequency wave loads and the resulting motions of the floater.

17 WIND ENERGY↗

NASA NTRS1982

The structure of untwisted magnetic flux tubes

While most previous investigations have concentrated on slender flux tubes, the present study of the equilibrium structure of an axisymmetric magnetic flux tube, confined by an external pressure that varies along the length of the tube, explores the properties of thick tubes in order to establish the degree to which slender tube theory is valid. It is found that slender flux tube results may in some cases give no indication of thick tube behavior in a nonuniform atmosphere. Depending on boundary conditions applied at the ends of the tube, it may expand or contract upon entering a region of increasing pressure. Rather than expanding indefinitely, the tube surface may form a cusped shape when a point of external pressure on the tube surface falls to equality with the internal pressure. Numerical solutions for an initially uniform tube give smaller expansions than would be expected from slender tube theory.

Browning, P. K.↗

NASA NTRS1983

Fundamental studies of heat load and thermal-structure analysis of large space structures

Investigation of the basic requirements for modeling slender member shadowing effects on thermally induced deformation continues. The theoretical formulation is complete and computer programming is underway. The basic requirements for thermal finite elements to model heat transfer in orbiting structures were also studied. The need for planar isothermal elements to model large space structures' antenna meshes was established. Finite Element approaches for modeling space structure cable and membrane components with thermal effects is underway. Three levels of structural modeling and analysis were identified: (1) a linear-elastic small deflection analysis that does not permit cable slackening; (2) a linear-elastic analysis that includes stress stiffening (the ANSYS program), but not large deflections; and (3) full nonlinear large deflection analysis with stress stiffening. Methods of determining cable initial tensions are currently being evaluated.

Thornton, E. A.↗

NASA NTRS1972

A parametric study of planform and aeroelastic effects on aerodynamic center, alpha- and q- stability derivatives. Appendix A: A computer program for calculating alpha- and q- stability derivatives and induced drag for thin elastic aeroplanes at subsonic and supersonic speeds

The computer program used to determine the rigid and elastic stability derivatives presented in the summary report is listed in this appendix along with instructions for its use, sample input data and answers. This program represents the airplane at subsonic and supersonic speeds as (a) thin surface(s) (without dihedral) composed of discrete panels of constant pressure according to the method of Woodward for the aerodynamic effects and slender beam(s) for the structural effects. Given a set of input data, the computer program calculates an aerodynamic influence coefficient matrix and a structural influence coefficient matrix.

Roskam, J.↗

NASA NTRS1984

Long Heat Pipe Transports 2.6 kW

High-capacity heat pipe employs slender artery-and-wick structure. Ribbon of stainless steel screen wrapped around copper mandrel in conical copper forming tool. Outside edge of wrapped screen welded to layer on which it rests. Long heat pipe transports thermal energy at rate of 2,600 watts at operating temperature of 923 K.

Ernst, D. M.↗

NASA NTRS1990

Analysis and testing of axial compression in imperfect slender truss struts

The axial compression of imperfect slender struts for large space structures is addressed. The load-shortening behavior of struts with initially imperfect shapes and eccentric compressive end loading is analyzed using linear beam-column theory and results are compared with geometrically nonlinear solutions to determine the applicability of linear analysis. A set of developmental aluminum clad graphite/epoxy struts sized for application to the Space Station Freedom truss are measured to determine their initial imperfection magnitude, load eccentricity, and cross sectional area and moment of inertia. Load-shortening curves are determined from axial compression tests of these specimens and are correlated with theoretical curves generated using linear analysis.

Lake, Mark S.↗

NASA NTRS1980

Deployable and erectable concepts for large spacecraft

The structural proportions of minimum-mass tetrahedral truss platforms designed for low earth and geosynchronous orbit are determined by means of computerized sizing techniques, taking into account multiple design requirements and constraints. Strut dimensions characterizing minimum mass designs are found to be significantly more slender than those used for conventional structural applications. It is also shown that the number of shuttle flights required by deployable trusses becomes excessive above certain critical stiffness values, and that an automated assembler can achieve rates of 1 min/strut, by comparison with 2-5 min/strut for two astronauts using manual labor.

