Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Non-linear Dynamics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Wauer, J.↗
NASA NTRS1978

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

Mukhopadhyay, A. K.↗
NASA NTRS1979

Stochastic modeling of the time-averaged equations for climate dynamics

Two analyses on climate dynamics are presented, both based on a simplified set of barotropic equations for representing large scale non-linear atmospheric circulation characteristics. The statistical properties of the set of equations were investigated for small values of a parameter k sub o, corresponding to the physical case of large zonal westerlies and relatively weak eddy motions. The effect of seasonal type forcing on the solution of these equations was also studied and some preliminary numerical results are presented.

Spreiter, J. R.↗
NASA NTRS1982

Blade loss transient dynamic analysis of turbomachinery

This paper reports on work completed to develop an analytical method for predicting the transient non-linear response of a complete aircraft engine system due to the loss of a fan blade, and to validate the analysis by comparing the results against actual blade loss test data. The solution, which is based on the component element method, accounts for rotor-to-casing rubs, high damping and rapid deceleration rates associated with the blade loss event. A comparison of test results and predicted response show good agreement except for an initial overshoot spike not observed in test. The method is effective for analysis of large systems.

Stallone, M. J.↗
NASA NTRS1978

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Khosla, P. K.↗
NASA NTRS1979

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Khosla, P. K.↗
NASA NTRS1985

Two types of chaos in non-linear mechanics

The two types of chaos, weak and strong, associated with the Liapunov and Hadamard instabilities respectively, are analyzed. The geometrical representation of weak chaos is considered, and criteria of this chaos are formulated using the geometrical interpretation of dynamics. Weak chaos in inertial motion of two-bar linkage is discussed. The analysis of strong chaos is restricted to a review of results published elsewhere.

Zak, M.↗
NASA NTRS1979

Mechanics of fracture - Fundamentals and some recent developments

An overview is presented of the fundamental aspects of and recent developments in fracture mechanics. Reference is made to linear elastic fracture mechanics including the state of stresses and displacements in the vicinity of cracks, effects of crack geometry and orientation on stress intensity factors, energy balance of Griffith, Irwin's stress intensity concept, and linear elastic fracture mechanics testing for fracture toughness. Other aspects of this paper include the non-linear behavior of materials and their influence on fracture mechanics parameters, consideration of viscoelasticity and plasticity, non-linear fracture toughness parameters as C.O.D., R-curve and J-integral, and a non-linear energy method, proposed by Liebowitz. Finite element methods applied to fracture mechanics problems are indicated. Also, consideration has been given to slow crack growth, dynamic effects on K(IC), Sih's criterion for fracture, Lee and Liebowitz's criterion relating crack growth with plastic energy, and applications of fracture mechanics to aircraft design. Suggestions are offered for future research efforts to be undertaken in fracture mechanics.

Liebowitz, H.↗
NASA NTRS1984

Elastic continua in high frequency excitation field

The response of elastic continua to high-frequency excitations is decomposed in two parts: 'slow' motion which practically remains unchanged during a vanishingly small period of time, and 'fast' motions whose mean value during this period is negligible but whose energy contribution is essential. After such a decomposition the 'slow' and 'fast' motions become non-linearly coupled by the corresponding governing equations. This coupling leads to an additional 'effective' potential energy which changes the 'mean' stiffness characteristics. The results can be used for dynamical stiffening of flexible structural elements, for a temporary increase of their stiffness in the course of occasional loads to prevent buckling or wrinkling.

Zak, M.↗
NASA NTRS1982

Second order non-linear equations of motion for spinning highly flexible line elements

The second order nonlinear equations of motion are formulated for spinning line elements having little or no intrinsic structural stiffness. The derivation is based on the extended Hamilton's principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

Salama, M.↗
NASA NTRS1985

Acceleration of cosmic rays in supernova-remnants

It is commonly accepted that supernova-explosions are the dominant source of cosmic rays up to an energy of 10 to the 14th power eV/nucleon. Moreover, these high energy particles provide a major contribution to the energy density of the interstellar medium (ISM) and should therefore be included in calculations of interstellar dynamic phenomena. For the following the first order Fermi mechanism in shock waves are considered to be the main acceleration mechanism. The influence of this process is twofold; first, if the process is efficient (and in fact this is the cas) it will modify the dynamics and evolution of a supernova-remnant (SNR), and secondly, the existence of a significant high energy component changes the overall picture of the ISM. The complexity of the underlying physics prevented detailed investigations of the full non-linear selfconsistent problem. For example, in the context of the energy balance of the ISM it has not been investigated how much energy of a SN-explosion can be transfered to cosmic rays in a time-dependent selfconsistent model. Nevertheless, a lot of progress was made on many aspects of the acceleration mechanism.

