Vibrational energy flow models for out-of-plane waves in finite thin shell

In this paper, an approximate energy flow model for the out-of-plane vibration of a finite thin shell was developed. The derived energy governing equation for the model was expressed in terms of the time- and locally space-averaged far-field wave energy density which can be used as the main equation for the prediction of the out-of-plane structural vibration levels of the energy density and intensity in medium-to-high frequency ranges. The derived model can be applied to the vibration energy problems of a cylindrical shell, spherical shell and doubly-curved shell, whose radius of curvature in each direction is constant, regardless of the position, assuming that the in-plane motion is relatively small. To verify the results of the derived model, wave numbers were obtained using an energy flow analysis and classical analysis, such as the method using Donnell-Mushtari equations. For the case of various types of finite thin shell, the derived energy equations were applied. The results for the spatial distributions and levels of the energy density and intensity were compared with classical displacement solutions, according to the changes in the frequency and internal loss factor of the shell.