One dimensional wave propagation theory is used to investigate the forces, velocities and displacements in structures consisting of a series of elastic rods connected to rigid elements. The method is applied to the case of multi mass drive systems (torsional waves), colliding subsystems (longitudinal waves) or multi-storeyed buildings (shear waves). The problem is reduced to a system of ordinary differential equations with shifted arguments which must be solved in a certain sequence. A simple, effective and stable numerical procedure is proposed for solving the system of equations and some numerical results are presented.
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