Abstract
The effect of kinematical non-linearities on the transverse vibration modes of a damped streched string is investigated using the asymptotic method of Krylov, Bogoliubov and Mitropolskii. It is shown that for times which are small compared with the decay time, the natural frequencies are increased by a term which is proportional to the square of the amplitude of vibration. The nature of this term is investigated in detail for a particular set of boundary conditions at the ends of the string.
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