Mode Count and Modal Density of Isotropic Circular Cylindrical Shells Using a Modified Wavenumber Space Integration Method

Abstract

A new method based on the wavenumber space integration algorithm is proposed in order to obtain mode count and modal density of circular cylindrical shells. Instead of the simplified equation of motion, the exact equation is applied in mode count calculations. Modal plots are changed significantly in the kspace when using the exact equation. Mode repetition in cylindrical shells is represented by additional mode count curves in the kspace. On the other hand, a novel technique is presented in order to implement boundary condition effects in mode count and modal density calculations. Integrating these two significant corrections, a modified wavenumber space integration (MWSI) method is developed. Mode count and modal densities of three shells with different geometrical and acoustical properties are obtained using the MWSI method and conventional WSI. Results are verified using the exact mode count calculations. Moreover, effects of geometrical properties are studied on mode count plots in the kspace. Modal densities are obtained for cylindrical shells of different lengths, radii, and thicknesses. Finally, modal densities of cylindrical shells are compared to flat plates of the same size and boundary condition. Interesting results are obtained which will contribute in calculation of acoustic radiation efficiency and sound transmission in cylindrical shells.