- 作者: 翁通楹
- 作者服務機構: 國立臺灣大學機械工程學系
- 中文摘要: 就斷面可以S(x)=S0emx及S(x)=S0(1+x/a)m表示的斷面不均勻直桿求出它們的縱向振動的解析解,並繪出其反應曲線(擴大率與振動數的關係曲線)。將這些結果與原來所用的分段直桿的結果相比後指出下列三點;(1)對斷面連續變化的直桿或分段直桿,第一次共鳴發生時的振動數皆隨著面積比(S2/S1)的減少而增加。僅對分段直桿而言,面積比保持不變時,細部長度的增加可使第一次共鳴振動數增加,(2)斷面連續變化直桿較分段直桿容易控制擴大率的變化,(3)因分段直桿有應力集中及細部皺曲的可能,強度較差,由上述三點可知斷面連續變化的直桿較分段直桿為合適。
- 英文摘要: Analytical solutions of longitudinal vibration of two straight bars with the variable cross sections S(x)=S0emx and S(x)=S0(1+x/a)m are obtained, and the response curves in a number of cases are shown. By comparing the results with those of a two-stepped bar, it was found that: (1) the first resonance frequency increases as the ratio S2/S1 decreases for both the bar with the continually varying cross section and the stepped bar, and the frequency also increases as the length of the smaller part of the stepped bar increases if the area ratio is kept unchanged, (2) to control the magnification factor within certain limit values for a bar with the varying cross section is easier than for a stepped bar, (3) because of the absence of abrupt cross section change
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