Non-linear vibration of Timoshenko damaged beams by a new p-version finite element method

A new p-version finite element is suggested to deal with geometrically non-linear vibrations of damaged Timoshenko beams. The novelty of the p-element comes from the use of new displacement shape functions, which are function of the damage location and, therefore, provide for more efficient models, where accuracy is improved at lower computational cost. In numerical tests in the linear regime, coupling between cross sectional rotation and longitudinal vibrations is discovered, with longitudinal displacements suddenly changing direction at the damage location and with a peculiar change in the cross section rotation at the same place. Geometrically non-linear, forced vibrations are then investigated in the time domain using Newmark’s method and further couplings between displacement components are found.