文档介绍：Journal of Sound and <ibration (2001) 242(1), 103}124
doi:.3362, available online at
FINITE ELEMENT VIBRATION ANALYSIS OF ROTATING
TIMOSHENKO BEAMS
S. S. RAO
Department of Mechanical Engineering, ;niversity of Miami, Coral Gables, F¸ 33124-0624, ;..
AND
R. S. GUPTA
Department of Mechanical Engineering, Punjab Engineering College, Chandigarh 11, India
(Received 12 January 2000, and in ,nal form 13 September 2000)
The sti!ness and mass matrices of a rotating twisted and tapered beam element are
derived. The angle of twist, breadth and depth are assumed to vary linearly along the length
of beam. The e!ects of shear deformation and rotary inertia are also considered in deriving
the elemental matrices. The "rst four natural frequencies and mode shapes in
bending}bending mode are calculated for cantilever beams. The e!ects of twist, o!set, speed
of rotation and variation of depth and breadth taper ratios are studied.
( 2001 Academic Press
1. INTRODUCTION
Generally, turbomachine blades are idealized as tapered cantilever beams. In order to re"ne
the analysis the e!ects of pre-twist and rotation are also included. As the blades are short in
some of the designs and may vibrate in higher-frequency ranges, the e!ects of shear
deformation and rotary inertia may be of considerable magnitude. Various investigators in
the "eld of turbine-blade vibrations have solved the di!erential equations of motion, by
taking into account one or more of the above-mentioned e!ects.
The analysis of tapered beams has been made by many investigators using di!erent
techniques. Rao [1] used the Galerkin method, Housner and Keightley [2] applied the
Myklestad procedure, Rao and Carnegie [3] used the "nite di!erences approach, Martin
[4] adopted a perturbation technique and Mabie and Rogers [5] solved the di!erential
equations using Bessel functions to "nd the natural frequencies of vibration of tapered
cantilever beams.
In analysing