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NASA NTRS1993

An efficient model for coupling structural vibrations with acoustic radiation

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Frendi, Abdelkader↗

NASA NTRS1985

The coalescence instability in solar flares

The nonlinear coalescence instability of current carrying solar loops can explain many of the characteristics of the solar flares such as their impulsive nature, heating and high energy particle acceleration, amplitude oscillations of electromagnetic and emission as well as the characteristics of two-dimensional microwave images obtained during a flare. The plasma compressibility leads to the explosive phase of loop coalescence and its overshoot results in amplitude oscillations in temperatures by adiabatic compression and decompression. It is noted that the presence of strong electric fields and super-Alfvenic flows during the course of the instability play an important role in the production of nonthermal particles. A qualitative explanation on the physical processes taking place during the nonlinear stages of the instability is given.

Tajima, T.↗

NASA NTRS1974

Theoretical investigation of nonlinear three-dimensional instabilities in liquid rockets with real nozzles

An approximate analytical technique has been developed for the solution of nonlinear three-dimensional, transverse and axial combustion-instability problems that are frequently observed in liquid-propellant rocket motors. This theory is an extension and generalization of previous analyses, which could analyze either transverse or axial instabilities in liquid combustors with quasi-steady nozzles, to the practical situations of three-dimensional instabilities in combustors with conventional DeLaval nozzles. Unlike the quasi-steady nozzle, the presence of a conventional nozzle imposes restrictions upon the behavior of both the amplitudes and phases of the oscillations at the nozzle entrance plane. The applicability of the solution technique, which is based on the Galerkin method, is demonstrated by analyzing the nonlinear stability of a cylindrical liquid-rocket combustor with uniform injection of propellants at one end and a conventional nozzle at the other end. Crocco's pressure-sensitive time-lag model is used to describe the unsteady combustion process.

Powell, E. A.↗

DOE OSTI2026

On-Chip Cavity Electroacoustics Using Lithium Niobate Phononic Crystal Resonators

Mechanical systems are pivotal in quantum technologies because of their long coherent time and versatile coupling to qubit systems. So far, the coherent and dynamic control of gigahertz-frequency mechanical modes mostly relies on optomechanical coupling and piezoelectric coupling to superconducting qubits. Here, we demonstrate on-chip cavity electroacoustic dynamics using our microwave-frequency electrically modulated phononic crystal resonators on lithium niobate. Leveraging the high dispersion of phononic crystal, our acoustic modes space unevenly in the frequency spectrum, emulating atomic energy levels. Atomiclike transitions between different acoustic modes are selectively achieved by applying electrical fields to modulate acoustic modes via the nonlinear piezoelectricity of lithium niobate. Among two modes, we demonstrate Autler-Townes splitting, ac Stark shift, and Rabi oscillation with a maximum cooperativity of 4.18. Extending to three modes, we achieve nonreciprocal frequency conversions with an isolation up to 20 dB. Nonreciprocity can be tuned by the time delay between the two modulating pulses. Finally, our cavity electroacoustic platform could find broad applications in sensing, microwave signal processing, acoustic computing, and quantum acoustics.

Rabi model↗

DOE OSTI2021

Quantum system dynamics with a weakly nonlinear Josephson junction bath

Here, we investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies, respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.

1-dimensional systems↗

NASA NTRS1988

Development of a computerized analysis for solid propellant combustion instability with turbulence

A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed.

Chung, T. J.↗

NASA NTRS1985

Equilibrium thermodynamics and stochastic nonlinear acoustic fields

A crystalline solid is considered to consist of a large number of incoherent nonlinear acoustic radiation sources identified with the vibrating particles of the crystalline lattice. Randomization of the field, together with the assumption of a stochastically independent, fluctuating, radiation field at the absolue zero of temperature, leads to an expression of the temperature-dependent radiation field in terms of the zero-point field. The equation is identified with the Planck distribution formula of quantum mechanics in the linear field limit. The thermodynamic state functions are also obtained in terms of the nonlinear acoustic modal energies per unit mass and reduce to the results of the Debye-Einstein stochastic quantum oscillator model in the linear field limit.

