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A method of design against vibration resonance of beams and shafts. (English) Zbl 0569.49009
We consider problems of designing vibrating beams or rotating shafts to obtain as large gaps as possible in the spectra of natural frequencies or critical speeds in order to avoid resonance or whirling instability for a wide range of external excitation frequencies or service speeds. Governing equations for such design problems are derived by variational analysis of a bound formulation, and a numerical solution to an example problem is discussed.

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49R50 Variational methods for eigenvalues of operators (MSC2000)
74H45 Vibrations in dynamical problems in solid mechanics
49M29 Numerical methods involving duality
74P99 Optimization problems in solid mechanics
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References:
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