Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams

Kananipour, Hassan; Ahmadi, Mehdi; Chavoshi, Hossein

doi:10.1590/s1679-78252014000500007

Cited by 13 publications

(10 citation statements)

References 7 publications

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“…In Eftekhari and Jafari (2012c) the capability of the DQM for handling the time-dependent Dirac-delta function was discussed at length and it was concluded that there are some major limitations in the choice of time steps and mesh sizes. Most recently, Nikkhoo et al (2012), Nikkhoo and Kananipour (2014) also Kananipour et al (2014) have proposed a formulation based on the DQM for transient dynamic analysis of curved beams traversed by moving concentrated loads. But, no details were given how the time-dependent Diracdelta function was approximated or treated numerically in their study.…”

Section: Introductionmentioning

confidence: 99%

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

Eftekhari

2015

Lat. Am. j. solids struct.

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The differential quadrature method (DQM) is one of the most elegant and efficient methods for the numerical solution of partial differential equations arising in engineering and applied sciences. It is simple to use and also straightforward to implement. However, the DQM is well-known to have some difficulty when applied to partial differential equations involving singular functions like the Dirac-delta function. This is caused by the fact that the Dirac-delta function cannot be directly discretized by the DQM. To overcome this difficulty, this paper presents a simple differential quadrature procedure in which the Dirac-delta function is replaced by regularized smooth functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. To demonstrate the applicability and reliability of the proposed method, it is applied here to solve some moving load problems of beams and rectangular plates, where the location of the moving load is described by a time-dependent Dirac-delta function. The results generated by the proposed method are compared with analytical and numerical results available in the literature. Numerical results reveal that the proposed method can be used as an efficient tool for dynamic analysis of beam-and plate-type structures traversed by moving dynamic loads.

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Section: Introductionmentioning

confidence: 99%

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

Eftekhari

2015

Lat. Am. j. solids struct.

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“…The procedure for solving equations (49) and (50) is similar to that described in the previous section. We assume that an equal number of grid points to be used for approximation of functions W(x, t) and '(x, t).…”

Section: (04x4l)mentioning

confidence: 99%

“…We assume that an equal number of grid points to be used for approximation of functions W(x, t) and '(x, t). By applying the DQ-IQ coupled approach, equations (49) and (50) are reduced to the following system of ODEs in time…”

Section: (04x4l)mentioning

confidence: 99%

A modified differential quadrature procedure for numerical solution of moving load problem

Eftekhari

2015

Proceedings of the Institution of Mechanical Engineers, Part C:

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The differential quadrature method is a powerful numerical method for the solution of partial differential equations that arise in various fields of engineering, mathematics, and physics. It is easy to use and also straightforward to implement. However, similar to the conventional point discretization methods like the collocation and finite difference methods, the differential quadrature method has some difficulty in solving differential equations involving singular functions like the Dirac-delta function. This is due to complexities introduced by the singular functions to the discretization process of the problem region. To overcome this difficulty, this paper presents a combined differential quadrature-integral quadrature procedure in which such singular functions are simply handled. The mixed scheme can be easily applied to the problems in which the location of the singular point coincides with one of the differential quadrature grid points. However, for problems in which such condition is not fulfilled (i.e. for the case of arbitrary arranged grid points), especially for moving load class of problems, the coupled approach may fail to produce accurate solutions. To solve this drawback, we also introduce two simple approximations and show that they can yield accurate results. The reliability and applicability of the proposed method are demonstrated herein through the solution of some illustrative problems, including the moving load problems of Euler-Bernoulli and Timoshenko beams. The results generated by the proposed method are compared with analytical and numerical results available in the literature and excellent agreement is achieved.

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“…However, Yan and Jiang [29] have investigated the electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects. In addition, a new numerical technique, the differential quadrature method, has been developed for dynamic analysis of the nanobeams in the polar coordinate system by Kananipour et al [30]. Moreover, Khater et al [31] have investigated the effect of surface energy and thermal loading on the static stability of nanowires.…”

Section: Introductionmentioning

confidence: 99%

Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

Ebrahimi

Daman²

2016

Journal of Engineering

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To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.

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Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams

Cited by 13 publications

References 7 publications

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

A modified differential quadrature procedure for numerical solution of moving load problem

Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

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