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- W413707624 abstract "Sizing optimization of transversely vibrating shafts with respect to eigenfrequencies, and with constraints on the design variables, has been almost fully investigated in recent years - as far as Bernoulli-Euler’s equation of motion is concerned.In the present paper we apply Timoshenko’s equations, i.e. the effects of shear and rotational energy are taken into account in the calculation of the transverse vibration modes and frequencies of the shaft. This is done via a finite element formulation, and the sensitivity analysis of the transverse vibration frequencies is based on analytical differentation of the stiffness- and mass matrices. The computer program developed, provides the user with an option to suppress the Timoshenko effects, such that the analysis can be carried out within Bernoulli-Euler theory as weIl, and comparisons be madeWe also consider torsional vibrations of the shafts, and here the vibration modes and natural frequencies are computed by means of a finite difference approach. Again, the sensitivity analysis is carried out analyticaly.We formulate and solve different optimization problems by selecting objective functions and behavioral constraints from among the fundamental frequencies, higher order frequencies and differences between adjacent frequencies of the vibrational types considered. The cross-sectional area function of the shaft is used as the design variable, and the total volume of structural material is assumed to be given, along with some sizing constraints. The shafts considered may be equipped with non-structural disks and flexible supports.Several results are presented, and some notable differences between optimized Timoshenko and Bernoulli-Euler shafts will be deliviatedKeywordsDesign VariableUnconstrained OptimizationTorsional VibrationTransverse VibrationSlenderness RatioThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W413707624 created "2016-06-24" @default.
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- W413707624 date "1989-01-01" @default.
- W413707624 modified "2023-09-27" @default.
- W413707624 title "Multipurpose Optimization of Vibrating Timoshenko Shafts" @default.
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- W413707624 doi "https://doi.org/10.1007/978-3-642-83707-4_23" @default.
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