AbstractThe problem of determining the limiting performance of vibrating systems under shock loading is solved by replacing portions of the system by control forces which can represent any design. For the class of problems treated here, the performance index and the constraints are linear combinations of system response variables such as displacements, velocities and accelerations. Furthermore, the equations of motion are linear, so that it is possible to formulate the optimization procedure as a linear programming problem. In expressing the performance index and the constraints as linear functions of the unknown control forces, a modal approach is used to simplify and improve previous treatments of this problem. In spite of these linearity requirements, the control forces are not required to be linear functions of the response variables.
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