Vibration of a Shaft Passing through a Critical Speed : (3rd Report, Approximate Solutions II)

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概要

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• This problem has been studied on the assumption of a constant angular acceleration (Ω) taking account of the damping effect (D). The exact solution of this problem has been obtained by using error functions with complex variables but it is not suitable to understand characteristics of the transient vibration. In this paper, approximate solutions, which show the characteristics of the transient vibration in simple forms, are derived by using the series and the asymptotic expansion for the error functions. From this analysis it is found that when DΩ is larger than √<2>, the characteristics of the transient vibration is simillar to that of the steady vibration. When DΩ is smaller than unity, and if √<1-D^2>+(1/Ω)√<2-D^3Ω^2><τ(τ : nondimensional time) the approximate solution is written in the following form, e/X_G=√<π/2>(√</1-D^2>)exp(-Ω^2D(τ-√<1-D^2>cos(Ω^2√<1-D^2>τ-Ω^2/2+Ω^2D^2-π/4)+1/√<1/(τ^2-1)^2+(2Dτ)^2>cos(1/2Ω^2τ^2-β) where the first term represents a free vibration and the second term a forced vibration.

• 一般社団法人日本機械学会の論文

著者

• Yanabe Shigeo

  Tokyo Institute Of Technology

関連論文

• Vibration of a Shaft Passing through Several Critical Speeds
• Vibration of a Shaft Passing through a Critical Speed : 2nd Report, Approximate Equations
• Vibration of a Shaft Passing through a Critical Speed : (3rd Report, Approximate Solutions II)

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