LATERAL VIBRATIONS OF TAPERED BARS

Publisher Website
Google Scholar
Abstract
The lateral vibration of a clamped-free bar is made the subject of the investigation in continuation of the author's article on vibrations of turbine blades, by taking the cross section and the moment of inertia to vary in a linear relation with the distance from a certain origin, and assuming the radius of gyration to be constant as in the previous note. First Rayleigh's method of an assumed type has been applied to find the frequency of the gravest mode of vibration, and then the smallest characteristic constant of an integral equation has been approximately calculated for the same end. The former method gives as is well known an upper limit to the frequency, while it is shown that a lower limit may be found by the latter method. On comparing these results with the root found by solving the boundary problem in the usual way, the lower limit is rather in good agreement with the true value, the error being 1.5% in the uniform bar, and 3.2% in the bar with a pointed tip. Lastly, the lateral vibration of a flexible bar in rotation has been considered by Rayleigh's method. The result may be combined with the frequency of the elastic bar in rest by Lamb-Southwell's method to find the approximate value of the frequency in rotation.

This publication has 0 references indexed in Scilit: