One-dimensional (longitudinal) dynamic analysis of an axisymmetric burst protection vessel

An analysis is made for the dynamic behaviour of systems in which the structural arrangement may change due to the opening and closing state of internal gaps. Thus, impacts can be initiated in a closed system as a result of transient deformations. The impact loadings are depending on the vibrations of a stucture; vibrations and impacts are in interaction. Based on the finite element method the mass of the system may be represented as a lumped mass or as continuously distributed masses (consistent). Linear-elastic behaviour is supposed, therefore the differential equations are solved in uncoupled form by modal analysis. The integration is based on a Runge-Kutta-procedure of fourth order. Moreover, the influence of prestressing without bonding on the behaviour of the gaps is taken into consideration. The suppositions for the analysis are 1) linear elastic material, 2) longitudinal vibrations only, the gaps can open or close only due to normal stresses (rod-elements), 3) the influence of transverse vibration can be simulated by beam-elements and used only for secondary impact investigations, 4) one-dimensional deformations. Systems with continuously distributed masses represent the real system better than lumped masses. Solutions by the continuous mass model are more accurate, the consistent eigenvalues are always greater than the exact values. The method of the frequency-dependent stiffness and mass matrices was not used because of the increasing numerical difficulties. (orig./HP)