关于非均质变截面弹性直杆的纵向自主振动
Longitudinal Free Vibration of an Elastic Non-uniform Strut
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摘要: 本文以集合木制螺旋桨作为启示的出发点,从而想使弹性直杆振动问题能初步臻于一个比较更一般的处理.文中把弹性模量、截面面积和单位杆长的质量施以依指数函数变化的规律之后,推出了一个通解,其中三个参数看为影响非均质变截面弹性直杆纵向自主振动频率的主要因素.Abstract: The aim of this paper is to give a more or less general treatment of vibration of elastic non-uniform strut,such as composite wooden screw-propeller.In this paper,elastic modulus,cross-sectional area,and mass per unit length are considered to be of exponential functions of longitudinal coordinates,A general solution is obtained together with these three para meters,which are fou nd to be the main factors closely related to the frequencies of free vibration of such an elastic-non-uniform strut.
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[1] Melan,E,and Parkus,H.,Wärmespannungen infolge Stationärer Temperaturfelder,Springer-Verlag,Wien(1953),p.106. [2] Rainville,E.D.,Intermediate Course in Differential Equations,John Wiley & Sons,London(1951). [3] 刘先志,推算楔形直杆纵振与扭振自主频率的一个方法.中国科学.1977年.第6期. [4] Liu Hsien-chih(刘先志),A New Method for Calculating Longitudinal and Torsional natural Vibration Frequencies of wedge-shaped straight Bars,SCIENTIA SINICA.No.6.(1977). -
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