Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory

Bhattacharya, Sarani; Das, Debabrata

doi:10.1016/j.compstruct.2019.01.080

Cited by 59 publications

(30 citation statements)

References 67 publications

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“…Esfahani et al [65] put the Gurtin-Murdoch surface elasticity to use to predict the nonlinear vibration response of electrostatic FG nanobeam resonator. Bhattacharya and Das [66] examined the free vibrations of bi-directional FG and double-tapered rotating Timoshenko microbeams incorporating couple stress size dependency.…”

Section: Introductionmentioning

confidence: 99%

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Xie

Sahmani

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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As one of the innovative materials, functionally graded (FG) composite materials have the capability to vary microstructure and design attributes from one side to other representing the desired material properties. The prime aim of this work is to analyze the surface stress effect on the nonlinear free vibration response of FG cylindrical nanoshells incorporating various modal interactions. To this end, the Gurtin-Murdoch theory of elasticity together with the von Karman geometrical nonlinearity is implemented to the classical shell theory to construct an efficient size-dependent shell model. In order to take the modal interactions between the main oscillation mode and various symmetric vibration modes, the lateral deflection of the FG nanoshell is expressed as combination of the simple main vibration mode and convergent symmetric modes. Thereafter, the solution of problem is considered as the summation of the homogenous and particular parts to put the Galerkin technique to use. Finally, the multiple timescales method is employed to achieve analytical expression for the surface elastic-based frequency response of FG nanoshells. It is displayed that in the presence of modal interaction, by increasing the shell deflection, the value of the frequency ratio decreases while in the absence of modal interaction, it enhances.

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Section: Introductionmentioning

confidence: 99%

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Xie

Sahmani

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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“…Yu et al [28] studied the bending and free vibration of small-size BDFG beam by employing NURBSbased isogeometric analysis combined with a nonclassical quasi-3D beam theory. Bhattacharya and Das [29] investigated the nonlinear chord-and flapwise vibration of BDFG double-tapered rotating microbeam by considering the high operating temperature. Rajasekaran and Khaniki [30] obtained the forced vibration response of nonuniform BDFG microbeam under a moving harmonic load/mass.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Lü¹,

Chen

2020

Shock and Vibration

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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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Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory

Cited by 59 publications

References 67 publications

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

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

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