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1

2D tolerance and asymptotic models in elastodynamics of a thin-walled structure with dense system of ribs

Michalak B.

Archives of Civil and Mechanical Engineering

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2015

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Vol. 15, no. 2

449--455

EN

The object of analysis is a plane structure reinforced by a system of thin parallel-distributed ribs. It will be assumed that the number of the ribs is very large. The thickness of neighbouring ribs can smoothly change. The aim of contribution is to derive 2D-macroscopic mathematical models describing elastodynamic behaviour of the plate structure in plane-stress state. The consideration will be based on the tolerance averaging technique 0045 and 0050. The general results of the contribution will be illustrated by the analysis of the free vibrations of a structure under consideration.

2

Commonly used earthquake source models

Liu Wenlong, Liu Yucheng

Geologos

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2012

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Vol. 18, No. 3

197--209

EN

Several important earthquake source models that have been extensively used in seismological research and earthquake prediction are presented and discussed. A new fault source model is used to explain the earthquake focal mechanism solution and tectonic stress field, which play a crucial role in earthquake initiation and preparation. The elastodynamic-dislocation theory is demonstrated which provides the theoretical background of most earthquake source models. Important earthquake source models reviewed here include the double-force-couple point-source model, the circular-shear dislocation model, the finite moving-source model, the Brune model, and the spherical explosive source model.

3

Root finding method for problems of elastodynamics

Krushynska A.

Computer Assisted Mechanics and Engineering Sciences

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2010

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Vol. 17, no. 1

3-11

EN

This paper presents a simple and efficient method for finding complex roots of dispersion equations occurring in many problems of elastodynamics. The method is characterized by high accuracy in root finding and absence of restrictions on function representation. The essence of the method is explained geometrically; initial guesses are found as the solutions to the appropriate problems of elastostatics. Numerical solutions to dispersion equations are obtained for two elastic isotropic waveguides: a plate of infinite cross-section and a rod of rectangular cross-section. For an infinite plate, the calculated results are in full conformity with those obtained by Newton-Raphson and bisection methods. For a waveguide of rectangular cross-section, the earlier unsolved problem of finding complex roots of dispersion equations is solved by the proposed method.

4

Discrete and continuum models in elastodynamics of micro-periodic solids

Rychlewska J.

Vibrations in Physical Systems

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2004

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Vol. 21

319--322

EN

The aim of this paper is to propose a new alternative approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell, [1], and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. The proposed discrete model can be formulated on different levels of accuracy. Considerations are restricted to problems in which the typical wavelength of the macroscopic deformation pattern is sufficiently large when compared to the unit cell diameter By applying smoothing operation the continuum models are derived directly from the discrete ones. The general equations obtained in the models proposed here are applied in order to investigate dispersion phenomena in the wave propagation problems.