Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration

Xia, Wei; Wang, Lin; Yin, Lei

doi:10.1016/j.ijengsci.2010.04.010

Cited by 265 publications

(70 citation statements)

References 37 publications

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“…The expression for Q x and Q y , can be written in a manner analogous to equations (15) or (17) Following the same procedures as before, it can be shown that Where i , j = 4,5 and h is the total laminate thickness.…”

Section: Formulationmentioning

confidence: 99%

Structural Analysis of Aileron Panel using Finite Element Method

Bharath¹,

Naidu²

2016

IOSR

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Section: Formulationmentioning

confidence: 99%

Structural Analysis of Aileron Panel using Finite Element Method

Bharath¹,

Naidu²

2016

IOSR

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“…equilibrium equation of forces and moment of forces. Soon after that, the modi ed couple stress theory became a popular non-classical theory to develop microbeam and microplate models as well as to deal with the size-dependent problems in MEMS [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

2017

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Abstract. In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam a ected by an electric eld, including the fringing eld e ect, was obtained based on strain gradient elasticity, couple stress, and classical theory. In uences of di erent parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear di erential equation was also solved by using the Homotopy Analysis Method (HAM). The in uence of HAM parameters on accuracy was studied speci cally in the vicinity of the pull-in voltage. Comparison of the results of pull-in voltage indicated that low-voltage good agreement exists between numerical and semi-analytical methods, while HAM results deviated from those of numerical methods at high voltages. Findings indicate that strain gradient and couple stress e ects result in a sti er microbeam than with classical theory. E ects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at di erent voltages and orders of HAM approximation.

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“…Simsek (2010) proposed analytical and numerical solution procedures for vibration of an embedded microbeam under action of a moving microparticle and studied the influences of the material length scale parameter, Poisson's ratio, velocity of the microparticle and the elastic medium constant on the maximum dynamic deflections of the microbeam. A size-dependent nonlinear Euler-Bernoulli beam model was presented by Xia et al (2010). They studied nonlinear size-dependent static bending, postbuckling and the free vibration of beams, and Asghari et al (2010) developed their model for Timoshenko beam theory.…”

Section: Introductionmentioning

confidence: 99%

A multi-spring model for buckling analysis of cracked Timoshenko nanobeams based on modified couple stress theory

Khorshidi

Shariati

2017

jtam

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This paper develops a cracked nanobeam model and presents buckling analysis of this developed model based on a modified couple stress theory. The Timoshenko beam theory and simply supported boundary conditions are considered. This nonclassical model contains a material length scale parameter and can interpret the size effect. The cracked nanobeam is modeled as two segments connected by two equivalent springs (longitudinal and rotational). This model promotes discontinuity in rotation of the beam and additionally considers discontinuity in longitudinal displacement due to presence of the crack. Therefore, this multi--spring model can consider coupled effects between the axial force and bending moment at the cracked section. The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations, boundary and continuity conditions. The influences of crack location, crack severity, material length scale parameter and flexibility constants of the presented spring model on the critical buckling load are studied.

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Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration

Cited by 265 publications

References 37 publications

Structural Analysis of Aileron Panel using Finite Element Method

Structural Analysis of Aileron Panel using Finite Element Method

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

A multi-spring model for buckling analysis of cracked Timoshenko nanobeams based on modified couple stress theory

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