Numerical analysis of the dynamics of rigid blocks subjected to support excitation

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps, which are not known in advance. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the stability and convergence properties of the numerical dynamic. The basic idea is to investigate how the error propagates in successive impacts by decomposing the numerical integration process of the overall system into a sequence of discretized perturbed problems.