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Elastic wave propagation in parallel: the Huygens' approach.

Javier Sabadell (2002)

Revista Matemática Complutense

The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...

Eliciting harmonics on strings

Steven J. Cox, Antoine Henrot (2008)

ESAIM: Control, Optimisation and Calculus of Variations

One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node π / q during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at π / q . The 'correct touch' is that b for which the modes, that do not vanish at π / q , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree q - 1 ....

Energy methods for curved composite beams with partial shear interaction

István Ecsedi, Ákos József Lengyel (2015)

Curved and Layered Structures

This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.

Energy of the harmonics in a vibrating string after the impact of a hammer

Franco Rampazzo (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota vengono usati alcuni risultati precedentemente ottenuti - v. [4] e [5] - riguardanti l'urto di un martelletto rigido e di una corda elastica. Da essi possono dedursi le condizioni della corda - deformazione e atto di moto - all'istante in cui essa rimane libera dall'influenza del martelletto. È dunque possibile determinare mediante l'analisi di Fourier, i valori delle energie delle varie armoniche, i quali, com'è ben noto, determinano il timbro del suono emesso dalla corda (timbro...

Entropy flux far from equilibrium in solids and in non viscous gases

M. S. Mongiovì, R. A. Peruzza (2004)

Bollettino dell'Unione Matematica Italiana

One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature T t h the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature θ the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some...

Epitaxially strained elastic films: the case of anisotropic surface energies

Marco Bonacini (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...

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