Vibration behaviors of a box-type structure built up by plates and energy transmission through the structure

Abstract

The vibration behaviors of a box-type built-up structure and energy transmission through the structure are investigated analytically. The modeling of the structure is developed by employing the improved Fourier series method and treating the structure as four elastically coupled rectangular plates. The general coupling and boundary conditions are accounted for using the artificial spring technique and can easily be obtained by assigning the springs with corresponding values. The exact double Fourier series solutions considering both the flexural and in-plane vibrations are obtained by using the Rayleigh–Ritz approach, which are validated by comparison with the Finite Element Method (FEM) results. Since the modification of any parameter in this analytical model from one case to another is as simple as modifying the material properties, and does not involve any change to the solution procedures, thus this will make a parametric study and further mechanism analysis easier compared to most existing procedures. Subsequently, special attention is focused on the energy transmission and mechanism of the box-type structure by structural intensity analysis. Numerical analyses cover several important parameters including symmetrical and non-symmetrical coupling conditions and the excitations, and three types of models, namely the rigidly, elastically and weakly coupled models are involved. The results of the power flow and structural intensity are presented to obtain a clear physical understanding of the physical mechanisms of energy transmission. It is shown that the energy transmission behaviors can be significantly influenced by the coupling conditions and location of the excitation as well as the excitation frequency. Some unexpected interesting phenomena on the energy transmission were revealed, especially for the non-symmetrical model, and the corresponding mechanisms were interpreted. This study provides new and interesting insights into the vibration behaviors and energy transmission of the class of built-up box-type structure.