Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear”

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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Films Containing Optically Nonlinear Diacetylene Monomer

Solid films exhibiting nonlinear optical properties prepared as mixtures of poly(methyl methacrylate) with various amounts of diacetylene monomer called "compound 1" in article, "Synthesizing Diacetylenes With Nonlinear Optical Properties" (MFS-26186). Useful as phase-conjugate mirrors in laser-beam communications and as optical switches in optical computers. This particular diacetylene monomer exhibits strong third-order nonlinear optical properties, both in pure form and in solution.

Paley, Mark S.↗
NASA NTRS1992

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Wu, Xuesong↗
NASA NTRS1992

Prediction of nonlinear optical properties of large organic molecules

The preparation of materials with large nonlinear responses usually requires involved synthetic processes. Thus, it is very advantageous for materials scientists to have a means of predicting nonlinear optical properties. The prediction of nonlinear optical properties has to be addressed first at the molecular level and then as bulk material. For relatively large molecules, two types of calculations may be used, which are the sum-over-states and the finite-field approach. The finite-field method was selected for this research, because this approach is better suited for larger molecules.

Cardelino, Beatriz H.↗
NASA NTRS1993

On the nonlinear interfacial instability of rotating core-annular flow

The interfacial stability of rotating core-annular flows is investigated. The linear and nonlinear effects are considered for the case when the annular region is very thin. Both asymptotic and numerical methods are used to solve the flow in the core and film regions which are coupled by a difference in viscosity and density. The long-term behavior of the fluid-fluid interface is determined by deriving its nonlinear evolution in the form of a modified Kuramoto-Sivashinsky equation. We obtain a generalization of this equation to three dimensions. The flows considered are applicable to a wide array of physical problems where liquid films are used to lubricate higher or lower viscosity core fluids, for which a concentric arrangement is desired. Linearized solutions show that the effects of density and viscosity stratification are crucial to the stability of the interface. Rotation generally destabilizes non-axisymmetric disturbances to the interface, whereas the centripetal forces tend to stabilize flows in which the film contains the heavier fluid. Nonlinear affects allow finite amplitude helically travelling waves to exist when the fluids have different viscosities.

Coward, Aidrian V.↗
NASA NTRS1993

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

Doyle, John C.↗
NASA NTRS1993

Nonlinear modes of the tensor Dirac equation and CPT violation

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Reifler, Frank J.↗
NASA NTRS1993

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗
NASA NTRS1992

Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis

In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.

Merchant, G. J.↗
NASA NTRS1992

Linear and nonlinear stability of the Blasius boundary layer

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Bertolotti, F. P.↗
NASA NTRS1991

Nonlinear time-series-based adaptive control applications

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Mohler, R. R.↗
NASA NTRS1992

Nonlinear vibration and radiation from a panel with transition to chaos

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Maestrello, Lucio↗
NASA NTRS1992

Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.

Maestrello, Lucio↗
NASA NTRS1993

Nonlinear effects of a modal domain optical fiber sensor in a vibration suppression control loop for a flexible structure

Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.

Lindner, D. K.↗
NASA NTRS1991

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.↗
NASA NTRS1993

On the nonlinear development of the most unstable Goertler vortex mode TLSP - Final report

The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Goertler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Goertler equations valid for O(1) Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗
NASA NTRS1993

Nonlinear optical parameters of 7-prime,7-prime-dicyano-7-prime-apo-beta-carotene in hexane by self-action techniques

Quantitative measurements of the nonlinear refractive index coefficient n(2) and the third-order nonlinear susceptibility chi(3) for a solution of 7-prime,7-prime-dicyano-7-prime-apo-beta-carotene (DCAC) in hexane have been measured at different concentrations. The measurements have been performed by both the self-trapping and self-phase modulation techniques using a CW Ar(+) laser. The results show that DCAC has a relatively large nonlinearity, attributed to a thermal mechanism, with n(2) of the order of 10 exp 9 times that of CS2.

Abdeldayem, Hossin A.↗
NASA NTRS1991

Growth of thin films of organic nonlinear optical materials by vapor growth processes - An overview and examination of shortfalls

Research on the growth of second- and third-order nonlinear optical (NLO) organic thin film by vapor deposition is reviewed. Particular attention is given to the experimental methods for growing thin films of p-chlorophenylurea, diacetylenes, and phthalocyanines; characteristics of the resulting films; and approaches for advancing thin film technology. It is concluded that the growth of NLO thin films by vapor processes is a promising method for the fabrication of planar waveguides for nonlinear optical devices. Two innovative approaches are proposed including a method of controlling the input beam frequency to maximize nonlinear effects in thin films and single crystals, and the alternate approach to the molecular design of organic NLO materials by increasing the transition dipole moment between ground and excited states of the molecule.

Frazier, D. O.↗
NASA NTRS1993

Nonlinear response of graphite-epoxy wide columns subject to eccentric load

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on 0(30)T and (30/0/-30 sub 5)s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stillnesses in the updated configuration.

Griffin, O. H., Jr.↗