This study is aimed at analysing damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, taking into account both external (non-rotating) and internal (rotating) damping distributions. As case-study giving rise to a set of coupled differential Mathieu-Hill equations with both damping and gyroscopic terms, a balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment, with the possibility of carrying additional inertial elements like discs or flywheels. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations, stability is studied via eigenproblem formulation, obtained by applying the harmonic balance method. The occurrence of simple and combination parametric resonances is analysed introducing the notion of characteristic circle on the complex plane and deriving analytical expressions for critical solutions, including combination parametric resonances, valid for a large class of rotors. A numerical algorithm is then developed for computing global stability thresholds in presence of both damping and gyroscopic terms, also valid when closed-form expressions of critical solutions do not exist. The influence on stability of damping distributions and gyroscopic actions is then analysed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams.

Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems / DE FELICE, Alessandro; Sorrentino, Silvio. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - 103:4(2021), pp. 3529-3555. [10.1007/s11071-020-06106-3]

Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems.

Alessandro De Felice;Silvio Sorrentino
2021

Abstract

This study is aimed at analysing damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, taking into account both external (non-rotating) and internal (rotating) damping distributions. As case-study giving rise to a set of coupled differential Mathieu-Hill equations with both damping and gyroscopic terms, a balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment, with the possibility of carrying additional inertial elements like discs or flywheels. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations, stability is studied via eigenproblem formulation, obtained by applying the harmonic balance method. The occurrence of simple and combination parametric resonances is analysed introducing the notion of characteristic circle on the complex plane and deriving analytical expressions for critical solutions, including combination parametric resonances, valid for a large class of rotors. A numerical algorithm is then developed for computing global stability thresholds in presence of both damping and gyroscopic terms, also valid when closed-form expressions of critical solutions do not exist. The influence on stability of damping distributions and gyroscopic actions is then analysed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams.
2021
5-gen-2021
103
4
3529
3555
Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems / DE FELICE, Alessandro; Sorrentino, Silvio. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - 103:4(2021), pp. 3529-3555. [10.1007/s11071-020-06106-3]
DE FELICE, Alessandro; Sorrentino, Silvio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1226742
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