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  • 1
    Electronic Resource
    Electronic Resource
    Some remarks on bounds to eigenvalues of Sturm-Liouville problems with discontinuous coefficients (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 647-657 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé On discute les bornes supérieures et inférieures des valeurs caractéristiques des problèmes de Sturm-Liouville avec des coefficients discontinus. Les approximations de Rayleigh-Ritz, basées sur le quotient de Rayleigh et le quotient jumelé de Rayleigh, sont utilisées pour obtenir les bornes supérieures des valeurs caractéristiques. Bien que les études antérieures aient indiqué que ces approximations donnent des résultats médiocres quand les coefficients ont de grandes discontinuités, on démontre dans cet article par des exemples numériques qu'on peut réaliser le même degré de convergence que pour les systèmes á coefficients continuous, pourvu que les fonctions d'essai admises aient des sauts arbitraires dans leurs dérivées á travers les points où les coefficients subissent des discontinuités. De nouvelles bornes inférieures sont déterminées sous une forme explicite en fonction des coefficients. On montre l'exactitude des nouveaux résultats par des exemples numériques.
    Notes: Abstract Upper and lower bounds on the eigenvalues of Sturm-Liouville problems with discontinuous coefficients are discussed. Rayleigh-Ritz approximations based both on Rayleigh's quotient and the dual Rayleigh quotient are used for obtaining upper bounds for the eigenvalues. Though previous studies have indicated that such approximations yield poor results when large discontinuities in the coefficients occur, it is shown in this paper by means of numerical examples that thesame rate of convergence can be achieved as for systems with continuous coefficients, provided the trial functions are allowed to have arbitrary jump discontinuities in their derivatives across the points where the coefficients suffer discontinuities. New explicit lower bounds in terms of the coefficients are also established. The accuracy of the new estimates is illustrated by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946976
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A simplified version of Gurtin's variational principles (1974)
    Springer
    Archive for rational mechanics and analysis 53 (1974), S. 131-149 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276580
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  • 3
    Electronic Resource
    Electronic Resource
    Exterior stable domain segmentation integral equation method for scattering problems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 777-792 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of an exterior domain segmentation method for the solution of two- or three-dimensional time-harmonic scattering problems in acoustic media. This method, based on a variational localized, symmetric, boundary integral equation formulation leads, upon discretization, to a sparse system of algebraic equations whose solution requires only O(N) multiplications, where N is the number of unknown nodal pressures on the scatterer surface. The new procedure is analogous to the one developed recently1 except that in the present formulation we avoid completely the use of the hypersingular operator, thereby reducing the computational complexity. Numerical experiments for a rigid circular cylindrical scatterer subjected to a plane incident wave serve to assess its accuracy for normalized wave numbers, ka, ranging from 0 to 30, both directly on the scatterer and in the far field, and to confirm that, contrary to standard boundary integral equation formulations, the present procedure is valid for critical frequencies.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370505
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  • 4
    Electronic Resource
    Electronic Resource
    Unified symmetric finite element and boundary integral variational coupling methods for linear fluid-structure interaction (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 8 (1992), S. 451-467 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article concerns the development of energy-based variational formulations and their corresponding finite element-boundary element Rayleigh-Ritz approximations for solving the time-harmonic vibration and scattering problem of an inhomogeneous penetrable fluid or solid object immersed in a compressible, inviscid, homogeneous fluid. The resulting coupled finite element and boundary integral methods (FEM-BEM) have the following attractive features: (1) Separate direct and complementary variational principles lead naturally to several alternative structure variable and fluid variable methodologies. (2) The solution in the exterior region is represented by a combined single- and double-layer potential which ensures the validity of the methods for all wave numbers; even though this representation introduces hypersingular integrals, for actual computations the hypersingular operator may be rewritten in terms of single-layer potentials, which can be integrated by standard techniques. (3) Since the discretized equations for the interior region and for the boundary are derived from the first variation of bilinear functionals the resulting algebraic systems of equations are always symmetric. In addition, the transition conditions across the interface are natural. This allows one to approximate the solutions within the interior and exterior regions independently, without imposing any boundary constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690080505
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  • 5
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    Seismic response of tied-back retaining walls (1991)
    Wiley
    Details
    Publication Date: 1991-01-01
    Print ISSN: 0098-8847
    Electronic ISSN: 1096-9845
