TY - EJOU
AU - Kumar, A.S Vinod
AU - Ganguli, Ranjan
TI - Analogy Between Rotating Euler-Bernoulli and Timoshenko Beams and Stiff Strings
T2 - Computer Modeling in Engineering \& Sciences
PY - 2012
VL - 88
IS - 6
SN - 1526-1506
AB - The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. The results provide physical insight into relation between rotating beams and stiff string which are useful for creating basis functions for approximate methods in vibration analysis of rotating beams.
KW - Rotating beam
KW - Centrifugal stiffening
KW - Finite element
KW - Bisection method
KW - Frequency
KW - Vibration
DO - 10.3970/cmes.2012.088.443