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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1975

Nonlinear resonances in a class of multi-degree-of-freedom systems

An analysis is presented of the superharmonic, subharmonic, and combination resonances in a multi-degree-of-freedom system which has cubic nonlinearity and modal viscous damping and is subject to harmonic excitation. It is shown that, in the absence of internal resonances, the steady-state response contains only the modes which are directly excited. It is shown that, in the presence of internal resonances, modes other than those that are directly excited can appear in the response. The strong influence of internal resonances is exhibited in numerical examples involving hinged-clamped beams. It is shown that when a multimode solution exists the lowest mode can dominate the response, even when it is not directly excited.

Sridhar, S.↗
NASA NTRS1976

The dynamics of spin stabilized spacecraft with movable appendages, part 2

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to (assumed) massless booms of fixed length whose orientation relative to the main part can change. The general three dimensional deployment dynamics of such a hinged system is considered without any restriction on the location of the hinge points. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis for the case of two dimensional and three dimensional motion. Analytic stability criteria are obtained from the necessary condition on the sign of all the coefficients in the system characteristic equation.

Bainum, P. M.↗
NASA NTRS1976

The motion and stability of spin stabilized spacecraft with hinged appendages

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to massless booms of fixed length whose orientation relative to the main part can change. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis. Analytic stability criteria indicate that hinge damping must be present and that for limiting cases, where the spin axis is an axis of symmetry, certain conditions relating the hinge point offset coordinates to the moment of inertia ratio and end masses must be satisfied. The hinge damping is always required for the nominal deployment of hinge members.

Sellappan, R.↗
NASA NTRS1977

The general solution to the classical problem of finite Euler Bernoulli beam

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Hussaini, M. Y.↗
NASA NTRS1978

The general solution to the classical problem of the finite Euler-Bernoulli beam

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Hussaini, M. Y.↗
NASA NTRS1980

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.

Bainum, P. M.↗
NASA NTRS1980

On the dynamics of large orbiting flexible beams and platforms oriented along the local horizontal

The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.

Bainum, P. M.↗
NASA NTRS1981

Nonlinear dynamic phenomena in the space shuttle thermal protection system

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Housner, J. M.↗
NASA NTRS1982

Sonic fatigue testing of an advanced composite aileron

The sonic fatigue test program to verify the design of the composite inboard aileron for the L-1011 airplane is described. The composite aileron is fabricated from graphite/epoxy minisandwich covers which are attached to graphite/epoxy front spar and ribs, and to an aluminum rear spar with fasteners. The program covers the development of random fatigue data by means of coupon testing and modal studies on a representative section of the composite aileron, culminating in the accelerated sonic fatigue proof test. The composite aileron sustained nonlinear panel vibration during the proof test without failure. Viscous damping coefficients as low as 0.4% were measured on the panels. The effects of moisture conditioning and elevated temperature on the random fatigue life of both undamaged and impact damaged coupons were investigated. The combination of impact damage, moisture, and a 180 F temperature could reduce the random fatigue life by 50%.

Soovere, J.↗
NASA NTRS1983

The dynamics of elliptical rings

The paper investigates the evolution of eccentric rings under the influence of (1) differential precession due to the planetary quadrupole moment; (2) self-gravity; (3) viscous forces due to interparticle collisions; and (4) eccentricity excitation by shepherd satellites. The principal conclusions are that: (1) uniform precession can be enforced by self-gravity; the resulting configuration is both dynamically and secularly stable. (2) due to viscous forces the line of apsides at the inner ring edge is not exactly aligned with the line of apsides at the outer edge; the apse shift may be detectable in the alpha and beta rings of Uranus; (3) the mean eccentricity is determined by a balance between viscous damping and excitation by shepherds; (4) and the dimensionless eccentricity gradient is expected to be positive and of order unity in most eccentric rings, as observed.

Borderies, N.↗
NASA NTRS1984

Forecasts of the 500 mb height using a dynamically oriented statistical model

The forecast skill of a simple dynamically inspired statistical model of the Northern Hemisphere 500 mb height field is evaluated in spectral and physical space for a variety of forecast lead times (1-32 days) and predictand averaging times (1-32 days). The model includes viscous damping, wave propagation, climatology and implicit stochastic forcing. The largest model skill was found for forecasts of the zonal flow and the largest waves. In general, the largest forecast skills were also associated with the largest forecast error, there being a slight geographic phase shift of the skill with respect to the error. Model skills for climate (time-averaged) forecasts are greater when using instantaneous rather than time averages to forecast time averages. Analysis of model errors suggests areas for improvement in representing forcing terms and model physics. However, the model error fields are largely 'white noise' which suggests that global forecast skills substantially larger than those obtained here are unlikely to be achieved by more sophisticated models.

