Formulas for the Determination of the Material Damping of a Cylindrical Shell by a Decaying Free Vibration. Appendix: Approximation Formulas for Bessel-and Hankel-Functions

摘要

Formulas are given to determine the structural damping of a thin cylindrical shell by a decaying free vibration in still air. The material damping is assumed to be of the viscous type. To account for the elastic forces the linearized Timoshenko equations and Reissner's shallow shell equations were used. To account for the acoustic pressure due to the surrounding air the acoustic pressure derived for a vibrating cylindrical shell of infinite length was employed. The trapezoidal rule is applied to the integral representations of Bessel and Hankel functions. In this way approximation formulas for these functions are obtained. (Author)