Fundamental frequency analysis of microtubules under different boundary conditions using differential quadrature method

Mallakzadeh, Mohammadreza; Zanoosi, A.A. Pasha; Alibeigloo, A.

doi:10.1016/j.cnsns.2012.12.014

Cited by 8 publications

(3 citation statements)

References 52 publications

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“…The Nontrivial Solutions of Viscoelastic Model. The differential and integral quadrature methods have been applied to study the nonlinear dynamics of continua [26,28,29]. In the following, the quadrature methods are applied to numerically calculate the nontrivial equilibrium solution.…”

Section: The Nontrivial Equilibriummentioning

confidence: 99%

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Ding

2014

Mathematical Problems in Engineering

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Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.

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Section: The Nontrivial Equilibriummentioning

confidence: 99%

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Ding

2014

Mathematical Problems in Engineering

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“…Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules was presented by Li et al (2006). The effects of boundary conditions on the vibration behavior of MTs modeled as elastic cylinder shells were studied by Malekzadeh et al (2013). They used the differential quadrature method (DQM) to solve the governing motion equations.…”

Section: Introductionmentioning

confidence: 99%

Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory

Arani

Abdollahian

Jalaei

2015

Journal of Theoretical Biology

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“…More recently, the differential quadrature method (DQM), is introduced for solving several engineering problems, such that in thermodynamics, aerodynamics, structural and fracture mechanics. The method possesses the capability to achieve accurate results with a minimal computational effort [10][11][12][13], The classical version of DQM can't deal with discontinuous or irregular domains. So, a new version of DQM, (termed by multi-domain differential quadrature technique), is developed for solving discontinuity problems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Cracked Plates Using Localized Multi¬Domain Differential Quadrature Method

Osman¹,

Matbuly²,

Mohamed³

et al. 2013

ACM

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In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it's focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.

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Fundamental frequency analysis of microtubules under different boundary conditions using differential quadrature method

Cited by 8 publications

References 52 publications

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory

Analysis of Cracked Plates Using Localized Multi¬Domain Differential Quadrature Method

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