One of the major divisions in the mathematical modelling of a tubular structure is to include the effect of the transverse shear stress and rotary inertia in vibration of members. In recent years, both researchers and practising engineers have recognised the efficiency of the spectral approach for solving a large vibrating structure. Most structures can be analysed and design by using the conventional finite element method. However, ill order to guarantee stability and accuracy of the solution, the number of elements used to model the structure may be very large indeed; more precisely, accurate result can be obtained after a substantial computational efforts. "Ibe purpose of this paper is to compare the results of the spectrally formulated finite element method for the Timoshenko theory with that derived from the conventional finite element method for a tubular structure. Using a computer program, the proposed formulation has been extended to derive the dynamic response of a tubular structure under a impact load.
It is well known that the application of finite element methods have had a profound effect on the vibration analysis of tubular structures. TIle idea of increasing the stability and efficiency of the conventional finite element method has been a major reason behind much research work in past decades. Problems of vibration of tubular beams and structures have been considered by many authors, and special attention has been devoted to the Timoshenko beam model; Timoshenko being the first to demonstrate the importance of shear deformation in the dynamic of elastic beams. In recent years, there has been considerable effort, also, to apply the method of spectral analysis to the vibration of a tubular structure. Both researchers and practising engineers have recognised the efficiency of the spectral approach for solving a large vibrating structure.
