Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor

Alsaleh, Ali; Sedighi, Hamid M.; Ouakad, Hassen M.

doi:10.1007/s11709-020-0647-y

Cited by 13 publications

(10 citation statements)

References 21 publications

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“…As seen in equations ( 37)-( 40), there are many constant matrices with time varying coefficients in the assembled vibration equation, equation (23), and these constant matrices are obtained by the matrix integral of the assumed modal matrices, as shown in the "matrix integral" step.…”

Section: Conventional Solution For Time Varying and Nonlinear Equationsmentioning

confidence: 99%

“…Sun et al 22 proposed a novel framework in which the sophisticated geometrical structure was considered by the finite solid element method, and efficient model order reduction was applied to the model. Alsaleh et al 23 demonstrated that a two-degree-of-freedom (DOF) model could predict flexural vibrations under rigid conditions with an error of less than 5%. They also illustrated the applicability of employing simple models to predict the dynamic response of a real rotor system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient method for vibration equations with time varying coefficients and nonlinearities

Yang

Xie

Chen

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.

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Section: Conventional Solution For Time Varying and Nonlinear Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient method for vibration equations with time varying coefficients and nonlinearities

Yang

Xie

Chen

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

“…In many practical cases, the effect of nonlinearities are negligibly small and the linear systems might provide reasonably accurate results. A lot of work on the analysis of linear systems are available in literatures [22,36,[43][44][45][46][47][48][49][50][51][52][53][54]. Analysis of the linear rotor system is essential to determine the effect of system parameters on the frequency response curves [13-15], etc.…”

Section: Introductionmentioning

confidence: 99%

Modelling and analysis of a continuous rotor systemPart I: Derivation of governing equations and analysis of linear system

Malgol,

et al. 2023

Preprint

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In this paper, a continuous rotor system is modelled by considering some critical factors, like the gyroscopic and rotary inertia effects of disc and shaft cross-sections, large shaft deformation, and restriction to shaft axial motion at the bearings. The bearings are replaced by springs along horizontal and vertical directions. Governing partial differential equations (PDE’s) for the vibrations of the disc along the horizontal and vertical directions are derived by employing the Hamiltonian principle. The governing equation is then transformed into a set of ordinary differential equations (ODEs) using method of modal projection. The large deformation and restriction to axial motion of the shaft yields nonlinearities in the system governing equations. Only the linear system is analysed in this first part. The parameters in the dimensionless form of the governing equations are functions of some independent variables which are associated to the material and geometrical properties of the rotor system. Understanding the effect of the system properties on the response characteristics will lead to an appropriate design. Exact analytical solutions for the motion along horizontal and vertical directions are obtained. The effect of the independent parameters on the system dynamics are analysed wherein the variation of the dependent parameters are also monitored. The system dynamics are explored using time-displacement responses, phase-plane plots, frequency response diagrams, phase angle plots and Campbell diagrams.

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“…Since the connection looseness is highly nonlinear, related research needs more advanced methods to explain the mechanism at the joint interface. Besides, Alsaleh and Ouakad (2018) and Alsaleh et al (2020) investigated the lateral vibrations of an unbalanced Jeffcott rotor by experimental and theoretical methods.…”

Section: Introductionmentioning

confidence: 99%

“…Liu and Hong (2021) applied the nonlinear normal modes to analyze failure in aero rotor systems and explained the mechanism of backward whirl motion. Alsaleh et al (2020) examined the fundamental vibrational characteristics of a spinning CNT-based nano-rotor based on the nonlocal elasticity Euler–Bernoulli beam theory.…”

Section: Introductionmentioning

confidence: 99%

Modeling and dynamic analysis for rotors with curvic-coupling looseness

Liu

Zhou

Zhang

et al. 2022

Journal of Vibration and Control

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The joint structures, such as flanges with bolts and curvic-couplings, are commonly applied in aero-engine rotors. Those joints tend to loosen when subjected to heavy load, and the local deformation of the joints can induce nonlinearities to the rotor and further affect its dynamic characteristics. However, much research focuses on the bolted joint loosening, while the studies of curvic-coupling loosening in rotor systems are seldom reported. In this paper, the modeling and dynamics analysis for rotors with curvic-coupling loosening are performed. First, an analytical model is proposed to describe the nonlinear stiffness caused by looseness at the joint interface. Then, a rotor with curvic-coupling looseness is modeled and the related dynamic equations are derived. Finally, the modal characteristics of the rotor with curvic-coupling looseness are analyzed based on the complex nonlinear modes method, and the rotor’s steady-state response is obtained using numerical methods. The results show that the softening behavior introduced by joint looseness can lead to eigen frequency reduction in modal analysis, amplitude jump in response, and bifurcation around the critical speed. The above dynamic characteristics can provide reference for fault diagnosis in the rotor system with curvic-coupling loosening.

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Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor

Cited by 13 publications

References 21 publications

An efficient method for vibration equations with time varying coefficients and nonlinearities

An efficient method for vibration equations with time varying coefficients and nonlinearities

Modelling and analysis of a continuous rotor systemPart I: Derivation of governing equations and analysis of linear system

Modeling and dynamic analysis for rotors with curvic-coupling looseness

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