等直弹性杆自由扭转电涡流比拟
Eddy Current Analogy of Torsion Problem
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摘要: 本文提出了测定弹性等截面直杆自由扭转剪应力和抗扭刚度的一种新的比拟理论和方法——电涡流比拟。在理论部分建立了电涡流和自由扭转的比拟关系。在实验部分依照比拟理论设计了试验装置和测量线路;并通过对某些具有解析解的截面形状进行了实际测量,所得实验数据验证了本理论的正确性;还对集肤效应和影响精度的一些主要因素进行了讨论。本文所得结果可以推广到其它类似的流场或者具有一定边界条件的泊松方程(或拉普拉斯方程)求解。Abstract: In as paper, an eddycurrent analogy and a brief sketch of required equipment are presented. Values oftorsional rigidity and shearing stresses of a prismatic bar under free torsion can be obtained experimentally to a high degree of accuracy in an instant with this equipment whether the cross-section is bounded bv a single boundary or multi-connected boundaries. The error is les than two per cent generally, as shown in Table 3. This new analogy can be used extensively to solve various physical problems expressed by Poisson's (or Laplace's) equation with constant boundary condition.
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[1] 钱伟长等,《弹性柱体的扭转理论》,科学出版社(1956). [2] 钱伟长、叶开沅,《弹性力学》,科学出版社(1980) [3] 荆广生.《弹性力学》.江苏工学院. [4] Timoshenko,S.P.and J.N.Goodier,Theory of Elasticity,Third Edition,McGraw-Hill Book Company(1970). [5] Grant,I.S.and W.R.Phillips,Electromagnetism,John Wiley and Sons Ltd.(1976). [6] Binns,K.J.and P.J.Lawrenson,Analysis and Computation of Electric and Magnetic Field Problems,2nd Edition,Pergemon Press(1973). [7] Kemmer,N.,Vector Analysis,Cambridge University Press(1977). -
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