Some Integrals Relating to the Vibration of a Cantilever Beam and Approximation for the Effect of Taper on Overtone Frequencies
- 1 May 1956
- journal article
- research article
- Published by Cambridge University Press (CUP) in Aeronautical Quarterly
- Vol. 7 (2) , 109-124
- https://doi.org/10.1017/s0001925900010179
Abstract
Summary In the investigation of approximate numerical values of overtone frequencies of a turbine blade it is desirable to know formulae for certain integrals of the modes of vibration of an ordinary cantilever beam. The first object of this paper is to obtain such formulae and to arrange them in tabulated form. By proceeding along the lines of the calculus of perturbations, these results may then be used to obtain new formulae which give second order approximations for the effects of uniform breadth and thickness tapers on the overtone frequencies. The theory gives good agreement with experiments for tapers which do not exceed about 0·5, which is present-day practice for turbine blading.Keywords
This publication has 4 references indexed in Scilit:
- On the lateral vibrations of bars of conical typeProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1922
- IX. The transverse vibrations of a rod of varying cross-sectionJournal of Computers in Education, 1913
- Mathematische Theorie der transversalen Schwingungen eines Stabes von veränderlichem QuerschnittAnnalen der Physik, 1888
- Ueber die Transversalschwingungen eines Stabes von veränderlichem QuerschnittAnnalen der Physik, 1880