TY - JFULL
AU - Chih-Ling Huang and Wen-Yi Lin and Kuo-Mo Hsiao
PY - 2009/9/
TI - Free Flapping Vibration of Rotating Inclined Euler Beams
T2 - International Journal of Mechanical and Mechatronics Engineering
SP - 974
EP - 981
VL - 3
SN - 1307-6892
UR - https://publications.waset.org/pdf/11504
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 32, 2009
N2 - A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
ER -