Cantrell, J. H.↗

NASA NTRS2017

Critical Fluctuations in Beam-Plasma Systems and Solar Type III Radio Bursts

The type III radio bursts are the most intense radio emissions from the sun. In Figure 1, we present a typical type III burst observed by the STEREO spacecraft. Ginzburg and Zheleznyakov (1958) were the first to suggest that Langmuir waves excited by the solar flare accelerated electrons are the source of these bursts. The in situ detection of electron beams and Langmuir waves in association with type III bursts together with tracking of type III burst sources in the interplanetary medium confirmed this plasma hypothesis. However, the dynamics of type III electron beams and their interaction with the ambient plasma through the excited Langmuir waves is an unsolved problem. In order that the electron beams don't lose their energy by resonantly interacting with Langmuir waves, various nonlinear processes, such as the induced scattering of Langmuir waves off the background ions in weak turbulence regime and oscillating two-stream instability in strong turbulence regime were invoked. However, the observed electron density fluctuations do not allow Langmuir waves to grow to very high intensities as pointed out by several authors. As far as the conversion of Langmuir wave energy into electromagnetic energy is concerned, there is no consensus either for the fundamental or for the second harmonic emission. In this paper, we address these issues in terms of critical fluctuations near the boundary of the beam-plasma instability which is analogous to the anomalously growing fluctuations near the phase transition points called critical points. We show that this phenomenon can account for the survival of electron beams over large distances as well as the intensities of Langmuir waves excited during this phase transition regime are sufficient to explain the peak intensities of the fundamental as well as harmonic emissions

Fluctuations↗

NASA NTRS1973

Synthesis of oscillating adaptive feedback systems

A synthesis theory is developed which allows system design to proceed from practical specifications on system command and/or disturbance response to a design which is very nearly optimal in terms of feedback sensor noise effects. The approach taken is to replace the nonlinear element by a mean square error minimizing approximation (dual-input describing function), and then use linear frequency domain synthesis techniques subject to additional constraints imposed by the limit cycle and the approximator. Synthesis techniques are also developed for a similar system using an externally excited oscillating signal with the above approach. The results remove the design of the systems considered from the realm of simulation and experimentation, permitting true synthesis and the optimization that accompanies it.

Smay, J. W.↗

DOE OSTI2022

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

NASA Tech Briefs, December 2005

Topics covered include: Video Mosaicking for Inspection of Gas Pipelines; Shuttle-Data-Tape XML Translator; Highly Reliable, High-Speed, Unidirectional Serial Data Links; Data-Analysis System for Entry, Descent, and Landing; Hybrid UV Imager Containing Face-Up AlGaN/GaN Photodiodes; Multiple Embedded Processors for Fault-Tolerant Computing; Hybrid Power Management; Magnetometer Based on Optoelectronic Microwave Oscillator; Program Predicts Time Courses of Human/ Computer Interactions; Chimera Grid Tools; Astronomer's Proposal Tool; Conservative Patch Algorithm and Mesh Sequencing for PAB3D; Fitting Nonlinear Curves by Use of Optimization Techniques; Tool for Viewing Faults Under Terrain; Automated Synthesis of Long Communication Delays for Testing; Solving Nonlinear Euler Equations With Arbitrary Accuracy; Self-Organizing-Map Program for Analyzing Multivariate Data; Tool for Sizing Analysis of the Advanced Life Support System; Control Software for a High-Performance Telerobot; Java Radar Analysis Tool; Architecture for Verifiable Software; Tool for Ranking Research Options; Enhanced, Partially Redundant Emergency Notification System; Close-Call Action Log Form; Task Description Language; Improved Small-Particle Powders for Plasma Spraying; Bonding-Compatible Corrosion Inhibitor for Rinsing Metals; Wipes, Coatings, and Patches for Detecting Hydrazines; Rotating Vessels for Growing Protein Crystals; Oscillating-Linear-Drive Vacuum Compressor for CO2; Mechanically Biased, Hinged Pairs of Piezoelectric Benders; Apparatus for Precise Indium-Bump Bonding of Microchips; Radiation Dosimetry via Automated Fluorescence Microscopy; Multistage Magnetic Separator of Cells and Proteins; Elastic-Tether Suits for Artificial Gravity and Exercise; Multichannel Brain-Signal-Amplifying and Digitizing System; Ester-Based Electrolytes for Low-Temperature Li-Ion Cells; Hygrometer for Detecting Water in Partially Enclosed Volumes; Radio-Frequency Plasma Cleaning of a Penning Malmberg Trap; Reduction of Flap Side Edge Noise - the Blowing Flap; and Preventing Accidental Ignition of Upper-Stage Rocket Motors.

