Periodic motions of vehicles on flexible guideways are explored as candidate “test” motions for optimization studies where it is necessary to compare large numbers of designs under equivalent conditions. Exact and approximate methods are developed for identifying initial conditions that lead to periodic motions of single vehicles or many equally spaced vehicles. Using exact equations, fundamental questions regarding the nature of these motions are addressed (existence, uniqueness, stability, etc.). Approximate equations are developed to reduce the computational burden of examining large numbers of designs. It is shown that the assumptions inherent in the approximate equations are valid provided that vertical accelerations of the vehicles are sufficiently small. This restriction is not considered serious because small vertical accelerations are required to satisfy ride comfort criteria. Two standard test motions are proposed for design evaluation, one for the single vehicle case and one for the multi-vehicle case. Numerical results showing peak vehicle acceleration and guideway response are presented for the single vehicle case.

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