A micro scale Timoshenko beam model based on strain gradient elasticity theory

Wang, Binglei; Zhao, Jianguo; Zhou, Shenjie

doi:10.1016/j.euromechsol.2009.12.005

Cited by 394 publications

(178 citation statements)

References 38 publications

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“…In Equation (10), the deviator stretch gradient tensor, symmetric gradient rotation tensor, and corresponding dilatation are defined as [2]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…To capture the effect of various parameters in micro-and nanoscale, some new theories have been developed. Eringen's nonlocal [1] and strain gradient [2] theories have been proposed to capture the effect of material length scale parameters in nano-and microscales, respectively. Studying the behavior of a three-layer microbeam can present important informations for researchers.…”

Section: Introductionmentioning

confidence: 99%

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Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied. ARTICLE HISTORY

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“…In Equation (10), the deviator stretch gradient tensor, symmetric gradient rotation tensor, and corresponding dilatation are defined as [2]:…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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“…As from previous considerations, the boundary conditions of the model involve, only, the local generalized forces and/or the prescribed displacements at the borders as N (l) (x 3i , t) = ∓N i , T (l) (x 3i , t) = ∓T i and M (l) (x 3i , t) = ±M i or, alternatively, the prescribed kinematic field reads u(x 3i , t) = u i (t), v(x 3i , t) = v i (t) and ϕ(x 3i , t) = ϕ i (t) with u i (t), v i (t) and ϕ i (t) (i = 0, L) denoting prescribed displacements and rotations at the ends of the beam. The MB Timoshenko beam model, governed by equation (3.3), along with the boundary conditions, exhibits non-local effects for general loading conditions [31,32] and not necessarily for distributed loads only, thus overcoming the paradox encountered in earlier studies [33][34][35][36][37][38]. The MB Timoshenko beam model is very versatile because it may reproduce a variety of material behaviours, either stiffer or softer than the local one, by proper selection of the physical parameters and the internal length scale of the material l 0 governing the maximum distance beyond which the long-range forces become negligible.…”

Section: The Mechanically Based Timoshenko Beam Modelmentioning

confidence: 99%

The mechanically based non-local elasticity: an overview of main results and future challenges

Paola¹,

Failla²,

Pirrotta³

et al. 2013

Phil. Trans. R. Soc. A.

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The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this pape

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“…They revealed that the static deformation obtained by the non-classical continuum theory is generally lower than that of the classical beam model. Wang et al [32] presented a refined Timoshenko beam formulations based on the strain gradient elasticity theory which can be easily reduced to those of the classical Timoshenko beam model. Ansari et al [33] studied the size-dependent free vibration behavior of Timoshenko microbeams made of functionally graded materials (FGMs) based on the modified strain gradient elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

Ansari

Pourashraf

Gholami

et al. 2015

International Journal of Optomechatronics

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In the present study, the resonant frequency and flexural sensitivity of atomic force microscope (AFM) microcantilevers are predicted incorporating size effects. To this end, the modified strain gradient elasticity theory is applied to the classical Euler-Bernoulli beam theory to develop a non-classical beam model which has the capability to capture sizedependent behavior of microcantilevers. On the basis of Hamilton's principle, the sizedependent analytical expressions corresponding to the frequency response and sensitivity of AFM cantilevers are derived. It is observed that by increasing the contact stiffness, the resonant frequencies of AFM cantilevers firstly increase and then tend to remain constant at an especial value. Moreover, the resonant frequencies of AFM cantilevers obtained via the developed non-classical model is higher than those of the classical beam theory, especially for the values of beam thickness close to the internal material length scale parameter.

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A micro scale Timoshenko beam model based on strain gradient elasticity theory

Cited by 394 publications

References 38 publications

Transient analysis of a three-layer microbeam subjected to electric potential

Transient analysis of a three-layer microbeam subjected to electric potential

The mechanically based non-local elasticity: an overview of main results and future challenges

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

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