A technique is presented, using mathematical programming methods, of determining the optimum values of the masses, spring and damping coefficients of a linear multi-degree-of-freedom shock isolation system. The problem posed is the one dimensional isolation of a mass from a shock of finite duration imposed by a supporting base. The work deals with the minimization of the maximum acceleration of the isolated mass subject to a constraint on the relative displcement between the mass and the base. In addition to the optimization of the M, C, and K coefficients, the problem of determing the optimum number of elements in the system (i.e., its topology) is also investigated. Discussion concerning this topic includes the question of uniqueness and absolute optimality of the solution.

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