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Théorie de la corde pincée en approximation linéaire

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We present a calculation, in the linear approximation of a stiff vibrating string, whose ends are simply supported or damped. We calculate the initial shape under the action of a point plucking, using the methods of linear elasticity. We have studied the characteristic modes and movement without damping. Finally we consider, analytically, the effect on the movement and on the force of experimental damping studied previously. The model shows the dominant role in the spectrum of the dispersion relation, compared to the relatively small importance of the geometrical stiffness.


Es wird eine lineare Näherungsrechnung für eine schwingende steife Saite vorgestellt, deren Enden aufgestützt oder eingespannt sind. Mit den Methoden der linearen Elastizität wird die Anfangsform bei punktuellem Anzupfen berechnet. Des weiteren werden die Schwingungsmoden und die Bewegung der Saite ohne Dämpfung untersucht. Schließlich wird die Auswirkung experimentell bestimmter Dämpfungen auf die Bewegung und auf die Kraft beriicksichtigt. Das Modell zeigt die wichtige Rolle der Dispersionsbeziehung bezüglich des Spektrums und die geringe Bedeutung der geometrischen Steife.


Nous présentons un calcul en approximation linéaire d'une corde vibrante dotée de raideur, dont les extrémités sont sur appuis simples ou encastrées. Nous calculons la forme initiale sous Paction d'un pincement ponctuel, par les méthodes de l' élasticite lineaire. Nous étudions les modes propres et le mouvement sans amortissement. Enfin nous prenons en compte analytiquement l'effet, sur le mouvement et sur la force, des amortissements expérimentalement étudies antérieurement. Le modèle montre le rôle prépondérant de la relation de dispersion pour le spectre, et le peu d'importance de la raideur géométrique.
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Document Type: Research Article

Publication date: May 1, 1990

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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