Spectral element-based prediction of active power flow in Timoshenko beams

The analysis of standing waves, which correspond to the reactive part of the power in structures, is not a sufficient tool for studying structural vibration problems. Indeed, the active power component (structural intensity) has shown to be of great importance in studying damped structural vibration problems. One of the most common numerical discretization methods used in structural mechanics is the finite element method. Although this procedure has its advantages in solving dynamic problems, it also has disadvantages mainly when dealing with high frequency problems and large complex spatial structures due to the prohibitive computational cost. On the other hand, the spectral element method has the potential to overcome this kind of problem. In this paper, the formulation of the Timoshenko beam spectral element is reviewed and applied to the prediction of the structural intensity in beams. A structure of two connected beams is used. One of the beams has a higher internal dissipation factor. This factor is used to indicate damping effect and therefore causes structural power to flow through the structure. The total power flow through a cross-section of the beam is calculated and compared to the input power. The spectral element method is shown to be more suitable to model higher frequency propagation problems when compared to the finite element method.