Dorfi, E. A.↗
NASA NTRS1980

Equations of motion for coupled n-body systems

Computer program, developed to analyze spacecraft attitude dynamics, can be applied to large class of problems involving objects that can be simplified into component parts. Systems of coupled rigid bodies, point masses, symmetric wheels, and elastically flexible bodies can be analyzed. Program derives complete set of non-linear equations of motion in vectordyadic format. Numerical solutions may be printed out. Program is in FORTRAN IV for batch execution and has been implemented on IBM 360.

Frisch, H. P.↗
NASA NTRSDate not supplied

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics↗
NASA NTRS1983

Transonic pressure distributions on a rectangular supercritical wing oscillating in pitch

Steady and unsteady aerodynamic data were measured on a rectangular wing with a 12 percent thick supercritical airfoil mounted in the NASA Langley Transonic Dynamics Tunnel. The wing was oscillated in pitch to generate the unsteady aerodynamic data. The purpose of the wind-tunnel test was to measure data for use in the development and assessment of transonic analytical codes. The effects on the wing pressure distributions of Mach number, mean angle of attack, and oscillation frequency and amplitude were measured. Results from the newly-developed XTRAN3S program (a non-linear transonic small disturbance code) and from the RHOIV program (a linear lifting surface kernel function code) were compared to measured data for a Mach number of 0.7 and for oscillation frequencies ranging from 0 to 20 Hz. The XTRAN3S steady and unsteady results agreed fairly well with the measured data. The RHOIV unsteady-result agreement was fair but, of course, did not predict shock effects.

Ricketts, R. H.↗
NASA NTRS1983

Solar maximum mission: Ground support programs at the Harvard Radio Astronomy Station

Observations of the spectral characteristics of solar radio bursts were made with new dynamic spectrum analyzers of high sensitivity and high reliability, over the frequency range 25-580 MHz. The observations also covered the maximum period of the current solar cycle and the period of international cooperative programs designated as the Solar Maximum Year. Radio data on shock waves generated by solar flares were combined with optical data on coronal transients, taken with equipment on the SMM and other satellites, and then incorporated into computer models for the outward passage of fast-mode MHD shocks through the solar corona. The MHD models are non-linear, time-dependent and for the most recent models, quasi-three-dimensional. They examine the global response of the corona for different types of input pulses (thermal, magnetic, etc.) and for different magnetic topologies (for example, open and closed fields). Data on coronal shocks and high-velocity material ejected from solar flares have been interpreted in terms of a model consisting of three main velocity regimes.

Maxwell, A.↗
NASA NTRS1972

Dual characterizations of optimal systems.

The complementary variational principle developed in a Hilbert space setting provides a duality principle in the calculus of variations with dynamic constraints. This concept is adopted in this paper to investigate dual characterizations of optimal control systems. Systems under consideration include those with dynamics governed by linear ordinary differential equations, linear partial differential equations and non-linear ordinary differential equations.

Chan, W. L.↗
NASA NTRS1979

Surprisal analysis of rotational-translational energy transfer - Non-linear versus linear rotors

Surprisal versus energy gap analyses of state-to-state cross sections are presented for a number of linear rigid rotors excited by collisions with atoms for H2-H, H2-He, HCl-He, HCl-Ar, CO-He, CS-H2 (j=0) OCS-H2 (j=0) and HN2(+)-He, where (j=0) indicates that the hydrogen molecule was constrained to remain in its lowest level. Different systems exhibit wide variations in the slope of the surprisal plot and in certain cases, enough to indicate that the energy gap may not be the static dynamical constraint. Similar analyses are presented for nonlinear rotors excited by atoms for H2CO-He and H2O-He. For these, the data show a great deal of scatter, indicating that the reduced energy gap is probably not the appropriate independent variable.

Green, S.↗
NASA NTRS1983

Development of monofilar rotor hub vibration absorber

A design and ground test program was conducted to study the performance of the monofilar absorber for vibration reduction on a four-bladed helicopter. A monofilar is a centrifugal tuned two degree-of-freedom rotor hub absorber that provides force attenuation at two frequencies using the same dynamic mass. Linear and non-linear analyses of the coupled monofilar/airframe system were developed to study tuning and attenuation characteristics. Based on the analysis, a design was fabricated and impact bench tests verified the calculated non-rotating natural frequencies and mode shapes. Performance characteristics were measured using a rotating absorber test facility. These tests showed significant attenuation of fixed-system 4P hub motions due to 3P inplane rotating-system hub forces. In addition, detuning effects of the 3P monofilar modal response were small due to the nonlinearities and tuning pin slippage. However, attenuation of 4P hub motions due to 5P inplane hub forces was poor. The performance of the 5P monofilar modal response was degraded by torsional motion of the dynamic mass relative to the support arm which resulted in binding of the dynamic components. Analytical design studies were performed to evaluate this torsional motion problem. An alternative design is proposed which may alleviate the torsional motion of the dynamic mass.

Duh, J.↗