This study presents a nonprobabilistic set theoretical approach to analyzing uncertainty in vehicle vibrations arising from motion along imperfectly known terrain. The uncertainty in the substrate is described by a set of allowed substrate profile functions. The analysis of the vehicle response consists in determining the range of variation of performance parameters, as the substrate profile varies over the set of allowed functions. This enables characterization of the uncertain but bounded motion of the vehicle as well as optimization of the vehicle design with respect to uncertainty in the substrate. Maximum acceleration during motion on an imperfectly known surface is determined and related to standard design guidelines for limiting exposure to vibrational acceleration. A method is developed for determining the greatest lower bound of the number of sign changes per second of the vibrational acceleration when moving over an irregular and incompletely specified substrate. Motion along uniformly bounded substrates is studied, as well as traversal of barriers.

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