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Einfache Anwendung des Hamiltonschen Prinzips bei Körperschallproblemen

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Hamilton's principle can be used to find the equations of motion of complicated systems and to derive the method of finite elements. It also can be used to calculate the wave numbers and loss factors of many configurations without explicitly knowing the wave equations. This application is similar to Rayleigh's principle for finding resonance frequencies, because it also is based on the equality of kinetic and potential energy. As examples, plates with tension and with elastic bedding, as well as multilayer plates are investigated.

Zusammenfassung

Mit dem Hamiltonschen Prinzip kann man nicht nur Bewegungsgleichungen komplizierter Systeme herleiten und die Methode der Finiten Elemente begriinden, man kann sie auch dazu verwenden, ohne den Umweg über die Bewegungsdifferentialgleichung, die Wellenzahlen und Verlustfaktoren von einer Reihe von Systemen zu ermitteln. Es handelt sich dabei urn eine Anwendung, die dem Rayleighschen Prinzip zur Bestimmung von Resonanzfrequenzen sehr ähnlich ist, weil einfach kinetische und potentielle Energie gleichgesetzt werden. Als Beispiele werden Platten mit Vorspannung und Bettung sowie Mehrschichtplatten untersucht.

Sommaire

Le principe d'Hamilton peut servir à trouver les équations du mouvement pour des systèmes compliqués et à fonder la méthode des éléments finis. On peut aussi l'utiliser pour déterminer les nombres d'ondes et les facteurs de perte de certains systèmes mécaniques sans avoir besoin d'établir explicitement les équations différentielles de leurs mouvements. De telles applications sont analogues à celles du principe de Rayleigh pour déterminer les fréquences de résonance puisque tous deux se fondent sur l'égalité de l'énergie cinétique et de l'énergie potentielle. A titre d'exemples, on a étudié des plaques précontraintes et encastrées ainsi que des plaques multicouches.
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Document Type: Research Article

Publication date: November 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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