Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Baghani, Mostafa; Mohammadsalehi, M.; Dabaghian, P.H.

doi:10.1590/1679-78252175

Cited by 8 publications

(3 citation statements)

References 35 publications

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“…Using power-law functions to ensure a smooth distribution of stresses along the longitude direction and all the interfaces, the FG material properties are expected to vary along the axis of the beam as [36]:…”

Section: Problem Formulationmentioning

confidence: 99%

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

2019

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In the current study, an analytical solution based on a modi ed couple stress theory for a nonlinear model describing the couple 3D motion of a functionally graded tapered micro-bridge is presented. The small scale e ects and the nonlinearity arising from the mid-plane stretching are taken into consideration. Governing equations of motion are derived utilizing modi ed couple stress theory and applying the Hamilton principle. Dynamic and static analyses to determine the e ects of lateral distributed forces and mid-plane stretching are investigated. Towards this aim, analytical the Homotopy-pade technique is employed to capture the nonlinear natural frequencies in high amplitude vibrations of tapered micro-bridges with di erent types of geometry and material composition. The obtained results of frequencies propose that there is good agreement between the present analytical results and the numerical ones, as opposed to the well-known multiple-scale method. Furthermore, comparing the results in 2D and 3D analyses shows that in 2D analysis, the sti ness and natural frequency of the micro-beam is underestimated and it is observed that increasing the tapered ratio has di erent impacts on natural frequencies for micro-beams with di erent slender ratios.

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Section: Problem Formulationmentioning

confidence: 99%

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

2019

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“…In the further work by , the authors analyzed the flapwise bending vibration response of a tapered rotating nanocantilever beam through the Eringen's nonlocal elastic theory, while using the pseudospectral collocation method based on Chebyshev polynomials to solve the problem. Based on a large parametric investigation, a pronounced sensitivity of the dynamic response was found to the nonlocal small scale, angular speed and non-uniform section of the nanocantilever.Despite the large application of nonlocal elastic theories, few works in the literature have applied the coupled stress theories (CSTs) to describe the mechanical behavior of non-uniform small scale beams [61][62][63][64], and found some closed form solutions for some particular loading and boundary conditions. This represents the main concern of the present investigation, where we propose a NMCST as higher-order continuum-based theory for the vibration size-dependent analysis of tapered composite…”

mentioning

confidence: 99%

“…Despite the large application of nonlocal elastic theories, few works in the literature have applied the coupled stress theories (CSTs) to describe the mechanical behavior of non-uniform small scale beams [61][62][63][64], and found some closed form solutions for some particular loading and boundary conditions. This represents the main concern of the present investigation, where we propose a NMCST as higher-order continuum-based theory for the vibration size-dependent analysis of tapered composite…”

mentioning

confidence: 99%

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

et al. 2020

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Due to the large application of tapered beams in smart devices, such as scanning tunneling microscopes (STM), nano/micro electromechanical systems (NEMS/MEMS), atomic force microscopes (AFM), as well as in military aircraft applications, this study deals with the vibration behavior of laminated composite non-uniform nanobeams subjected to different boundary conditions. The micro-structural size-dependent free vibration response of composite laminated Euler–Bernoulli beams is here analyzed based on a modified couple stress elasticity, which accounts for the presence of a length scale parameter. The governing equations and boundary conditions of the problem are developed using the Hamilton’s principle, and solved by means of the Rayleigh–Ritz method. The accuracy and stability of the proposed formulation is checked through a convergence and comparative study with respect to the available literature. A large parametric study is conducted to investigate the effect of the length-scale parameter, non-uniformity parameter, size dimension and boundary conditions on the natural frequencies of laminated composite tapered beams, as useful for design and optimization purposes of small-scale devices, due to their structural tailoring capabilities, damage tolerance, and their potential for creating reduction in weight.

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