Discrete singular convolution method for one-dimensional vibration and acoustics problems with impedance boundaries

Abstract

Discrete Singular Convolution (DSC) method has proved its accuracy in free and forced vibration analyses of structures with several simple boundary conditions. However, classical boundary implementation procedure of the DSC fails for the structures having more complex boundaries. This study improves the DSC to make it applicable for more complex boundaries such as structures having mechanical and acoustic impedance boundaries. The impedance boundary condition implementation is carried out by employing Taylor series expansion rather than using classical procedure. In this study, for vibration analyses, mechanical impedance is modelled via mass-damper-spring elements attached to the end of a bar. Natural frequencies and vibration frequency response to a harmonic excitation of the bar are obtained for mechanical impedance boundary condition. For acoustic analyses, several acoustic impedances are firstly applied to the end of a duct. In this analysis, sound pressure level distribution along the tube for two different frequencies is obtained. Then the frequency response of sound pressure to a monopole source of a duct with a glasswool material attached to both ends is also computed. Frequency dependent surface acoustic impedance of this glasswool material is experimentally determined by using impedance tube method. All results are verified by analytical (if available) and finite element computations. It is clearly shown that the introduced procedure is an accurate way in handling impedance boundaries for vibration and acoustic analysis via the DSC.