High Frequency Approximation for the Modal Acoustic Impedance Coefficients of a Circular Plate Located at the Boundary of the Three-Wall Corner Region

Abstract

The high frequency asymptotic formulas for the acoustic impedance modal coefficients of a clamped circular plate located at the boundary of the three-wall corner region have been obtained. The method of contour integral analysis, the series for the Bessel and Neumann functions and the stationary phase method have been used. Some sample modal coefficients of the acoustic resistance and reactance together with the absolute approximation error have been illustrated as the functions of a parameter proportional to the vibration frequency. The computational efficiency of the presented asymptotic formulas has been compared with the computational efficiency of the integral formulas. The cases, in which the asymptotic formulas allow to reduce the calculation time in comparison with the integral formulas, have been determined. The presented formulas can be used to decrease the computation time of the acoustics power radiated by a clamped circular plate located at the boundary of the three-wall corner region. Moreover, the sound pressure calculations can be performed much faster by using these formulas when the acoustic attenuation is included.

Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

“…The results were validated experimentally. Szemela (2013) developed rigorously the asymptotic formulas of the acoustic impedance modal coefficients of a clamped circular plate located at the boundary of the three-wall corner. Oberst, Lai, and Marburg (2013) presented guidelines for the numerical vibration and the acoustic analysis of brake squeal using models of simplified brake systems with the friction contact.…”