A hybrid approach which combines the reduced sequential quadratic programing (SQP) method with the shooting method is proposed to search the worst resonance response of nonlinear systems. The shooting method is first employed to construct the nonlinear equality constraints for the constrained optimization problem. Then, the complex optimization problem is simplified and solved numerically by the reduced SQP method. By virtue of the coordinate basis decomposition scheme which exploits the gradients of nonlinear equality constraints, the nonlinear equality constraints are eliminated, resulting in a simple optimization problem subject to bound constraints. Moreover, the second-order correction (SOC) technique is adopted to overcome Maratos effect. The novelty of the approach described lies in the capability to efficiently handle nonlinear equality constraints. The effectiveness of the proposed algorithm is demonstrated by two benchmark examples seen in the literature.
The Reduced Space Shooting Method for Calculating the Peak Periodic Solutions of Nonlinear Systems
Beijing Institute of Technology,
Beijing 100081, China
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 20, 2017; final manuscript received February 18, 2018; published online April 12, 2018. Assoc. Editor: Brian Feeny.
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Liao, H., and Wu, W. (April 12, 2018). "The Reduced Space Shooting Method for Calculating the Peak Periodic Solutions of Nonlinear Systems." ASME. J. Comput. Nonlinear Dynam. June 2018; 13(6): 061001. https://doi.org/10.1115/1.4039682
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