    Topics: Architecture, Civil Engineering, Surveying
    Published by Wiley
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  • 6
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    Memory-efficient displacement-based internal friction for wave propagation simulation (2011)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2011-11-01
    Description: The characterization of anelastic losses due to material internal friction has become increasingly important in geophysical exploration and other seismological applications, as these losses greatly affect the amplitude and dispersion of seismic waves. Anelasticity is usually specified in terms of the material’s quality factor, Q. Different viscoelastic models have been used to represent Q as a function of frequency. Most of these models are defined in terms of stresses and strains as the primary variables. Thus, in three dimensions, a separate model needs to be associated with each of the six strain components. We introduce an internal friction model that uses, instead, displacements as primary variables. For a fiber, the proposed model consists of a set of three distinct elements in parallel with different relaxation mechanisms: namely, two elements that consist of a spring and a dashpot in series (Maxwell) and a third element that consists of a spring and a dashpot in parallel (Voigt). In addition to saving memory, this formulation is particularly suitable for finite-element schemes. The model exhibits an almost constant quality factor within the frequency range of interest, with a tolerance of 5% with respect to the target Q value, and provides a close approximation to the variation of the phase-velocity with frequency—as has been observed in empirical data. The extension of this model to 3D anelastic problems and its use in idealized cases, such as an infinite-space, a half-space, and a layered half-space, and the comparison of results with semi-analytical reference solutions obtained from theory and previous, similar studies, corroborates the validity of the proposed model for incorporating anelastic losses in wave propagation problems.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 7
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    A single theory for some quasi-static, supersonic, atomic, and tectonic scale applications of dislocations (2015)
    Elsevier
    Details
    Publication Date: 2015-11-01
    Print ISSN: 0022-5096
    Electronic ISSN: 1873-4782
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Elsevier
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  • 8
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    Some remarks on bounds to eigenvalues of Sturm-Liouville problems with discontinuous coefficients (1981)
    Springer
    Details
    Publication Date: 1981-01-01
    Print ISSN: 0044-2275
    Electronic ISSN: 1420-9039
    Topics: Mathematics , Physics
    Published by Springer
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  • 9
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    Regional seismic ground‐motion simulation and observation with engineering applications (2020)
    Wiley
    Details
    Publication Date: 2020-10-22
    Print ISSN: 0098-8847
    Electronic ISSN: 1096-9845
    Topics: Architecture, Civil Engineering, Surveying
    Published by Wiley
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  • 10
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    Simulation of site and topographic effects on ground motion in Los Alamos, NM mesas (2019)
    Oxford University Press
    Details
    Publication Date: 2019-12-12
    Description: SUMMARY Mesas, which consist of an elevated area of land with a flat top and steep cliffs at the sides, are one of the common geological formations present in the Los Alamos region. Previous research has shown that geological formations such as sedimentary canyons can amplify soil response during earthquakes. There have also been parametric studies to understand the response of an idealized and isolated mountain/canyon under inclined plane waves. In this study, a 2-D linear anelastic soil domain, with topography modelled after the Los Alamos region with many mesas and canyons, is considered to understand site-specific topographic effects in the presence of non-isolated topographical features. Various earthquake sources configurations ranging from point sources to finite faults with varying rupture length, dip angles and spatial slip distributions are considered. To isolate the effect of topography, three other soil domains—a homogeneous half-space, homogeneous half-space with mesas and canyons, and a computational domain with just the soil properties from the Los Alamos region on a flat soil domain is also considered. 2-D site-response analyses of these soil domains under earthquake excitation show that the free-field response of the soil can be amplified or de-amplified depending on the topography of the region and the location of the station relative to the fault. These studies also show that even relatively small mesas with height less than 100 m can significantly amplify the response (by a factor of 2 or more), which differ from the much smaller amplification factors (≤1.2) specified by standard building codes such as Eurocode-8 (2000) for topographical features with a similar slope. De-amplifications are also fairly common, especially close to the canyons. The results from this study agree qualitatively with those from the ambient vibration study conducted by Stolte et al. on a mesa from the Los Alamos region. Thus, such site-specific studies provide important insights into the variability of the topographic amplification factors within a region of interest. Such knowledge is important in the design of safety-related critical infrastructure located within that region.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Royal Astronomical Society.
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