Acoustic Analysis of Elliptical Cylindrical Mufflers

Anglický jazyk

Acoustic Analysis of Elliptical Cylindrical Mufflers

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O knihe

This monograph highlights a comprehensive account of the three-dimensional analysis and design of reactive (rigid-wall) elliptical cylindrical mufflers for automotive applications. A general solution of the Helmholtz equation in elliptical cylindrical co-ordinates is presented in terms of the Mathieu and modified Mathieu modal functions. This is followed by tabulation and analysis, for the first time, of the parametric zeros and the corresponding non-dimensional resonance frequencies of the transverse modes of a rigid-wall elliptical waveguide for a complete range of its aspect ratio. The modal shape patterns of the first few circumferential, radial and cross-modes are examined along with the significance of the associated pressure nodal lines in context with location of inlet/outlet ports. (Additionally, the Appendix tabulates the non-dimensional resonance frequencies of a clamped elliptical membrane for a complete range of aspect-ratio.)

A theoretical formulation is then outlined for characterizing single-inlet and single-outlet (SISO) elliptical cylindrical chamber mufflers with arbitrary location of ports, either on the end face or side surface. The ensuing chapters are devoted towards analyzing the Transmission Loss (TL) performance of different configurations, namely, (a) the straight-flow or flow-reversal mufflers having inlet ports on the opposite or same end face, respectively, (b) mufflers having an end/side-inlet and side/end-outlet as well as (c) mufflers having a side-inlet and a side-outlet. The analytical framework explains how to exploit the principle of suppression or excitation of certain transverse (evanescent) modes by locating the ports on pressure nodes of these modes towards achieving a broadband TL performance. On this basis, design guidelines are then formulated in terms of optimal port locations for the aforementioned configurations, in particular, for short straight-flow/flow-reversal elliptical end-chambers that yield a broadband attenuation, a practically useful outcome for an automotive muffler designer. Furthermore, the validity of the one-dimensional transverse plane wave theory in the low-frequency range for short chambers is explained by observing the first few transverse mode shapes and through the three-dimensional Green's function's formulation. Some directions for future work are also indicated towards the end.

In summary, this monograph is a one-stop solution for a practicing automotive engineer designing mufflers, applied mathematicians studying acoustic wave propagation in elliptical geometries, and also for students of engineering acoustics.