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A coordinated test and analysis program was conducted to determine whether a previously proposed, linear, analytical model could be adapted to simulate low speed impacts for vehicles with various combinations of energy absorbing bumpers (EAB). The types of bumper systems impacting one another in our program included, in various combinations; foam, piston and honeycomb systems. Impact speeds varied between 4.2 and 14.4 km/h (2.6 and 9.0 mph) and a total of 16 tests in 6 different combinations were conducted. The results of this study reveal that vehicle accelerations vary approximately linearly with impact velocity for a wide variety of bumper systems and that a linear mass-spring-damping model may be used to efficiently model each vehicle/bumper-system for low speed impacts.

This paper is written from the perspective of a participant and an observer of the development of “cyclic-symmetry” concepts as applied to structural mechanics problems over the past 25 years. The paper has four principal parts, namely: (i) a simple illustrative example, (ii) boundary conditions at the central axis, (iii) static and dynamic nonlinear behavior, and (iv) analyses with multiple central axes of symmetry. The simple illustrative example involves vibrations of a N-sided equilateral polygon, which permits a closed-form solution. Boundary conditions at the central axis (of symmetry) have been generally handled by an artifice heretofore, and the paper presents a correct formulation such as used previously for the vibration and buckling of shells of revolution. Most formulations have generally been linear in nature, and qualitative discussions of static and dynamic nonlinear behavior involving cyclic-symmetry are given herein.

The dynamic response of turbo-pumps has traditionally been modeled mathematically using electrical networks. A recently developed computer program is used herein to adjust the model parameters (L - inductance, R - resistance, C - capacitance, etc.) of the electrical network in an attempt to bring the analytical response of the network into closer agreement with newly-available experimental results. Results are presented for a fully-wetted (non-cavitating) test of a Space-Shuttle Turbo-Pump and a significant improvement in the dynamic model is achieved.