M. S. Dorofeev

Lomonosov Moscow State University

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АВ

А. В. Шанин

Moscow State University

Oleg V. Motygin

Institute of Problems of Mechanical Engineering

Maria V. Perel

St Petersburg University

Peter G. Malischewsky

Friedrich Schiller University Jena

I. A. Shereshevskii

Institute for Physics of Microstructures

G. A. Maximov

Acoustic Institute named after NN Andreev

N. S. Vinogradov

Timiryazev Institute of Plant Physiology

A. A. Matskovskiy

Steklov Mathematical Institute

A. V. Permyakov

St Petersburg University

Franz Scherbaum

FZI Research Center for Information Technology

Cooperative Institutions

Russian Academy of Sciences

Lomonosov Moscow State University

St Petersburg University

N. I. Lobachevsky State University of Nizhny Novgorod

Moscow State University

Prokhorov General Physics Institute

Institute of Problems of Mechanical Engineering

Steklov Mathematical Institute

Friedrich Schiller University Jena

Schiller International University

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Wave modes in periodic systems of thin tubes

Days on Diffraction (2008)

А. В. Шанин M. S. Dorofeev

The problem of wave propagation in a periodic system of thin tubes is studied. The waves are described by the dispersion diagrams, i.e. by the dependencies of the propagation constants on the temporal frequency. The main question under consideration is how many modes can propagate in a particular system. The paper presents a method of finding the dispersion diagrams, and an inequality for the number of modes, linking the number of modes with the topological properties of the system.

Dispersion relation

Mode (computer interface)

Source

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Citations (1)

Resonances in a discrete system of variable length

Acoustical Physics (2009)

M. S. Dorofeev А. В. Шанин

Chain (unit)

Spectral composition

10.1134/s106377100903004x

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Citations (1)

Estimation of number of modes in periodic graphs

Waves in Random and Complex Media (2009)

M. S. Dorofeev А. В. Шанин

The problem of acoustic wave propagation in a one-periodic system of thin pipes is studied. A dispersion equation linking the time frequency ω with the propagation constant (quasimomentum) γ is derived. A particular question is studied, namely how many different values of γ can obey the dispersion equation for a fixed ω. A simple estimation of this amount is obtained in terms of the properties of the graph representing a single period of the system.

Constant (computer programming)

Propagation constant

Dispersion relation

10.1080/17455030902785519

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Citations (1)

Nonlinear Generation of Airborne Sound by Waves of Ultrasonic Frequencies

Acoustical Physics (2005)

N. S. Vinogradov M. S. Dorofeev А. И. Коробов S. G. Mikhailov O. V. Rudenko

Nonlinear acoustics

Sound wave

10.1134/1.1884489