Rigorous theory of vibration analysis of rotating blade based on transfer matrix method (1st report, State equations of the static balance and natural vibration of a rotating non-uniform beam)

摘要

State equations of the natural vibration of a rotating blade are derived from Hamilton's principle. The state equations are based on the beam theory. Bending-shear deflection, torsion, longitudinal expansion-contraction, and warping are adopted as deformations. The following 6 factors are taken into consideration: (1) the discrepancy between the figure center and shear center in blade cross section, (2) rotary inertia, (3) centrifugal tension, (4) Coriolis force, (5) warping rigidity, (6) bending and shear rigidity variation due to twist-hack of the blade body. Lateral-torsional coupled vibration is induced by the first and third factors, and lateral-longitudinal coupled vibration is induced by the fourth factor. The natural vibration analysis of a rotating blade should be divided into three steps: (1) the distribution of centrifugal tension, (2) twist-back of the blade body, (3) natural vibration. The second step determines the neutral position for vibration.