Acoustic End-Correction in a Flow-Reversal End Chamber Muffler: A Semi-Analytical Approach

2016 ◽  
Vol 24 (02) ◽  
pp. 1650004 ◽  
Author(s):  
A. Mimani ◽  
M. L. Munjal
Keyword(s):  
Plane Wave ◽  
Analytical Approach ◽  
Transmission Loss ◽  
A Priori ◽  
Low Frequency ◽  
Wave Model ◽  
Flow Reversal ◽  
Axial Plane ◽  
Experimental Result ◽  
Analytical Technique

This work presents a semi-analytical technique based on the Green’s function and uniform-piston driven model to determine the end-correction length [Formula: see text] in an axially long flow-reversal end chamber muffler having an end-inlet and an end-outlet. The semi-analytical procedure is based on the 3D analytical uniform piston-driven model for obtaining the impedance [Z] matrix parameters and numerically evaluating the frequency [Formula: see text] at which the imaginary part of the cross-impedance parameter [Formula: see text] crosses the frequency axis at the first instance. The frequency [Formula: see text] corresponds to the low-frequency peak in the transmission loss (TL) spectrum of the axially long flow-reversal end-chamber muffler obtained a priori to its computation by considering the influence of higher order evanescent transverse modes. The effective chamber length (and thence, the end-correction length) in the low-frequency range are determined by using the expression for resonance frequency of a classical quarter-wave resonator. This method is employed to determine the end-correction in axially long elliptical cylindrical end chambers and circular cylindrical end chambers (with or without a rigid concentric circular pass-tube). The TL graph predicted by the 1D axial plane wave model (incorporating the end-correction length) is shown to be in an excellent agreement with that obtained by the 3D analytical approach and an experimental result (from literature) up to the low-frequency limit, thereby validating the semi-analytical technique. Parametric studies are conducted using the proposed semi-analytical method to investigate and qualitatively explain the effect of angular location and offset distance of the end ports and the pass-tube diameter on the end-correction length, thereby yielding important insights into the influence of transverse evanescent modes on dominant axial plane wave modes of the axially long end-chamber. Development of an empirical end-correction expression in a flow-reversal circular end-chamber with offset inlet and outlet ports is a practically useful contribution of this work.

scholarly journals Analytical and Numerical Investigations Applied to Study the Reflections and Transmissions of a Rectangular Breakwater Placed at the Bottom of a Wave Tank

Geosciences ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 430
Author(s):  
Mohammed Loukili ◽  
Denys Dutykh ◽  
Chioukh Nadjib ◽  
Dezhi Ning ◽  
Kamila Kotrasova
Keyword(s):  
Plane Wave ◽  
Numerical Method ◽  
Analytical Approach ◽  
Relative Length ◽  
Wave Model ◽  
Reflection And Transmission Coefficients ◽  
Singular Boundary ◽  
Computational Domain ◽  
Reflection And Transmission ◽  
Transmission Coefficients

The purpose of the work presented in this paper is to study the reflection and transmission coefficients resulting from the interactions of regular waves with a rectangular breakwater sited at the bottom of a tank. The present investigation is devoted to the analysis of the reflection and transmission coefficients within the framework of linearized potential flow theory using two methods, a numerical method based on the improved version of the meshless singular boundary method, and the analytical approach within the plane wave model. The numerical method is first validated by studying the accuracy of the numerical computations with respect to the number of boundary nodes and the location of the vertical boundaries of the computational domain, for different immersion ratios (h/d) and different relative lengths (w/d) of the obstacle. To assess the limitations of the analytical approach, a comparison analysis is carried out between the analytical and numerical results. To improve the calculations and the effectiveness of the analytical model, slight adjustments are made to the analytical procedure, which is termed here the corrected analytical plane wave model. Finally, the effects of the immersion ratio (h/d) and the relative length (w/d) of the obstacle on the reflection and transmission coefficients are computed using the three methods, and discussed for several wave and structural conditions.

Analytical approach of membrane-type acoustic metamaterial with ring masses

2018 ◽  
Vol 14 (5) ◽  
pp. 828-836 ◽  
Author(s):  
Hongyan Tian ◽  
Ding Tong ◽  
Yourui Tao
Keyword(s):  
Analytical Approach ◽  
Transmission Loss ◽  
Low Frequency ◽  
Ring Structure ◽  
Acoustic Metamaterials ◽  
Acoustic Response ◽  
Content Type ◽  
Frequency Regime ◽  
Geometrical Effects ◽  
Membrane Type

Purpose Membrane-type acoustic metamaterials (MAMs) recently have been emerged to display useful sound attenuation properties in a low-frequency regime. The purpose of this paper is to present an analytical approach to investigate the transmission loss (TL) of a square membrane-ring structure of MAM. The geometrical effects of ring mass on the TL peak and dip frequencies of the MAM are obtained and discussed. Design/methodology/approach In this paper, based on the wave propagation and vibration theory, considering the effects of ring mass and acoustic pressure on the membrane, an analytical model is presented to analyze acoustic response of MAM. Findings Multiple peak frequencies and wide bandwidth appear in the membrane-ring structure, and they can be tuned by changing the location or numbers of the ring mass on the membrane. It is a useful method for designing such type of metamaterial. Originality/value In this paper, an analytical method is presented to evaluate the effects of ring geometric on the TL performance of square membrane-type locally resonant metamaterial. It is proved that achieving broadband and multi-peak TL profile in a single cell can indeed happen by increasing additional ring mass. The TL and frequency bandwidth can be tuned by changing the location, adding numbers and varying mass distribution of the ring masses on the membrane.

An Analytical Model for the Interaction of Mass Inclusions in Heterogeneous (HG) Blankets

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
A. Wagner ◽  
M. E. Johnson ◽  
K. Idrisi ◽  
D. P. Bartylla
Keyword(s):  
Elastic Layer ◽  
Analytical Approach ◽  
Low Frequency ◽  
Control Device ◽  
Effective Stiffness ◽  
Special Focus ◽  
Dynamic Vibration Absorber ◽  
Low Frequencies ◽  
Dynamic Vibration ◽  
The Masses

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.

Mode Interactions and Sound Power Transmission Loss of Expansion Chambers

2006 ◽  
Vol 129 (2) ◽  
pp. 141-147 ◽  
Author(s):  
C. K. Lau ◽  
S. K. Tang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Wave ◽  
Industrial Application ◽  
Power Transmission ◽  
Transmission Loss ◽  
Wave Power ◽  
Sound Power ◽  
The Finite Element Method ◽  
Mode Interactions

The mode interactions and the sound transmission loss across the expansion chambers with and without tapered sections are studied by the finite element method in the present investigation. Results from chambers with symmetrical inlet and outlet suggest lower sound power transmission loss at frequencies below that of the first symmetrical transverse chamber mode when the tapered section angle is reduced. Weak sound power transmission loss is also observed for this chamber type at frequency higher than that of the first symmetrical duct mode. Numerous high and low sound power transmission loss regions are observed between these two eigenfrequencies. Higher plane wave power transmission loss can be found at smaller tapered section angle only if one of the chamber endings is not tapered. Such chamber bears important industrial application.

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