Source record↗

DOE OSTI2020

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

42 ENGINEERING↗

NASA NTRS1976

IR pumped third-harmonic generation and sum-frequency generation in diatomic molecules

The potential efficiency of using nonlinear up-conversion techniques for the high efficiency type lasers (CO,CO2, and chemical) is assessed. Results indicate that: the small pump photon energy necessitates the use of molecular media for conversion if resonance enhancement is to be used and that molecular systems present several problems. These difficulties include: their levels are complex; their transition probabilities are often unknown; and the oscillator strengths among vibrational levels in the ground electronic state of a molecule are much smaller than those among electronic states of an atom, thus limiting the magnitude of nonlinear interactions. It is shown that this problem can be eliminated by making use of vibronic transitions which, being primarily electronic transitions have much larger matrix elements and efficient conversion can be achieved with molecular systems.

She, C. Y.↗

NASA NTRS2015

Aeroelastic Analysis of SUGAR Truss-Braced Wing Wind-Tunnel Model Using FUN3D and a Nonlinear Structural Model

Considerable attention has been given in recent years to the design of highly flexible aircraft. The results of numerous studies demonstrate the significant performance benefits of strut-braced wing (SBW) and trussbraced wing (TBW) configurations. Critical aspects of the TBW configuration are its larger aspect ratio, wing span and thinner wings. These aspects increase the importance of considering fluid/structure and control system coupling. This paper presents high-fidelity Navier-Stokes simulations of the dynamic response of the flexible Boeing Subsonic Ultra Green Aircraft Research (SUGAR) truss-braced wing wind-tunnel model. The latest version of the SUGAR TBW finite element model (FEM), v.20, is used in the present simulations. Limit cycle oscillations (LCOs) of the TBW wing/strut/nacelle are simulated at angle-of-attack (AoA) values of -1, 0 and +1 degree. The modal data derived from nonlinear static aeroelastic MSC.Nastran solutions are used at AoAs of -1 and +1 degrees. The LCO amplitude is observed to be dependent on AoA. LCO amplitudes at -1 degree are larger than those at +1 degree. The LCO amplitude at zero degrees is larger than either -1 or +1 degrees. These results correlate well with both wind-tunnel data and the behavior observed in previous studies using linear aerodynamics. The LCO onset at zero degrees AoA has also been computed using unloaded v.20 FEM modes. While the v.20 model increases the dynamic pressure at which LCO onset is observed, it is found that the LCO onset at and above Mach 0.82 is much different than that produced by an earlier version of the FEM, v. 19.

Bartels, Robert E.↗

DOE OSTI2020

Three-colour digital holographic microscopy based on a Mach – Zender interferometer and a solid-state RGB laser

We have developed a facility for recording colour digital holograms involving a Mach – Zender interferometer and a pulsed solid-state RGB laser, which radiates simultaneously at three wavelengths: 451, 532, and 634 nm. These wavelengths are obtained in the conversion of the radiation of a pulsed Nd{sup 3+} : YAG laser (1064 nm), which operates in the regime of intracavity parametric oscillation at a wavelength of 1570 nm, with the subsequent conversion of its frequencies to the red, green, and blue spectral regions in nonlinear KTP-crystal elements. The combination of this three-wavelength pulsed light source with the Mach – Zender interferometer provides the simultaneous recording of three spectral digital holograms with one matrix RGB radiation detector. Pulsed three-colour digital holography shows promise for the analysis of fast processes and rapidly varying colour phase objects. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1996

