Dynamic model for free vibration and response analysis of rotating beams

Kim, Hyungrae; Yoo, Hong Hee; Chung, Jintai

doi:10.1016/j.jsv.2013.06.004

Cited by 101 publications

(43 citation statements)

References 17 publications

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“…In order to explore the effects of nonlinearities of both geometric and dynamic origin when investigating the free vibration characteristics of rotating beams, interested readers are referred to the works of Turhan and Bulut [21], Lacarbonara et al [22], Arvin et al [23], Kim et al [24] and Sotoudeh and Hodges [25,26].…”

Section: Scope and Limitations Of The Theorymentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

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a b s t r a c tThe paper addresses the in-plane free vibration analysis of rotating beams using an exact dynamic stiffness method. The analysis includes the Coriolis effects in the free vibratory motion as well as the effects of an arbitrary hub radius and an outboard force. The investigation focuses on the formulation of the frequency dependent dynamic stiffness matrix to perform exact modal analysis of rotating beams or beam assemblies. The governing differential equations of motion, derived from Hamilton's principle, are solved using the Frobenius method. Natural boundary conditions resulting from the Hamiltonian formulation enable expressions for nodal forces to be obtained in terms of arbitrary constants. The dynamic stiffness matrix is developed by relating the amplitudes of the nodal forces to those of the corresponding responses, thereby eliminating the arbitrary constants. Then the natural frequencies and mode shapes follow from the application of the Wittrick-Williams algorithm. Numerical results for an individual rotating beam for cantilever boundary condition are given and some results are validated. The influences of Coriolis effects, rotational speed and hub radius on the natural frequencies and mode shapes are illustrated.

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Section: Scope and Limitations Of The Theorymentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

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“…[25] 3.1416 6.2832 9.4248 Ref. [26] 3.1416 6.2832 9.4248 Table 3 Comparison of first three modes of vibration of fixed tapered and classical clamped-free rod ( = 0, p = 0, ≠ 0)…”

Section: Rayleigh-ritz Methodsmentioning

confidence: 99%

“…Along with this notion, rotation effect in terms of rotation velocity upon frequencies of the system is to be investigated. Stiffening effects on dynamic characteristics of rotating beams is reported by Kim et al [26]. Ghafarian and Ariaei [27] carried out a research regarding vibration behavior of a system of interconnected Timoshenko beams capturing rotating effects.…”

Section: Introductionmentioning

confidence: 93%

Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh–Ritz method, determination of discernible patterns and chaotic regimes

Babaei

2019

SN Appl. Sci.

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Axial vibration analysis of an optimized MEMS gyroscope is investigated in this paper. For this purpose; a model of rotating, axially functionally graded (tapered) nano-rod is represented. Along with classical continuum mechanics, Eringen's non-local theory is adopted. Using Hamilton's variational approach along with coupled displacement field concept which is derived from Babaei and Yang, governing equations of motion are derived. Rayleigh-Ritz approximate method is used to solve the equation for both clamped-clamped and clamped-free rod model. Verification of current results is ratified by comparison with results available in technical literature. Incorporation of taper parameter, non-local effect and rotation effects reveals predictable patterns along with unpredictable chaotic behavior of the optimized gyroscope. Such outcomes report necessity of precise and case-by-case perusal as for some specific values of taper and non-local parameters; system results unpredictable responses. In such chaotic regimes, pattern detection based on response of the gyroscope is impossible and a kind of real-time monitoring and analysis is required. Excluding critical values of the mentioned parameters of non-locality and taper; generally rotations around a fixed axis leads to lessening the oscillations, enhancing the non-locality yields weak vibrations, and intensifying the taper effects makes the system oscillate with greater frequencies wherein for quite high values of taper parameter, gyroscope model behavior turns out independent. It is good to mention that only case in which increment of taper parameter suppresses vibrations occurs when cross-section area of clamped-free nano-rod model is increasing. Eventually, influential factors of current model are revealed.

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“…These studies concluded that the natural frequencies of flexural vibration tended to increase above those for the non-rotating beams, because of the centrifugal force and the subsequent stiffening effects [1]. The free vibration analysis of rotating beams have been widely studied using different numerical approximation methods, such as, the Rayleigh or Rayleigh-Ritz methods [1,2,3,4,5], the finite element method [6,7,8,9,10], the differential transform method [11] and Galerkin's method [12]. Moreover, AL-Said et al [13,14] analysed the free vibration of a Timoshenko beam modelled by a massless torsional spring, to simulate the flapwise vibration of a thick rotating beam.…”

Section: Introductionmentioning

confidence: 99%

Simplified modelling and analysis of a rotating Euler-Bernoulli beam with a single cracked edge

Yashar

Ferguson

Tehrani

2018

Journal of Sound and Vibration

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The natural frequencies and mode shapes of the flapwise and chordwise vibrations of a rotating cracked Euler-Bernoulli beam are investigated using a simplified method. This approach is based on obtaining the lateral deflection of the cracked rotating beam by subtracting the potential energy of a rotating massless spring, which represents the crack, from the total potential energy of the intact rotating beam. With this new method, it is assumed that the admissible function which satisfies the geometric boundary conditions of an intact beam is valid even in the presence of a crack. Furthermore, the centrifugal stiffness due to rotation is considered as an additional stiffness, which is obtained from the rotational speed and the geometry of the beam. Finally, the Rayleigh-Ritz method is utilised to solve the eigenvalue problem. The validity of the results is confirmed at different rotational speeds, crack depth and location by comparison with solid and beam finite element model simulations. Furthermore, the mode shapes are compared with those obtained from finite element models using a Modal Assurance Criterion (MAC).

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Dynamic model for free vibration and response analysis of rotating beams

Cited by 101 publications

References 17 publications

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Longitudinal vibration responses of axially functionally graded optimized MEMS gyroscope using Rayleigh–Ritz method, determination of discernible patterns and chaotic regimes

Simplified modelling and analysis of a rotating Euler-Bernoulli beam with a single cracked edge

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