Nonstationary analysis of nonlinear rotating shafts passing through critical speed excited by a nonideal energy source

Mahmoudi, Abdelkader; Hosseini, S.A.A.; Zamanian, M.

doi:10.1177/0954406216684364

Cited by 8 publications

(11 citation statements)

References 22 publications

(45 reference statements)

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“…It is observed that in the case of larger driving torque, the response amplitude is smaller. In this case, the angular acceleration is large and the system does not enough time to take the maximum response . On the other hand, when the driving torque is small, amplitude increases and this condition holds up to the steady‐state situation.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Angular velocity vector ω of an arbitrary shaft cross section is acquired from Euler's angle as

\begin{matrix} left ω = ω_{1} e_{1} + ω_{2} e_{2} + ω_{3} e_{3} = (\overset{β}{true} + \overset{φ}{true} - \overset{ψ}{true} prefixsin θ) e_{1} \\ left + (\overset{ψ}{true} prefixsin (β + φ) prefixcos θ + \overset{θ}{true} prefixcos β) e_{2} + (\overset{ψ}{true} prefixcos (β + φ) prefixcos θ - \overset{θ}{true} prefixsin β) e_{3} \end{matrix}

where the symbol (·) denotes the derivative with respect to time. Position and velocity of an arbitrary point

(x, y, z)

on the deformed shaft can be calculated as

\begin{matrix} left boldR = (x + u) e_{X} + v e_{Y} + w e_{Z} + (a_{y} + y) e_{2} + (a_{z} + z) e_{3} \\ left \overset{R}{true} = \overset{u}{true} e_{X} + \overset{v}{true} e_{Y} + \overset{w}{true} e_{Z} + ω \times [(a_{y} + y) e_{2} + \end{matrix}

…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

“…One can check the precision of the equations above with two methods: First, if the rotational speed is made constant, the equations of motion reduce to those in []. Second, if the material is assumed to be isotropic, and the remaining coefficients change proportionally, the equations reduce to those presented in []. Given these, one may conclude that the equations of motion are correct.…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

“…They discussed the magneto‐rheological damper and magnetically levitated body in order to decrease the vibration amplitude. Mahmoudi et al . investigated nonstationary analysis of nonlinear rotating shafts.…”

Section: Introductionmentioning

confidence: 99%

“…So, the dynamic analysis of stationary cases was merely possible. In other studies, such as [], the dynamic behavior of isotropic shafts was investigated. Of course, it is quite useful to investigate the non‐stationary dynamics of a composite shafts with geometrical nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Kafi

Hosseini

2019

Z Angew Math Mech

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In this article, nonlinear nonstationary vibration of a rotating composite shaft passing through critical speed excited by non-ideal energy source is investigated. Geometrical nonlinearity, gyroscopic effect, rotary inertia and coupling due to material anisotropy are considered, while shear deformation is neglected. By using Hamilton principle, axial-flexural-flexural-torsional-rotational equations of motion for a composite shaft with variable rotational speed are derived. External source is assumed as non-ideal that causes the interaction between external torque and vibrating system.To obtain the approximate analytical solution, perturbation theory (multiple scales method) is applied to reduce the equations in the neighborhood of the first critical speed. Although, the analysis is done for the first critical speed, one-mode discretization is not enough. Indeed, at least two modes is required to obtain accurate results.The effects of external damping, eccentricity, angle of fibers, resistive torque, nonlinear terms, and also the effect of the extensional-torsional coupling on occurrence of Sommerfeld effect are investigated. It is shown that nonlinearity and coupling possess significant effect on the prediction of Sommerfeld phenomenon. Moreover, as observed, with appropriate implementation of layup and stacking sequence, one can obtain the best performance for the nonstationary behavior of composite shaft. K E Y W O R D Scomposite rotor, multiple-scales method, non-ideal source, nonstationary motion, sommerfeld effect

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Section: Numerical Examplesmentioning

confidence: 98%

“…Angular velocity vector ω of an arbitrary shaft cross section is acquired from Euler's angle as