On the Oscillations of "Summed and Differential Types of Higher Order" under Parametric Excitation

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概要

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• In the vibratory systems of multiple degrees-of-freedom with natural frequencies p_i, p_j, etc. and under parametric excitation of frequency ω, unstable oscillations of summed and differential types of higher order with frequencies ω_i (≒p_i), ω_j (≒p_j) take place when sω (s=2,3,……) becomes nearly equal to a sum of or a difference in two natural frequencies p_i and p_j, i.e., sω≒p_i±p_j=p_<ij>. Any possibility of occurrence of the oscillations of summed and differential types with sth order does not exist until the small quantities of sth order, i.e., the terms of order ε^s are taken into account ; it follows there from that these oscillations do not appear until the sth approximation. Further, it is concluded that there is no unstable oscillation of differential type of higher order as well as the first order, and that the effects of damping on these oscillations are similar to those of the first order, that is, the existence of damping does not always reduce the width of unstable region.

• 一般社団法人日本機械学会の論文

著者

• Yamamoto Toshio

  Faculty Of Engineering Nagoya University

• Saito Akihiko

  Faculty Of Engineering Nagoya University

• Yamamoto Toshio

  Faculty Of Engineering Nagoya University.

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