连通管内理想液柱振动微分方程两种推导的比较
A Comparison of Two Methods for Deriving the Differential Equation of Oscillation of an Ideal Liquid in Communica-tion Tube with Different End Cross Sections
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摘要: 对于连通管内理想液柱振动的同一问题,本文列举了两种求解方法;一种是迄今曾在文献中沿用已久的,另一种是本文提出的,曾把两个结果作了比较.本文认为,沿用已久的推导是不够妥当,本文推得的振动周期可以蜕出Isaac Newton、Johann Bernoulli和Danielis Bernoulli的相应振动周期公式.Abstract: Possibly not shorter than a half century, there has been ezisting a method for deriving the differential equation for the oscillation of an ideal liquid in communication tube with different end cross sections in the scientific literature, which,according to our opinion, is somewhat defective. With this paper we present another derivation in aiming to make possibly a convincing comparison. Our method leads to results from which the three different laws for vibration period setting up in the antiquity by Isaac Newton, Johann Bernoulli and Danielis Bernoulli can be degenerated outcomes.
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[1] Newton,Isaac,Plzilosophioe Naturalis Prineipia Mathenaatiea, London 1687. [2] Bernoulli,Johann,Commentarii Academiae Seientiarum Petropolitanae,1727. [3] de Lagrené,H,,Gours de Navigation intérieure,Paris, 1869. [4] Bernoulli,Danielis, Hydrody;amica (Argentorati,1738). [5] Liu Hsien-Chih(刘先志),Beitrag zur Kenntnis der Eigensch wingung einer idealen Flüssigkcit in kommunizierenden Rohren,ZAMP, IV,1953. [6] Wittenbauer, F.,Aufgaben aus der Teehnischen Mechanik,Ⅲ.Band, Julius Springer,Berlin 1921. [7] Liu Hsien-Chih(刘先志)Eigensch wingungen einer idealen Fliissigkeit in Rohrleitungen mit verschiedenen Endquerschnitten,Ing,-Archiv,1952. [8] Liu Hsien-Chih(刘先志),Über schwingungen einer idealen Fliissigkeit in ellipsen-and kreisbogéniörmigen,kommuniziercnden Röhren, Ing.Archiv,1952. [9] A Handbook on Torsional Vibration,B.I.C.E.I2.A,,Cambridge University Press, 1958. -
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