Dynamic pull-in instability of a micro-actuator made from nonlinear elasticity materials

Jian-she, Peng; Yang, Lijun; Yang, Jie

doi:10.1088/0964-1726/23/6/065023

Cited by 12 publications

(6 citation statements)

References 22 publications

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“…Therefore, in this paper, this model, presented in equation (2), is going to be used in the first integrant in equation (1) to include the effects of material nonlinearity on the magneto-elastic behavior of the embedded nanobeams. The appropriateness of the model was proved experimentally [46] and applied already in computational studies [49][50][51][52].…”

Section: Mathematical Formulationmentioning

confidence: 94%

Effects of combined material and geometric nonlinearities on dynamic response of embedded nanobeams

Fakhrabadi¹

2020

Phys. Scr.

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Exact prediction of the mechanical behavior of nano-sensors and nano-actuators directly depends on the models applied to analyze their nano-components. From their dynamic behavior point of view, despite many studies related to the geometrical nonlinearities in modeling the nanostructures, one of the main issues that has not been addressed appropriately is the effects of material nonlinearity. Hence, this paper intends to fill this gap and deals with an investigation of combined geometrical and material nonlinearities on the nonlinear dynamic response of the embedded nanobeams in their free vibration as well as the primary and superharmonic resonances. The material nonlinearity considered in this research is formulated based on the sum of linear and cubic relations between the stress and strain. The results reveal that, for the material and boundary conditions of the embedded nanobeam studied in this research, the material nonlinearity tries to cause softening effects while the geometrical nonlinearity attempts to make hardening influences. The competition between these two effects leads to interesting nonlinear behaviors of the nanobeam for different dimensions and dynamic regimes that are scrutinized in this paper. In addition, the effects of applying external magnetic fields on the nonlinear responses of the nanobeams are investigated.

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Section: Mathematical Formulationmentioning

confidence: 94%

Effects of combined material and geometric nonlinearities on dynamic response of embedded nanobeams

Fakhrabadi¹

2020

Phys. Scr.

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“…On basis of the normal stress-strain constitutive relationships of nonlinear elasticity materials mentioned above, we had done some work to study their mechanical behavior and dynamics. By using a first and third powers function to fit the nonlinearly elastic normal stress-strain model of Al-1%Si (Florando and Nix, 2005), a typical case of nonlinear elasticity material, we had obtained the results of some work such as a nonlinear dynamic analysis (Peng et al, 2014b) and the dynamic pull-in instability (Peng et al, 2014a) of micro-actuators and nonlinear electrodynamic analysis (Peng et al, 2017) and nonlinear free vibration (Lin et al, 2021) of sizedependent microbeams, where the studied structures were made of Al-1%Si. The obtained results showed that the effect of nonlinear elasticity was important, in other words, nonlinearly elastic normal stress-strain constitutive relationships softened bending stiffness and lateral vibration frequencies compared with approximatelysimplified linear ones.…”

Section: Mmms 184mentioning

confidence: 99%

“…By using a first and third powers function to fit the nonlinearly elastic normal stress-strain model of Al-1%Si (Florando and Nix, 2005), a typical case of nonlinear elasticity material, we had obtained the results of some work such as a nonlinear dynamic analysis (Peng et al. , 2014b) and the dynamic pull-in instability (Peng et al. , 2014a) of micro-actuators and nonlinear electro-dynamic analysis (Peng et al.…”

Section: Introductionmentioning

confidence: 99%

An indirect method to determine nonlinearly elastic shear stress-strain constitutive relationships for nonlinear torsional vibration of nonlinearly elastic shafts

Fan

Jian-she²,

Xue³

et al. 2022

MMMS

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PurposeIn this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.Design/methodology/approachIn this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.Findings The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.Originality/valueThe study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

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“…On the other hand, because the elastic moduli of NcMs are likely to decrease due of the interface effect, the material structure can affect the rigidity through a softening mechanism depending on the grain size. Therefore, the classical mathematical models [17,[55][56][57] lose the accuracy to estimate the pull-in voltage values of actuated beams. Moreover, including only couple stress effect in the mathematical model [32,33,34] results in an overestimation of the pull-in voltage values of actuated beams.…”

Section: Materials Structure and Couple Stress Effects On The Static Dmentioning

confidence: 99%

Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications

Shaat

Abdelkefi

2015

International Journal of Mechanical Sciences

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Dynamic pull-in instability of a micro-actuator made from nonlinear elasticity materials

Cited by 12 publications

References 22 publications

Effects of combined material and geometric nonlinearities on dynamic response of embedded nanobeams

Effects of combined material and geometric nonlinearities on dynamic response of embedded nanobeams

An indirect method to determine nonlinearly elastic shear stress-strain constitutive relationships for nonlinear torsional vibration of nonlinearly elastic shafts

Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications

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