Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory

Bağdatlı, Süleyman Murat

doi:10.1016/j.compositesb.2015.05.030

Cited by 51 publications

(13 citation statements)

References 61 publications

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“…Ozturk and Coskun [29] proposed the homotopy perturbation method. The multiple scale method was used to analyze the nonlinear vibration of CNT [30][31][32][33]. He's variational method exhibited more advantages [12,[34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

et al. 2018

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Abstract:In the present study, the nonlinear vibration of a nanobeam resting on the fractional order viscoelastic Winkler-Pasternak foundation is studied using nonlocal elasticity theory. The D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. A detailed parametric study is conducted, and the effects of the variation of different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have a significant effect on the natural frequency and the amplitude of vibrations.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

et al. 2018

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“…Since the early works by Peddieson et al [55] and Sudak [56], there have been a large number of articles devoted to the modelling of nanobeams and CNTs using the nonlocal EBT model. For example, Zhang et al [57] [67] and Bagdatli [68].…”

Section: Beam Models 221 Nonlocal Models Based On the Ebtmentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

316

112

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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“…Beni et al (2014) studied the transverse vibration of cracked nano-beam based on modified couple stress theory. Further, Bagdatli (2015) presented the non-linear vibration of nanobeams. Now, literature related to development of various approaches of Differential Quadrature (DQ) method have also been briefly mentioned herein.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method

Jena

2018

Front. Built Environ.

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In this article, free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) is investigated by using the Differential Quadrature Method (DQM). Here width of the cross-section is assumed to vary exponentially along the length of the nano-ribbon. Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of boundary conditions. Convergence study is carried out to illustrate the efficiency of the method and obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are depicted to show the effects of the nonuniform parameter, nonlocal parameter, aspect ratio and edge conditions on the frequency parameters.

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Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory

Cited by 51 publications

References 61 publications

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

A review of continuum mechanics models for size-dependent analysis of beams and plates

Free Vibration Analysis of Variable Cross-Section Single-Layered Graphene Nano-Ribbons (SLGNRs) Using Differential Quadrature Method

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