{"title":"Did S. P. Timoshenko and P. Ehrenfest Overestimate the Importance of the Fourth-Order Time Derivative in Their Beam Theory?","authors":"I. Elishakoff","doi":"10.1115/1.4055975","DOIUrl":null,"url":null,"abstract":"\n In this study, we investigate the importance of the fourth-order time derivative that appears in the equations derived by Jacques Antoine Charles Bresse in 1859, as well as in equations that were derived by Stephen Prokofievich Timoshenko and Paul Ehrenfest during years 1912-1913 and reported by Timoshenko in the 1916 book on theory of elasticity in the Russian language and then in two papers dated 1920 and 1921, in English. The first part of the study demonstrates that Timoshenko and Ehrenfest did not overestimate the importance of the fourth-order derivative term in their equations. The second part deals with the debate on the so called “second spectrum” attendant in original set of equations. It is shown that in the truncated Timoshenko-Ehrenfest equations--which is asymptotically consistent with elasticity theory—“the second spectrum” issue does not arise. Thus, two parts of this study are intricately interrelated with each other.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Vibration and Acoustics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4055975","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this study, we investigate the importance of the fourth-order time derivative that appears in the equations derived by Jacques Antoine Charles Bresse in 1859, as well as in equations that were derived by Stephen Prokofievich Timoshenko and Paul Ehrenfest during years 1912-1913 and reported by Timoshenko in the 1916 book on theory of elasticity in the Russian language and then in two papers dated 1920 and 1921, in English. The first part of the study demonstrates that Timoshenko and Ehrenfest did not overestimate the importance of the fourth-order derivative term in their equations. The second part deals with the debate on the so called “second spectrum” attendant in original set of equations. It is shown that in the truncated Timoshenko-Ehrenfest equations--which is asymptotically consistent with elasticity theory—“the second spectrum” issue does not arise. Thus, two parts of this study are intricately interrelated with each other.
S. P. Timoshenko和P. Ehrenfest在他们的光束理论中是否高估了四阶时间导数的重要性?
在本研究中，我们研究了出现在Jacques Antoine Charles Bresse于1859年推导的方程中的四阶时间导数的重要性，以及Stephen Prokofievich Timoshenko和Paul Ehrenfest在1912-1913年间推导的方程，这些方程由Timoshenko在1916年的俄语弹性理论书中报告，然后在1920年和1921年的两篇英文论文中报告。研究的第一部分表明Timoshenko和Ehrenfest并没有高估四阶导数项在他们的方程中的重要性。第二部分讨论了关于原方程组中所谓“第二谱”的争论。结果表明，在截断的Timoshenko-Ehrenfest方程中(与弹性理论渐近一致)，不会出现“第二谱”问题。因此，本研究的两个部分是错综复杂地相互关联的。
期刊介绍：
The Journal of Vibration and Acoustics is sponsored jointly by the Design Engineering and the Noise Control and Acoustics Divisions of ASME. The Journal is the premier international venue for publication of original research concerning mechanical vibration and sound. Our mission is to serve researchers and practitioners who seek cutting-edge theories and computational and experimental methods that advance these fields. Our published studies reveal how mechanical vibration and sound impact the design and performance of engineered devices and structures and how to control their negative influences.
Vibration of continuous and discrete dynamical systems; Linear and nonlinear vibrations; Random vibrations; Wave propagation; Modal analysis; Mechanical signature analysis; Structural dynamics and control; Vibration energy harvesting; Vibration suppression; Vibration isolation; Passive and active damping; Machinery dynamics; Rotor dynamics; Acoustic emission; Noise control; Machinery noise; Structural acoustics; Fluid-structure interaction; Aeroelasticity; Flow-induced vibration and noise.
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