Nonlinear Dynamics of a Spinning Shaft with Non-Constant Rotating Speed
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Дата
2016
Автори
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
NTU "KhPI"
Анотація
Reported research on spinning shafts is mostly restricted to cases of constant rotational speed without
examining the dynamics thatoccursduringtheir spin-up or spin-down operation. In suchcases, the motion is
described by a nonlinear system of Partial Differential Equations (PDEs) coupled with an Integro-Differential
Equation (IDE). The nonlinear system of PDEs with IDE, projected onto the infinite basis of the modes of the
underlying linear system, results in a system of nonlinear Ordinary Differential Equations (ODEs). In this
articleis appliedthe multiple scales perturbation method for dynamic analysis and the system in first order
approximation takes the form of two coupled sets of pairedequations. The first pair describes torsional and
rigid body rotation whilst the secondconsists of the equations describing the two lateral bending motions.
Although in this system non-conservative forces are not considered in terms of damping or explicit externally
applied load (torques/forces), the solution of the Is'order approximation of the first set of equations indicates
that there are no periodic motions. The solution of the second set of equations of 1st order approximation
coincides with the case of constant rotating speed. It isshown, that the Normal Modes in bending motions are
the critical speeds of the shaft. It is shown that the frequencies in the Campbell diagram coincide with the
frequencies associated with the 1st order solution of the nonlinear system. Moreover, the analytical solution of
the first pair of equations is in good agreement with direct numerical simulations. This work paves the way for
the development of the Nonlinear Campbell diagram that can be used to determine the dynamic behaviour of
rotating structures during spin-up or spin-down operation.
Опис
Ключові слова
non-constant rotating speed, spin-up, spin-down, normal modes, Campbell diagram
Бібліографічний опис
Georgiades F. Nonlinear Dynamics of a Spinning Shaft with NonConstant Rotating Speed / F. Georgiades // Nonlinear Dynamics–2016 (ND-KhPI2016) : proceedings of 5th International Conference, dedicated to the 90th anniversary of Academician V. L. Rvachev, September 27-30, 2016 = Нелінійна динаміка–2016 : тези доп. 5-ї Міжнар. конф., 27-30 вересня 2016 р. – Kharkov : NTU "KhPI", 2016. – P. 277-286.