AbstractThe transient extensional vibrations of a slender and uniform bar, which is clamped at one end and is subjected to an axial force at the other free end, are investigated by applying three methods: the Laplace transform method, the normal mode and Newmark β methods in conjunction with the finite element method (FEM); the errors caused by the spatial discretization of the FEM and the direct integration of the Newmark β method are studied and compared with those of the previous paper where the flexural vibrations of a cantilever beam were considered. The reason why the extensional vibration problem is investigated here is that the condition seems to be severe due to the closeness of adjacent natural frequencies, the larger values of natural frequencies and the smaller number of nodal variables of the FEM in comparison with those of the flexural vibration problem. The numerical results show that the errors in response of the extensional vibration problem are large. However, if one follows the criterion proposed in this paper, accurate response is obtainable by the Newmark β method, which requires less computer time than either of the other methods mentioned abo