This review article gives a historical perspective of the achievements in the theory and methods of optimization of isolation systems and outlines the most important results, including some practical applications. The effectiveness of shock isolation is reviewed and the fact that in some cases the utilization of isolators does not lead to a reduction in the force transmitted to the body to be protected is discussed. Mathematical formulations of basic problems of optimization of shock isolation systems are surveyed, including those for the case where the external disturbance is not precisely prescribed. Particular attention is given to the limiting performance analysis aimed at the establishment of an absolute optimum of the response of the system, irrespective of its design and engineering implementation. A significant portion of this paper is devoted to the basic achievements in the theory of shock isolation of systems with one degree of freedom. Analytical solutions for such systems are reviewed in detail. Various computational techniques are outlined and compared. Promising potential directions of further developments are discussed. An extensive bibliography of relevant publications is provided. Included in this review are numerous publications from the former Soviet Union which heretofore have not received much exposure elsewhere. This review article contains 234 references.

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