This work presents a new strategy in design optimization of nonlinear vibration absorbers with continuous and discontinuous motions. A cluster-based harmonic balance aided optimization technique using force balance or energy balance as the basis is generalized and adapted for nonlinear systems. It is found that optimal design parameters form a cluster in the parameter space and points from the parameter space inside the cluster satisfies design considerations. One of the main disadvantages of using existing optimization methods in nonlinear systems is that the parameter regimes, which provide periodic solutions, are not known beforehand, so one has to first do bifurcation studies to arrive at periodic regimes and optimization has to be conducted in the range. Proposed method combines these two steps as it converges to periodic clusters alone. Since the method admits only periodic solutions, occurrence of conditions such as chaos and quasi periodicity can be eliminated from the dynamics of the system. The proposed method can also be used to find the optimal parameters of both linear and nonlinear dynamical systems.

This work presents a novel cluster based optimization procedure for estimating parameter values that yield stable, periodic responses with desired amplitude in nonlinear vibrating systems. The parameter values obtained by conventional nonlinear optimization schemes, with minimization of amplitude as the objective, may not furnish periodic and stable responses. Moreover, global optimization strategies may converge to isolated optima that are sensitive to parametric perturbations. In practical engineering systems, unstable or isolated optimal orbits are not practically realizable. To overcome these limitations, the proposed method tries to converge to a cluster in the r-dimensional parameter space in which the design specifications including the specified optimality, periodicity, stability and robustness are satisfied. Thus, it eliminates the need for computationally expensive bifurcation studies to locate stable, periodic parameter regimes before optimization. The present method is based on a hybrid scheme which involves the algebraic form of the governing equations in screening phase and its differential form in the selection phase. The method is validated with Den Hartog's vibration absorbers and is then applied to vibration absorbers with material nonlinearity and asymmetric vibration isolators with geometric nonlinearity. In both the cases, the converged cluster is shown to yield stable, periodic responses satisfying the amplitude condition. Parametric perturbation studies are conducted on the cluster to illustrate its robustness.

No abstract