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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Waveform synthesis of surface waves in a laterally heterogeneous earth by the Gaussian beam method

The present investigation is concerned with an application of the Gaussian beam method to surface waves in the laterally heterogeneous earth. The employed method has been developed for ray tracing and synthesizing seismograms of surface waves in cases involving the laterally heterogeneous earth. The procedure is based on formulations derived by Yomogida (1985). Vertical structure of the wave field is represented by the eigenfunctions of normal mode theory, while lateral variation is expressed by the parabolic equation as in two-dimensional acoustic waves or elastic body waves. It is demonstrated that a large-amplitude change can result from a slight perturbation in the phase velocity model.

Yomogida, K.↗
NASA NTRS1986

A fourth order accurate finite difference scheme for the computation of elastic waves

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Bayliss, A.↗
NASA NTRS2020

Composite Piezoelectric Resonator 1D Modeling with Loss

Abstract – Maximizing the benefit of applying piezoelectric materials in composite structures, which are a mix of piezoelectric and elastic elements, requires analytical modeling. In this paper we describe two main classes of resonators and how to model using network equivalent including material losses. These include extensional devices where the layer areas are parallel to the direction of wave travel as found in a variety of thickness or length mode transducers (BC. Stress T1 = T2 at boundary) and transverse mode resonators (BC. Strain S1 = S2 at boundary) where the major layer area is perpendicular to the wave direction as is found in radial mode or length thickness mode composite resonators. In order to illustrate these models we will use Mason’s equivalent circuits with elastic, dielectric and piezoelectric loss. It is noted that in order to maintain consistency with the linear equations of piezoelectricity and the wave equation care is required when applying complex loss coefficients to the models. Although these techniques are applicable to other models we use Mason’s network equivalent circuit because it is intuitive for composite modeling due to the frequency independent turns ratio and the independence of the equations describing the elastic layers from the adjoining layer properties which aids in understanding the boundary conditions to impose on the layer boundaries. We will present network models for a variety of applications with loss and show how to calculate their impedance spectra, interface stress, strain velocity and displacement spectra.

Sherrit, Stewart↗
NASA NTRS2014

D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems

In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.

D-wave↗
NASA NTRS2005

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.

Qin, Zhanming↗
NASA NTRS1982

Noise transmission into semicylindrical enclosures through discretely stiffened curved panels

An analytical study of sound transmission into semicylindrical enclosures through discretely stiffened curved elastic panels is presented. The transmitted sound is estimated by solving the acoustic wave equation for the interior acoustic field, a Galerkin-like method being used. This solution is then coupled to the vibration of the stiffened panels. The response characteristics of these panels are determined by using a modal analysis where the modes are obtained by the finite element-strip method. Numerical results include spectra of the interior sound pressure due to white noise, turbulent boundary layer and propeller noise inputs.

Chang, M. T.↗
NASA NTRS1977

Impact on multilayered composite plates

Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.

Kim, B. S.↗
NASA NTRS1979

Dynamics of film

The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.

Zak, M.↗
NASA NTRS2001

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.↗
NASA NTRS1988

Approximate method for predicting the permanent set in a beam in vacuo and in water subject to a shock wave

An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions.

Stiehl, A. L.↗
NASA NTRS1977

Transient wave propagation in composite plates due to impact

Stress-wave propagation in a composite plate due to an impact has been examined using anisotropic elasticity theory. The plate is modelled as a number of identical anisotropic layers whose elastic moduli are given. Mindlin's (1959) approximate theory of plates is then applied to each layer to obtain a set of difference-differential equations of motion by using the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions these equations are solved for an arbitrary number of layers in the plate, and the transient propagation of a stress wave is calculated by means of a fast Fourier transform algorithm.

Sung Kim, B.↗
NASA NTRS1979

Acoustic plane waves normally incident on a clamped panel in a rectangular duct

The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.

Unz, H.↗
NASA NTRS1989

Wave propagation in a thin cylinder that includes point masses

The propagation of elastic waves of the type induced by impact are studied for a special class of cylinders. In this class are thin finite cylinders, for which Mindlin's equations are appropriate, on which point masses are attached. An approximation is derived valid for frequencies below cutoff of the lowest shear mode. An eigenfunction expansion is used to compute the transient response of the coupled system.

El-Raheb, Michael↗
NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