Bush, H. G.↗

NASA NTRS1980

Deployable and erectable concepts for large spacecraft

Computerized structural sizing techniques were used to determine structural proportions of minimum mass tetrahedral truss platforms designed for low Earth and geosynchronous orbit. Optimum (minimum mass) deployable and erectable, hexagonal shaped spacecraft are sized to satisfy multiple design requirements and constraints. Strut dimensions characterizing minimum mass designs are found to be significantly more slender than those conventionally used for structural applications. Comparison studies show that mass characteristics of deployable and erectable platforms are approximately equal and that the shuttle flights required by deployable trusses become excessive above certain critical stiffness values. Recent investigations of eractable strut assembly are reviewed. Initial erectable structure assembly experiments show that a pair of astronauts can achieve EVA assembly times of 2-5 min/strut and studies indicate that an automated assembler can achieve times of less than 1 min/strut for around the clock operation.

Bush, H. G.↗

DOE OSTI2026

Influence of Numerical Modeling Approaches on Damped Behavior of Flexible Beams: Preprint

Composites structures are widely used in aerospace and wind energy applications for their excellent stiffness and strength-to-weight properties. In these structures, structural damping is critical to predict vibration amplitudes, performance, and reliability. Structural damping is of particular interest for slender wings, rotorcraft blades, and wind turbine blades that can exhibit complex vibration phenomena and are frequently modeled with geometrically exact beam theory (GEBT). Standard approaches of stiffness proportional or modal damping merely assign user defined values and cannot predict damping behavior. This work compares stiffness proportional damping to two more advanced damping approaches: modal strain energy and Prony series. The modal strain energy approach uses a sectional analysis tool to calculate the beam stiffness and postprocess internal stresses from GEBT simulations. The internal stresses are then used to calculate modal damping factors. The Prony series is implemented within GEBT to directly model viscoelastic behavior of the composites. These approaches are compared by modeling the evolution of the damping factors of a realistic flexible wind turbine blade with varying rotational speed. Discrepancies between the approaches suggest areas for future modeling development, but differences in nonlinear damping values are less than current uncertainties about the magnitude of structural damping.

17 WIND ENERGY↗

NASA NTRS1980

Vibration characteristics of a steadily rotating slender ring

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Lallman, F. J.↗

NASA NTRS2000

Shape Measurement of Large Aerospace Structures Using Sensitivity Electrical TDR Distributed Strain Sensor

Electrical time domain reflectometry (ETDR) sensing technique can be best described as "closed-loop radar," where the information is derived from the reflections of a voltage pulse sent through a transmission medium. The ETDR sensing technique is a well-developed method and has been widely used to locate and evaluate discontinuities in long coaxial power transmission cables. The ETDR technique provides a true distributed sensing capability which can not only sense the distributed loading condition of the structure but also can pin-point the location of disturbance, such as the locations of stress concentration and structural damages. Proof-of-concept experiments have been conducted using photoelastic specimens with embedded commercial coaxial cables, i.e., RG85/U and RG174, to demonstrate the stress/strain sensing capability of ETDR sensors for structural health monitoring application. Although the test results showed that the ETDR sensor signals capture specimen deformation pattern both in bending and tension and indicate the location and type of crack damages of the photoelastic specimen; yet, the low signal-to-noise ratio of the sensor signal smears the details of the strain measurement that the ETDR signals can convey. A high-sensitivity ETDR coaxial strain sensor prototype newly developed at Clark Atlanta University will be presented. The construction of the prototype sensing cable as well as its electrical properties relevant to distributed strain sensing application will be shown in details. Test results of the sensitivity and tension responses of the ETDR signal of the prototype sensor will be presented and compared with those of commercial coaxial cables. Promising potentials of the ETDR distributed strain sensing method for shape measurement application of large aerospace structures will also be demonstrated using long slender beam with surface-bonded ETDR distributed strain sensor.

