A support hyperplane method is presented to find the response set defined for a linear time-invariant vibration system with the excitations modeled by some convex sets. The method is based on analytical results characterizing the solutions to a class of optimization problems that determine support hyperplanes of the response set. The problem of deriving the convex responses of a multiple-degree-of-freedom vibration system is changed into finding a response set. The analytical expressions are obtained for some typical convex models, and a comparison of the results is given.
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