Discrete Singular Convolution Method for Acoustic Transmission Lines
- PDF / 1,025,401 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 62 Downloads / 210 Views
ORIGINAL PAPER
Discrete Singular Convolution Method for Acoustic Transmission Lines M. Kara1,2 · A. Seçgin2 · T. Baygün2 Received: 8 January 2020 / Accepted: 19 March 2020 © Australian Acoustical Society 2020
Abstract Discrete singular convolution (DSC) algorithm is an accurate dynamic analysis method for single structures. However, vibration analysis of connected structures via the DSC method is limited to step beams and plates. This paper extends the applicability of the DSC method in handling acoustic transmission lines composed of several duct elements with different diameter ratios. Connections of elements are handled by setting up continuity equations at geometric discontinuities. Conformity of DSC equations at these connections is carried out using Taylor series expansion. In this study, natural frequencies, mode shapes and power transmission coefficients of acoustic transmission lines are performed to test the proposed DSC implementation. Power transmission coefficients are obtained through the two-load method using the data provided by the DSC approach. The results are compared with finite element method and analytical solutions (if applicable), and the analytical transfer matrix method is also used for validating the power transmission coefficients. This paper shows that the DSC method is accurate and reliable, and so applicable for acoustic transmission line analysis. Keywords Discrete singular convolution · Taylor series expansion · Muffler · Acoustic transmission lines · Power transmission coefficient · Acoustic modes
1 Introduction Noise control is a challenging issue for a wide range of industrial products such as automobiles, heating and ventilation systems, airplanes, etc. Acoustic transmission lines composed of connections of several duct elements with different diameters are the simplest acoustic filters. They are commonly used in noise reduction studies in different ways and combinations. Analyses of these systems are generally performed by the finite element method (FEM) [1], boundary element method [2, 3], analytical or experimental transfer matrix method [4, 5]. Although these methods are very successful, more efficient numerical methodologies with regard to memory and solution time are still being investigated. Discrete singular convolution (DSC) is an accurate solver for partial differential equations in a physical discrete
B
M. Kara [email protected] A. Seçgin [email protected]
1
Department of Mechanical Engineering, Bolu Abant ˙Izzet Baysal University, Bolu, Turkey
2
Department of Mechanical Engineering, Dokuz Eylül University, ˙Izmir, Turkey
domain. The DSC algorithm has been applied to different mathematical, physical and engineering problems. Wei and his colleagues performed analyses of strings, bars, rods and atomic structures [6], uncompressible fluids [7, 8], bending beams [9], bending plates with common, mixed and non-uniform boundary conditions [10, 11] and internal supports [12, 13], high frequency vibration analysis of bending plates [14] and solution of t
Data Loading...