Lin, Mark W.↗

NASA NTRS1988

Large-scale wind turbine structures

The purpose of this presentation is to show how structural technology was applied in the design of modern wind turbines, which were recently brought to an advanced stage of development as sources of renewable power. Wind turbine structures present many difficult problems because they are relatively slender and flexible; subject to vibration and aeroelastic instabilities; acted upon by loads which are often nondeterministic; operated continuously with little maintenance in all weather; and dominated by life-cycle cost considerations. Progress in horizontal-axis wind turbines (HAWT) development was paced by progress in the understanding of structural loads, modeling of structural dynamic response, and designing of innovative structural response. During the past 15 years a series of large HAWTs was developed. This has culminated in the recent completion of the world's largest operating wind turbine, the 3.2 MW Mod-5B power plane installed on the island of Oahu, Hawaii. Some of the applications of structures technology to wind turbine will be illustrated by referring to the Mod-5B design. First, a video overview will be presented to provide familiarization with the Mod-5B project and the important components of the wind turbine system. Next, the structural requirements for large-scale wind turbines will be discussed, emphasizing the difficult fatigue-life requirements. Finally, the procedures used to design the structure will be presented, including the use of the fracture mechanics approach for determining allowable fatigue stresses.

Spera, David A.↗

NASA NTRS1981

Critical requirements for the design of large space structures

The requirements for the design of a large space structure which will be deployed, erected, assembled or fabricated in space are delineated in terms of operational loads, stiffness requirements, structure-control interaction, deformations, precision requirements and member slenderness. Design examples for a truss antenna reflector, interorbit propulsion loads and free-flying solar reflectors are given. It is concluded that the demand for dimensional accuracy and stability form the primary requirements.

Hedgepeth, J. M.↗

NASA NTRS1983

Stability, vibration and passive damping of partially restrained imperfect columns

A theoretical and experimental study of slender tubular columns for possible use in space structures is conducted in the presence of partial rotational end restraints. Explicit formulas are derived for computing the buckling load and the lowest natural frequency of perfectly straight uniform elastic members with rotational end restraints possessing linear moment-rotation characteristics. An exact solution in the form of a transcendental equation, and a numerical solution using second-order finite-differences are also presented. The presence of an initial imperfection is also incorporated into the numerical procedure. Vibration tests are conducted on an imperfect tubular steel member in the absence of an axial load. A damping concept consisting of a string-mass assembly is explored. Three passive damping configurations involving combinations of three lead shots were investigated. The three lead shot configurations provided considerably greater damping than the single lead shot.

Razzaq, Z.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-14571-DND

Structural dynamics major concern for Ares I - Highest slenderness ratio of any vehicle ever flown - First bending mode within control bandwidth - Phase stabilization of first bending mode required - Gain stabilization of higher modes Ares I-X provided early flight test of first stage flight for model and modeling method validation - Dynamically scaled at liftoff - Dummy upper stage, Orion/LAS, and 5th segment Made with surplus materials… - Booster & TVC – expired Shuttle RSRM - RoCS – disassembled from Peace Keeper ICBM - BDM’s and BTM’s – Old Shuttle BSM motors - Avionics – Atlas V

Eugene Heim↗

NASA NTRS1971

The development of a sonic boom simulator with detonable gases

A sonic boom pressure profile was simulated in the far-field by detonation of a methane-oxygen mixture contained in a slender, shaped Mylar envelope. Ideal N-waves were synthesized with peak overpressures from two to five psf and durations of 30 to 75 milliseconds. The detonation of the gas mixture was initiated by a single Primacord strand running the length of balloon. The N-wave producing balloon was synthesized as a composite structure, utilizing experimental pressure profiles obtained from the detonations of slender, axisymmetric balloons with elementary, non-cylindrical shapes.

Strugielski, R. T.↗

NASA NTRS1979

Topology of two-dimensional and three-dimensional separated flows

It is shown that topology rules can define a small number of singular points on an aerodynamic surface and in the flow which can be combined in various ways to create the structures and characterize the physical mechanisms of three-dimensional separated flows. This topological development is based on the hypothesis that vector fields of skin-friction lines and external streamlines remain continuous. Among examples treated are the lee-side separated flows about slender bodies at angle of attack with symmetric or asymmetric wake structures; about a protuberance normal to a wall; and over a rearward-facing axisymmetric step.

Tobak, M.↗

NASA NTRS1989

Stability and dynamic analysis of a slender column with curved longitudinal stiffeners

The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.

Lake, Mark S.↗