Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

Babaei, Alireza; Yang, Cai Xia

doi:10.1007/s00542-018-4047-3

Cited by 34 publications

(15 citation statements)

References 33 publications

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“…x novel concept, rotational displacement of the rod is supposed to be a linear proportional function of rod translational axial displacement (Babaei and Yang [31]). In details, this concept states that rotation of the rod at each specific point of the infinitesimal element times length of the element x is a multiple of the axial displacement of the element.…”

Section: Kinematic Relationsmentioning

confidence: 99%

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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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Section: Kinematic Relationsmentioning

confidence: 99%

“…Constraint between the axial displacement and rotational displacement is an optimized idea firstly introduced by Babaei and Yang [31]. They proposed a coupled linear displacement field for the first time to analyze the dynamic-vibration behavior of a uniform nano-rod model of a MEMS gyroscope.…”

Section: Introductionmentioning

confidence: 99%

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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“…Babaei [12] investigated the forced vibration analysis of small-scaled rods subject to impulse, step and ramp inputs. Babaei and Yang [40] conducted a research analyzing the vibration analysis of a rotating rod using the coupled displacement filed theory. They showed the significance of the angular velocity and rotations of the system.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

Babaei

Arabghahestani

2021

Applied Mechanics

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In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating around a fixed axis perpendicular to the axial direction of the beam. For the first time, displacement filed is introduced as a coupled field to the translational field. In other words, the mentioned rotational displacement field is expressed as a proportional function of translational displacement field using first (axial), second (lateral), and third (angular or rotational) velocity factors. Utilizing Hamilton’s approach as a variational method, dynamic-vibration equations of motion of the proposed model are derived. Galerkin’s method is adopted to solve the equation corresponding to the Euler–Bernoulli and Timoshenko beams. For the case considering shear deformation effects, Navier method is chosen. For evaluation of current results and models, they are compared with those available at the benchmark. In this paper; effects of slenderness ratio, axial, lateral, and angular velocity factors, and rotations of the beam on the frequency are reported. Based on the results presented, mentioned factors should be counted in the analysis and design of such rotating micro-systems.

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“…During the last decade, improved computing hardware and software has led to the prosperous application of machine learning (ML) in different areas of oil industry such as seismic data, petrophysical analysis including synthetic log generation or prediction [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], which has shown to be a promising tool to help address their problems in a rigorous, repeatable way. Such methods, by considering various available parameters, can give a better prediction of the missing data than simple linear methods [10,26,27].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning: A Useful Tool in Geomechanical Studies, a Case Study from an Offshore Gas Field

Khatibi

Aghajanpour

2020

Energies

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For a safe drilling operation with the of minimum borehole instability challenges, building a mechanical earth model (MEM) has proven to be extremely valuable. However, the natural complexity of reservoirs along with the lack of reliable information leads to a poor prediction of geomechanical parameters. Shear wave velocity has many applications, such as in petrophysical and geophysical as well as geomechanical studies. However, occasionally, wells lack shear wave velocity (especially in old wells), and estimating this parameter using other well logs is the optimum solution. Generally, available empirical relationships are being used, while they can only describe similar formations and their validation needs calibration. In this study, machine learning approaches for shear sonic log prediction were used. The results were then compared with each other and the empirical Greenberg–Castagna method. Results showed that the artificial neural network has the highest accuracy of the predictions over the single and multiple linear regression models. This improvement is more highlighted in hydrocarbon-bearing intervals, which is considered as a limitation of the empirical or any linear method. In the next step, rock elastic properties and in-situ stresses were calculated. Afterwards, in-situ stresses were predicted and coupled with a failure criterion to yield safe mud weight windows for wells in the field. Predicted drilling events matched quite well with the observed drilling reports.

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Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

Cited by 34 publications

References 33 publications

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

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

Free Vibration Analysis of Rotating Beams Based on the Modified Couple Stress Theory and Coupled Displacement Field

Machine Learning: A Useful Tool in Geomechanical Studies, a Case Study from an Offshore Gas Field

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