A new technique is proposed for the optimum design of suspension systems for rotating shafts. In this approach the conventional method of trial and error search for optimum parameter values for a prescribed design configuration has been replaced by an efficient two-stage procedure. In the first stage a generic force is substituted for the suspension system to be designed and the absolute optimum (or limiting) performance characteristics of the shaft are computed. In the second stage, using a chosen suspension system configuration, parameter identification techniques are applied to find the design parameters so that the suspension system will respond as close as possible to the absolute optimal performance. In this approach the repetitive shaft analyses required in the conventional search techniques are avoided. Hence, the new technique is relatively efficient computationally and is suitable for large systems. Both linear and nonlinear suspension systems can be designed. A simple Jeffcott rotor is used to demonstrate the new technique.

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A computational capability for the evaluation of the limiting performance of transient dynamic systems is described. This capability permits the peak response (acceleration, force, displacement, or stress) of a system to be computed if portions of the system are optimally controlled or isolated. Thus, the worst occurrence to a human or vehicle can be determined under prescribed impact conditions if restraints such as seat belts or bumpers were to react in a time-optimal fashion and if response constraints on the system were not violated. No design configurations of the controllers or isolators are specified. Several specific applications of the capability to human and transportation systems are presented. In terms of design, this capability allows the designer to ascertain on the basis of response specifications alone the feasibility of a proposed design; in addition, he can measure and monitor his success during the design process. This is possible because the capability provides characteristics of the theoretically best, i.e., the limiting, design concept. Without the characteristics of the limiting design, the evaluation of proposed designs can be made only by performing a multitude of analyses for each candidate design. The problem is formulated in terms of linear programming. The controllers can be nonlinear, linear, active, or passive, while the remainder of the system must be linear. The linear programming formulation permits the use of off-the-shelf computer programs for the solution and, because of the capability of standard linear programs, means that multidegree-of-freedom, multi-isolator problems subjected to multiple, alternative sets of transient loading can be treated.