Optimum Design of Systems Operating in Random Vibration Environment

Abstract A large class of systems operate in random vibration environment generated by a diverse range of sources, such as: acoustic pressure field due to jet noise; boundary layer turbulence; atmospheric turbulence; ground motion during earthquakes; ground induced vibration in vehicles; ocean waves etc. The random nature of excitation in such cases makes the probabilistic approach a realistic basis for design. In the formulation of the optimization problem, the system failure is specified in terms of (i) first excursion above a given level; (ii) fraction of time spent above a given level; and (iii) cumulative damage, as in fatigue or inelastic deformation. In addition, the optimization problem may also involve other behavior and side constraints, and constraints on eigenvalues. The present status of the optimum design of systems operating in random vibration environment is reviewed. The reduction of the optimization problem to a standard nonlinear programming problem is discussed and the present status of the approximations involved in this process is reviewed. Three examples are included to illustrate the application of present techniques.

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