Examinando por Autor "Gomez, Juan"
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Ítem Analysis of the role of diffraction in topographic site effects using boundary element techniques(Springer. Seismological Society of China, 2013-10) Gomez, Juan; Jaramillo, Juan Diego; Restrepo, Dorian; Valencia, Camilo; Juan Gomez (jgomezc1@eafit.edu.co); Mecánica AplicadaThe role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.Ítem Analytic approximation to the scattering of antiplane shear waves by free surfaces of arbitrary shape via superposition of incident, reflected and diffracted rays(OXFORD UNIV PRESS, 2013-03-01) Jaramillo, Juan; Gomez, Juan; Externo - Escuela - Ciencias; Vergara, Juan; Mecánica AplicadaThe scattering induced by surface topographies of arbitrary shapes, submitted to horizontally polarized shear waves (SH) is studied analytically. In particular, we propose an analysis technique based on a representation of the scattered field like the superposition of incident, reflected and diffracted rays. The diffraction contribution is the result of the interaction of the incident and reflectedwaves, with the geometric singularities present in the surface topography. This splitting of the solution into different terms, makes the difference between our method and alternative numerical/analytical approaches, where the complete field is described by a single term. The contribution from the incident and reflected fields is considered using standard techniques, while the diffracted field is obtained using the idea of a ray as was introduced by the geometrical theory of diffraction. Our final solution however, is an approximation in the sense that, surface-diffracted rays are neglected while we retain the contribution from corner-diffracted rays and its further diffraction. These surface rays are only present when the problem has smooth boundaries combined with shadow zones, which is far from being the typical scenario in far-field earthquake engineering. The proposed technique was tested in the study of a combined hill-canyon topography and the results were compared with those of a boundary element algorithm. After considering only secondary sources of diffraction, a difference of 0.09 per cent (with respect to the incident field amplitude) was observed. The proposed analysis technique can be used in the interpretation of numerical and experimental results and in the preliminary prediction of the response in complex topographies. © The Authors 2012. Published by Oxford University Press on behalf of The Royal Astronomical Society.Ítem Construction of rational models for topographic effects and size-conditioned-response-spectra(Elsevier Ltd, 2021-01-01) Vergara, Juan; Sierra C.; Mario Saenz; Jaramillo, Juan; Gomez, Juan; Mecánica AplicadaWe used the decay-with-distance effect of diffracted waves generated from the interaction of a plane wave with a geometric singularity, to establish the connection between the spectral response of a topographic profile and the minimum required sizeÍtem A Superposition Based Diffraction Technique to Study Site Effects in Earthquake Engineering(Hindawi Publishing Corporation, 2016-01-01) Gomez, Juan; Jaramillo, Juan; Mario Saenz; Vergara, Juan; Mecánica AplicadaA method to study the response of surface topographies submitted to incident SH waves is presented. The method is based on the superposition of diffracted sources described in Jaramillo et al. (2013). Since the technique proceeds in the frequency domain in terms of the superposition of incident, reflected, and diffracted waves, it has been termed like a superposition based diffraction approach. The final solution resulting from the superposition approach takes the form of a series of infinite terms, where each term corresponds to diffractions of increasing order and of decreasing amplitude generated by the interactions between the geometric singularities of the scatterer. A detailed, step-by-step algorithm to apply the method is presented with regard to the simple problem of scattering by a V-shaped canyon. In order to show the accuracy of the method we compare our time and frequency domain results with those obtained from a direct Green's function approach. We show that fast solutions with an error of the order of 6.0% are obtained.Ítem Variational principles and finite element Bloch analysis in couple stress elastodynamics(Elsevier, 2021-06-16) Guarín-Zapata, Nicolás; Gomez, Juan; Hadjesfandiari, Ali Reza; Dargush, Gary F.; Universidad EAFIT; Central Connecticut State University; University at Buffalo; Universidad EAFIT. Escuela de Ingeniería. Grupo de Investigación Mecánica AplicadaWe address the numerical simulation of periodic solids (phononic crystals) within the framework of couple stress elasticity. The additional terms in the elastic potential energy lead to dispersive behavior in shear waves, even in the absence of material periodicity. To study the bulk waves in these materials, we establish an action principle in the frequency domain and present a finite element formulation for the wave propagation problem related to couple stress theory subject to an extended set of Bloch-periodic boundary conditions. A major difference from the traditional finite element formulation for phononic crystals is the appearance of higher-order derivatives. We solve this problem with the use of a Lagrange-multiplier approach. After presenting the variational principle and general finite element treatment, we particularize it to the problem of finding dispersion relations in elastic bodies with periodic material properties. The resulting implementation is used to determine the dispersion curves for homogeneous and porous couple stress solids, in which the latter is found to exhibit an interesting bandgap structure