The Dynamics of Ultrasonically Levitated Drops in an Electric Field

Ultrasonic and electrostatic levitation techniques have allowed the experimental investigation of the nonlinear oscillatory dynamics of free droplets with diameter between 0.1 and 0.4 cm. The measurement of the resonance frequencies of the first three normal modes of large amplitude shape oscillations in an electric field of varying magnitude has been carried out with and without surface charges for weakly conducting liquids in air. These oscillations of nonspherical levitated drops have been driven by either modulating the ultrasonic field or by using a time-varying electric field, and the free decay from the oscillatory state has been recorded. A decrease in the resonance frequency of the driven fundamental quadrupole mode has been measured for increasing oblate deformation in the absence of an electric field. Similarly, a decrease in this frequency has also been found for increasing DC electric field magnitude. A soft nonlinearity exists in the amplitude dependence of the resonant mode frequencies for freely decaying as well as ultrasonically and electrically driven uncharged drops. This decrease in resonance frequency is accentuated by the presence of free surface charge on the drop. Subharmonic resonance excitation has been observed for drops in a time-varying electric field, and hysteresis exists for resonant modes driven to large amplitude. Mode coupling from lower-order resonances to higher-order modes has been found to be very weak, even for fairly large amplitude shape oscillations. Most of these results are in general agreement with predictions from recent analytical and numerical investigations.

Trinh, E. H.↗

NASA NTRS1995

The Dynamics of Ultrasonically Levitated Drops in an Electric Field

Ultrasonic and electrostatic leviation techniques have allowed the experimental investigation of the nonlinear oscillatory dynamics of free droplets with diameter between 0.1 and 0.4 cm. The measurement of the resonance frequencies of the first three normal modes of large amplitude shape oscillations in an electric field of varying magnitude has been carried out with and without surface charges for weakly conducting liquids in air. These oscillations of nonspherical levitated drops have been driven by either modulating the ultrasonic field or by using a time-varying electric field, and the free decay from the oscillatory state has been recorded. A decrease in the resonance frequency of the driven fundamental quadrupole mode has been measured for increasing oblate deformation in the absence of an electric field. Similarly, a decrease in this frequency has also been found for increasing DC electric field magnitude. A soft nonlinearity exists in the amplitude dependence of the resonant mode frequencies for freely decaying as well as ultrasonically and electrically driven uncharged drops. This decrease in resonance frequency is accentuated by the presence of free surface charge on the drop. Subharmonic resonance excitation has been observed for drops in a time-varying electric field, and hysteresis exists for resonant modes driven to large amplitude. Mode coupling from lower-order resonances to higher-order modes has been found to be very weak, even for fairly large amplitude shape oscillations. Most of these results are in general agreement with predictions from recent analytical and numerical investigations.

Ultrasonically↗

DOE OSTI2025

Global optimization of harmonic oscillator basis in covariant density functional theory

The present investigation focuses on the improvement of the accuracy of the description of binding energies within moderately sized fermionic basis. Using the solutions corresponding to infinite fermionic basis it was shown that in the case of meson exchange (ME) covariant energy density functionals (CEDFs) the global accuracy of the description of binding energies in the finite $N_F$ = 16 - 20 bases can be drastically (by a factor ranging from ~3 up to ~9 dependent on the functional and $N_F$) improved by a global optimization of oscillator frequency of the basis. This is a consequence of the unique feature of the ME functionals in which with increasing fermionic basis size fermionic and mesonic energies approach the exact (infinite basis) solution from above and below, respectively. As a consequence, an optimal oscillator frequency $\hbar\omega_0$ of the basis can be defined which provides an accurate reproduction of exact total binding energies by the ones calculated in truncated basis. This leads to a very high accuracy of the calculations in moderately sized $N_F=20$ basis when mass dependent oscillator frequency is used: global rms differences $\delta B_{rms}$ between the binding energies calculated in infinite and truncated bases are only 0.025 MeV and 0.031 MeV for the NL5(Z) and DD-MEZ functionals, respectively. Optimized values of the oscillator frequency $\hbar\omega_0$ are provided for three major classes of CEDFs, i.e. for density dependent meson exchange functionals, nonlinear meson exchange ones and point coupling functionals.

Binding energy & masses↗