Consistent matrices in rotor dynamic
Copyright policy )Consistent matrices in rotor dynamic
The expressions for the consistent mass and gyroscopic matrices for a constant section shaft element are obtained taking into account both shear deformation and transversal inertia. The results are compared with closed form solutions, which are available in simple cases. The results obtained show that the study of the dynamic behaviour of the rotor with a model which includes rotational inertia but not shear deformation is, at least in the case examined, misleading. Formulae for matrix condensation and for taking into account the effects of axial load and of a linear unbalance distribution are given. Damped systems can be studied using the same model, provided that damping can be assumed to be of either viscous or hysteretic type. Some formulations found in the literature are however not considered correct. An application of consistent matrices to a model which includes damping and uses matrix condensation is shown.
first approximation, eigenvalue problems, effects of axial load, third approximation, matrix condensation, constant section shaft element, consistent mass, rotational inertia, viscous or hysteretic type, Vibrations in dynamical problems in solid mechanics, Damped systems, shear deformation, Rods (beams, columns, shafts, arches, rings, etc.), gyroscopic matrices, compared with closed form solutions, linear unbalance distribution, second approximation, transversal inertia, dynamic behaviour of the rotor
first approximation, eigenvalue problems, effects of axial load, third approximation, matrix condensation, constant section shaft element, consistent mass, rotational inertia, viscous or hysteretic type, Vibrations in dynamical problems in solid mechanics, Damped systems, shear deformation, Rods (beams, columns, shafts, arches, rings, etc.), gyroscopic matrices, compared with closed form solutions, linear unbalance distribution, second approximation, transversal inertia, dynamic behaviour of the rotor
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