境界に横方向移動質量を持つ弦の非線形振動

概要

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Analytical results are presented for nonlinear vibrations of a stretched string connected with a laterally movable end mass at one end. Applying the modified Galerkin method to the basic equations, a set of ordinary differential equations with cubic nonlinearity is obtained. The steady-state response is determined by the harmonic balance method. Numerical calculations are carried out for the various values for the end mass to the string and the geometry of the string. It is found that if the mass of the end mass increases to greater than that of the string, the resonant response in the first mode of vibration can be treated as a linear vibration up to a sufficiently large amplitude. However, the resonant curves in the higher mode of vibration show responses with a strong nonlinearity within a small amplitude. The increment of the cross section area of the string also gives a strong nonlinearity to the response in every mode of vibration.
社団法人日本機械学会の論文
1989-06-25