The influence of size effect on flapwise vibration of rotating microbeams

Dehrouyeh-Semnani, Amir Mehdi

doi:10.1016/j.ijengsci.2015.05.009

Cited by 62 publications

(18 citation statements)

References 68 publications

(14 reference statements)

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“…Modified couple stress theory (MCST), developed by Yang et al, 43 is one such theory that the researchers have been using extensively over the past few years. 44 MCST-based research articles dealing with homogeneous [45][46][47][48][49] and FGM [50][51][52][53][54] rotating micro beams with straight configuration (i.e. without pre-twist) have been published in the recent years.…”

Section: Introductionmentioning

confidence: 99%

Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

Bhattacharya

Das

2019

Proceedings of the Institution of Mechanical Engineers, Part L:

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An improved mathematical model of pre-twisted tapered rotating micro beams made of bidirectional functionally graded material (BFGM) is presented to study its free vibration behavior. The effects of spin-softening and Coriolis acceleration are incorporated, and modified couple stress theory is employed to address the size effect. The mathematical formulation is based on first-order shear deformation theory and is developed in a global non-inertial frame incorporating appropriate transformations between the global inertial frame and the local non-inertial frame. Two different but interrelated steps are employed, where the first step determines the centrifugally deformed configuration using minimum potential energy principle, and the second step determines the free vibration behavior through tangent stiffness of the deformed rotating beam using Hamilton's principle. The direct use of tangent stiffness considers the centrifugal stiffening effect through von Kármán non-linearity and bypasses the need of strain energy functional for the vibrating beam. The governing equations are transformed to an eigenvalue problem through state-space approach and solved following Ritz method. The effects of spin-softening, Coriolis acceleration, and pre-twist angle are shown and discussed. The effects of different parameters such as size-dependent parameter, aspect ratio, material gradation indices, operating temperature, FGM constituent, taperness parameters, and slender parameter are discussed.

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Section: Introductionmentioning

confidence: 99%

Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

Bhattacharya

Das

2019

Proceedings of the Institution of Mechanical Engineers, Part L:

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“…Most of these research works were based on either modified couple stress theory or modified strain gradient theory, both being continuum based non-classical theories. Some of those studies are found in [23][24][25][26] dealing with homogeneous beams and in [27][28][29][30][31][32] dealing with FGM beams. Review of the domain of literature on nano-structures reveals that Eringen's NET is considered to be a foundation, on which most of the theoretical research investigations on nano-size structures are based.…”

Section: Introductionmentioning

confidence: 99%

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

Malik

Das

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Free vibration behavior of rotating bidirectional functionally graded nano-beams is studied based on Eringen’s nonlocal theory. The beam material consists of ceramic and metal constituents, and the material is graded across the length and thickness directions. The mathematical formulation is framed on Euler–Bernoulli beam theory, and the system of governing equations is derived in variational form using Hamilton’s principle. The governing equations are discretized and transformed to an eigen value problem using Ritz method. The model is formulated to study the flapping and lead-lag motions due to free vibration. The model is verified with the available numerical results. The numerical results are presented in non-dimensional frequency-speed plane to study the influence of normalized nonlocal parameter, length gradient parameter, thickness gradient parameter, root radius parameter, and section aspect ratio. Some normalized mode shapes are presented to illustrate the mode switching phenomenon. The mathematical model of a nonlocal rotating bidirectional functionally graded material nano-beam is presented for the first time through this work and the reported results are new of its kind.

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“…Thereafter, many models were established to capture the dynamic stiffening effect, which can be roughly divided into three categories. The dynamic stiffening models of the first category added the additional potential energy induced by centrifugal force to describe the centrifugal stiffening effect [9][10][11][12][13][14]. In the second type of dynamic stiffening models [15][16][17][18][19][20][21][22], the axial deformation is described by using the stretch deformation (i.e.…”

Section: Introductionmentioning

confidence: 99%

On dynamics of a rotating hub-flexible rod-concentrated mass system considering rigid-flexible coupling effect

Fang¹,

Xiao²,

Li³

et al. 2020

J. vibroeng.

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Rotating hub-flexible rod system is a typical rigid-flexible coupling dynamic mechanism, which has a wide range of industrial applications. In this paper, a comprehensive nonlinear dynamical model of a rotating hub-flexible rod-concentrated mass system considering rigid-flexible coupling effect is established to study its dynamic properties. By employing the Hamilton principle and classical beam theory, a set of differential equations of motion are derived including the couplings of the elastic deformation of the rod and the rigid rotation of the hub. The additional centrifugal force, tangential force and Coriolis force due to the rigid-flexible coupling effect are elaborated. The derived governing partial differential equations are solved by the Galerkin method. The validity of the present model is verified by a comparative study. The tip motion trajectories of the rod for the prescribed rotation, the dynamic responses of the hub and the rod for an external torque acting on the hub and the dimensionless natural frequencies of the system for the steady-state rotation are graphically presented. The influences of parameters such as rotational speed ratio, concentrated mass ratio, concentrated mass location ratio and initial eccentricity ratio on the dynamics are discussed in detail.

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The influence of size effect on flapwise vibration of rotating microbeams

Cited by 62 publications

References 68 publications

Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

On dynamics of a rotating hub-flexible rod-concentrated mass system considering rigid-flexible coupling effect

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