Flap-wise and chord-wise vibrations of axially functionally graded tapered beams rotating around a hub

Mazanoglu, Kemal; Güler, Serkan

doi:10.1016/j.ymssp.2016.07.017

Cited by 28 publications

(8 citation statements)

References 20 publications

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“…Table 2 presents a comparison with Mazanoglu and Guler 29 of non-dimensional vibration frequencies of the first three modes, each for lead-lag and flapping motions, for a rotating axially FGM classical/local beam (μ=0) at Ω*=2. It is mentioned that Table 2 corresponds to κ = 1, β = 0, L/h = 66.67, E = 70 GPa, ρm = 2702 kg m −3 , Ec = 200 GPa, ρc = 5700 kg m −3 .…”

Section: Resultsmentioning

confidence: 99%

“…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%

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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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Section: Resultsmentioning

confidence: 99%

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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“…The objective of the research is to model FGM structures for turbines and rotating discs. Various authors quoted here, analyzed the vibration of rotating thin-walled beams [54][55][56][57][58][59][60][61]. The Timoshenko beam was a common beam theory used to model thin-walled rotating laminated beams [62][63][64].…”

Section: Literature Surveymentioning

confidence: 99%

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

Gee¹

2021

Preprint

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The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.

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“…Except for flapwise vibration, many researchers studied the linear and nonlinear free vibrations of other directions considering the coupling effects. Mazanoglu and Guler (2017) presented two-dimensional vibration analysis for an axially functionally graded tapered beam with centrifugal stiffening effects. Yoo et al (2001) and Oh and Yoo (2016) developed new structural dynamic models of rotating uniform and functionally graded (FG) blades with a pre-twisted angle by using Kane's method, and investigated the bending-bending coupling vibration.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear forced vibration analysis of a rotating three-dimensional tapered cantilever beam

Zhou

Zhang

Yao

2020

Journal of Vibration and Control

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In this article, nonlinear forced vibration analysis is carried out for a rotating three-dimensional tapered cantilever beam subjected to a uniformly distributed load. Considering the effects of Coriolis terms, static axial deformation and geometric nonlinearity in modeling process, nonlinear partial motion equations of a rotating tapered Euler–Bernoulli beam are established by using Hamilton’s principle. Galerkin’s procedure is used to discretize the equations to obtain the dynamic response of the beam. Frequency responses, the time-history response, the phase diagram, and the Poincaré map are introduced to study the effects of the taper ratio, rotating velocity, radius of hub, and external excitation on the nonlinear resonances and detailed responses of the rotating three-dimensional tapered beam. Results show that the fundamental natural frequency increases with the increase of the taper ratio, radius of hub, and rotating velocity. Besides, by increasing the taper ratio and excitation amplitude and decreasing the rotating velocity and radius of hub, the nonlinearity and vibration amplitude of the rotating beam intensify.

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Flap-wise and chord-wise vibrations of axially functionally graded tapered beams rotating around a hub

Cited by 28 publications

References 20 publications

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

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

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

Nonlinear forced vibration analysis of a rotating three-dimensional tapered cantilever beam

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