The strongest rotating rod

The strongest rotating rod

By using the Rayleigh quotient, we present the variational formulation for the strongest rotating rod stable against buckling. This variational formulation is converted to fifth-order singular non-linear boundary value problem. The optimal shape and the critical rotating speed are determined with sp...

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Veröffentlicht in:International journal of non-linear mechanics 2005-06, Vol.40 (5), p.747-754
Hauptverfasser: Atanackovic, T.M., Braun, D.J.
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Sprache:eng
Schlagworte:
Optimal shape
Pontryagin's principle
Rotating rod
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creator Atanackovic, T.M.
Braun, D.J.
description By using the Rayleigh quotient, we present the variational formulation for the strongest rotating rod stable against buckling. This variational formulation is converted to fifth-order singular non-linear boundary value problem. The optimal shape and the critical rotating speed are determined with special numerical–analytical integration procedure. We found the explicit linear relation between the volume and the squared critical speed. Although, in general, the linear stability problem for the optimal rotating rod does not have purely discrete spectra, we show that in the present case, the critical speed is determined with lowest eigenvalue. This fact verifies our optimization strategy based on a linear spectral problem.
doi_str_mv 10.1016/j.ijnonlinmec.2004.09.002
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subjects Optimal shape
Pontryagin's principle
Rotating rod
title The strongest rotating rod
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