円板における多モード形結合調波振動

概要

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Combination tones in a circular plate subjected to excitation having two harmonic components with frequencies Ω_1 and Ω_2 are investigated for the case in which Ω_1 and Ω_2 and one of the natural frequencies P_<ll'> of the plate satisfy m_1Ω_1+ m_2Ω_2≒NP<ll'> for integers m_1, m_2, and positive integers N. For theoretical analysis, the von Karman-type equation of motion of a circular plate is reduced to the modal equations using Galerkin's procedure. Then the modal equations are solved by the perturbation method of multiple scales. From the analysis, it is found that combination tones with frequencies (±2Ω_1+Ω_2), (2Ω_1-Ω_2) and (±Ω_1+2Ω_2), and subcombination tones with frequencies (±Ω_1+Ω_2)/2 can occur in multiple modes which exist in pairs for the natural frequency P_<ll'>. Numerical examples are given, and it is shown that the combination tones in multiple modes can take the form of a travelling wave.
1995-06-25