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Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin’s maximum principle. (English) Zbl 1382.74098
Summary: Optimal configurations of circular bars under free torsional and longitudinal vibration are investigated using the Pontryagin’s maximum principle (PMP). The necessary optimality condition of PMP is analysed by considering the cross-sectional area of bars as control variable and by using Maier objective functional to control the final state of the objective functional. Optimal configurations associated to different orders of eigen frequencies, eigen vectors, and specific boundary conditions are demonstrated. Their relations are also explained qualitatively. Numerical results show the equivalent about optimal configurations and eigen frequencies under specific boundary conditions.
##### MSC:
 74P10 Optimization of other properties in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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