![]() ![]() ![]() Li, F.M., Kishimoto, K., Huang, W.H.: The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method. Furthermore, some interesting phenomena are found, e.g., the same even-order frequencies of different three-span beams are equal under specific disorder degree. The increase in the span number of the multi-span beams with equal spans leads to the decrease in the displacement amplitude and the period of the structures. It is observed that the displacement amplitude and the vibration period at the midpoint of the three-span Timoshenko beams are reduced when the disorder degree and the length–thickness ratio are reduced. The influences of the length–thickness ratio, the disorder degree and the span number on the free vibration of the structure are also analyzed. The numerical results demonstrate good agreement between the present results and those from the open literature and the ANSYS software. Hamilton’s principle is applied to establish the equation of motion of the structure, and the natural circular frequencies and the free vibration responses of the multi-span beams are obtained. In this paper, the multi-span Timoshenko beams are investigated, and the mode shapes of the beams are modified by the interpolation functions to model the vibration modes of the multi-span beams. Although some investigations on the vibration properties of multi-span beams have been conducted, studies on multi-span Timoshenko beams by using the assumed mode method have been relatively few. ![]()
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