On the propagation constant of higher order modes in a cylindrical waveguide

Kergomard, Jean; Bruneau, Michel; Bruneau, Anne‐Marie; Herzog, Ph.

doi:10.1016/0022-460x(88)90408-7

Cited by 15 publications

(11 citation statements)

References 2 publications

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“…A detailed analysis of this topic, however, is not within the scope of the present study, see e.g. [78,54,79,53,80]. The displacement of the membrane is zero at the edges, i.e.…”

Section: Low Reduced Frequency Modelmentioning

confidence: 89%

Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

Beltman

1999

Journal of Sound and Vibration

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“…A detailed analysis of this topic, however, is not within the scope of the present study, see e.g. [78,54,79,53,80]. The displacement of the membrane is zero at the edges, i.e.…”

Section: Low Reduced Frequency Modelmentioning

confidence: 89%

Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

Beltman

1999

Journal of Sound and Vibration

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“…However, in the intermediate steps that then followed only boundary layer effects were taken into account ͑the mentioned dispersion relation was corrected in a subsequent paper, see Ref. 27; if, though, only the axisymmetric modes are considered, as is the case here, it remains unchanged͒. The expressions for the propagation parameters ⌫ n presented in Eqs.…”

Section: ͑165͒mentioning

confidence: 99%

On the calculation of the transmission line parameters for long tubes using the method of multiple scales

Scheichl

2004

The Journal of the Acoustical Society of America

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The present paper deals with the classical problem of linear sound propagation in tubes with isothermal walls. The perturbation technique of the method of multiple scales in combination with matched asymptotic expansions is applied to derive the first-order solutions and, in addition, the second-order solutions representing the correction due to boundary layer attenuation. The propagation length is assumed to be so large that in order to obtain asymptotic solutions which extend over the whole spatial range the first-order corrections to the classical attenuation rates of the different modes come into play as well. Starting with the case of the characteristic wavelength being large compared to the characteristic dimension of the duct, the analysis is then extended to the case where both of these quantities are of the same order of magnitude. Furthermore, the transmission line parameters and the transfer functions relating the sound pressures at the ends of the duct to the axial velocities are calculated.

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“…͑7͒ and ͑8͒ in Ref. 30, differ quite significantly from the expressions for the propagation parameters ⌫ nm presented in Eqs. ͑80͒ and ͑A1͒.…”

Section: ͑80͒mentioning

confidence: 63%

“…͑80͒ is given in the Appendix and can be compared with results given in the literature: Kergomard et al 30 calculated the propagation parameters for the higher order modes, starting from a generalized dispersion equation ͑see also Refs. 8 and 31͒.…”

Section: ͑80͒mentioning

confidence: 98%

Linear and nonlinear propagation of higher order modes in hard-walled circular ducts containing a real gas

Scheichl

2005

The Journal of the Acoustical Society of America

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This paper deals with the linear and nonlinear propagation of sound waves through a real gas contained in a circular tube with rigid, isothermal walls. Special emphasis is placed on the asymptotically correct treatment of the higher order modes and their interaction with the acoustic boundary layer. In the first part, a linear perturbation analysis is carried out to calculate the correction terms arising from the viscothermal damping mechanisms present in the system. In extension to previous work, the propagation length is assumed to be so large that the exponentially growing boundary layer effects do not only affect the second order terms of the sound pressure but also the leading order terms. The series expansions derived for the propagation parameters extend the results given in the literature with additional terms resulting from viscosity and heat conduction in the core region. The second part is concerned with the nonlinear modulation of a wave packet transmitted through a real gas. A damped nonlinear Schrödinger equation is derived and its solutions for positive as well as negative values of the nonlinearity parameter are studied. In particular, the case of wave propagation in ducts containing a so-called BZT fluid is discussed.

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On the propagation constant of higher order modes in a cylindrical waveguide

Cited by 15 publications

References 2 publications

Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

Viscothermal Wave Propagation Including Acousto-Elastic Interaction, Part I: Theory

On the calculation of the transmission line parameters for long tubes using the method of multiple scales

Linear and nonlinear propagation of higher order modes in hard-walled circular ducts containing a real gas

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