Roads, J. O.↗
NASA NTRS1985

A study of internal and distributed damping for vibrating turbomachiner blades

Internal and distributed damping as possible methods for reducing the vibration response of turbomachine blades and theoretical methods for analyzing damped vibration were studied. It is demonstrated how the Ritz-Galerkin methods may be used to straightforwardly to analyze forced vibrations with damping. This is done directly without requiring the free vibration eigenfunctions. The Galerkin method is an effective technique for these types of problems. The Ritz method has the further advantage of not needing to satisfy the force type boundary conditions, which is particularly important for plates and shells. But proper functionals representing the forcing and damping terms must be developed, and this is done. Two types of damping--viscous and material (hysteretic) are considered. Both distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. Studies showing the rates of convergence of the solutions are made. In the case of the cantilever beam, approximate solutions from the present methods are compared with the exact solutions.

Leissa, A. W.↗
NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗
NASA NTRS1986

Identification of differences between finite element analysis and experimental vibration data

An important problem that has emerged from combined analytical/experimental investigations is the task of identifying and quantifying the differences between results predicted by F.E. analysis and results obtained from experiment. The objective of this study is to extend and evaluate the procedure developed by Sidhu for correlation of linear F.E. and modal test data to include structures with viscous damping. The desirability of developing this procedure is that the differences are identified in terms of physical mass, damping, and stiffness parameters instead of in terms of frequencies and modes shapes. Since the differences are computed in terms of physical parameters, locations of modeling problems can be directly identified in the F.E. model. From simulated data it was determined that the accuracy of the computed differences increases as the number of experimentally measured modes included in the calculations is increased. When the number of experimental modes is at least equal to the number of translational degrees of freedom in the F.E. model both the location and magnitude of the differences can be computed very accurately. When the number of modes is less than this amount the location of the differences may be determined even though their magnitudes will be under estimated.

Lawrence, C.↗
NASA NTRS1985

Protostellar angular momentum transport by spiral density waves

The application of rotational stability criteria to a specific model of star formation leads to the conclusion that the growth of stellar angular momentum is limited by its transfer to the disk. Excess accreted angular momentum can be transferred by torques connected with spiral density waves induced by even a slight protostellar triaxiality. In addition, viscous damping of the density waves is likely to cause the excess angular momentum to be deposited within a small region close to the protostar. Thus, it would be appropriate to treat that part of the growing protostellar disk beyond the outer Lindblad resonance as an accretion disk with a torque applied to its inner edge. It is noted that this situation is directly relevant to certain models of the evolution of the protosun and solar nebula.

Yuan, C.↗
NASA NTRS1986

Viscous normal modes on coronal inhomogeneities and their role as a heating mechanism

Viscous damping of Alfven surface waves is examined both analytically and numerically using incompressible MHD. Normal modes are shown to exist on discontinuous as well as continuously varying interfaces in Alfven speed. The waves experience negligible decay below the transition zone. High-frequency waves damp just above the transition region, while those of lower frequency lose energy further out. A comparison of dissipative decay rates shows that wave damping by viscosity proceeds approximately two orders of magnitude faster than by resistivity.

Steinolfson, R. S.↗
NASA NTRS1985

Theoretical and experimental studies of baroclinic processes

An experimental study in a baroclinic annulus with heating and cooling on the upper and lower horizontal surfaces was completed. Four basic regimes of flow were observed: (1) axisymmetric flow, (2) cellular (deep) convection, (3) convective rolls (boundary layer), and (4) baroclinic instability. There was no symmetric (or nearly symmetric) baroclinic instability observed, although it was determined by numerical calculations that we transversed regions in parameter space where the symmetric instability was present. The non-symmetric baroclinic instability (Eady type) was observed instead. Although the vertical depth was rather small and hence viscous damping was strong, large-amplitude baroclinic waves were made possible by imposing a very weak static stability.

Miller, T.↗
NASA NTRS1986

Development and first flight of a sounding rocket payload to investigate the phenomena of rapidly varying space plasma

NASA Goddard Space Flight Center, Wallops Flight Facility has developed, flown, and recovered a unique plasma physics payload. This sounding rocket payload was developed to measure varying aspects of Alfven's critical velocity effect in a space plasma by using conical-shaped barium explosives. These measurements could possibly duplicate conditions that existed in the early solar system. This paper provides details of the payload and subpayload development, with specific emphasis on the extensive dynamic analysis of the barium release modules. Other key elements which are expanded on in the paper are: (1) design, development, and testing acceptance for the science/inertia booms using a viscous damping system for high spin rate deployment; (2) vehicle dynamic analysis; (3) apogee and impact dispersion analysis to satisfy the science and NASA safety requirements; (4) a comparison of predicted versus actual flight events.

Buchanan, R. P.↗