Micro-inertia effects on the dynamic characteristics of micro-beams considering the couple stress theory

Fathalilou, Mohammad; Sadeghi, Mostafa; Rezazadeh, Ghader

doi:10.1016/j.mechrescom.2014.06.003

Cited by 38 publications

(8 citation statements)

References 21 publications

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“…Asghari et al [11] showed that from the two existing material length-scale parameters in the constitutive equations of the couple stress theory, only one of them would appear. Fathalilou et al [29] showed that bending rigidity of couple stress theory was closer than that of modi ed couple stress theory to the experimental results.…”

Section: Introductionmentioning

confidence: 86%

An analytical Solution for Bending Problem of micro Plate using New Displacement Potential Function

Yakhkeshi

Neya

2019

Scientia Iranica

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In this paper, to include small-scale e ect, the augmented Love Displacement Potential Functions (DPF) are developed for isotropic micro or nano-scale mediums based on couple stress theory. By substituting the new DPF into the equilibrium equations, the governing equations were simpli ed to two linear partial di erential equations of sixth and fourth orders. Then, the governing di erential equations were solved for simply supported rectangular plate using the separation of variable method by satisfying exact boundary conditions without any simpli cation assumptions. Displacements, bending and torsional moments of rectangular plate were obtained for di erent length-scale parameters and aspect and Poisson's ratios. The obtained results were compared with other studies, which showed excellent agreement.

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Section: Introductionmentioning

confidence: 86%

An analytical Solution for Bending Problem of micro Plate using New Displacement Potential Function

Yakhkeshi

Neya

2019

Scientia Iranica

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“…The strain energy density based on the CST can be expressed as [42,45]: u = 1 2 " ij " ij + " ij " ij + 2 ij ij + 2 0 ij ij ; (6) where and are the classic Lam e constant and shear modulus, respectively. Moduli and 0 are constants which correspond to the couple stress e ects.…”

Section: Strain Energymentioning

confidence: 99%

“…In order to overcome this shortcoming, the non-classical theories, such as nonlocal elasticity [35], Couple Stress Theory (CST) [36][37][38], strain gradient theory [39], modi ed couple stress theory [40], etc., have been developed to consider the size e ect on theoretical continuum models. Despite other size-dependent theories, limited research has been conducted on modeling the ultra-small structures using the CST [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

et al. 2017

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Abstract. The present research is devoted to theoretical study of the pull-in performance of double-sided and paddle-type NEMS actuators fabricated from cylindrical nanowire operating in the Casimir regime and in the presence of the centrifugal force. D'Alembert's principle was used to transform the angular velocity into an equivalent static, centrifugal force. Using the couple stress theory, the constitutive equations of the actuators were derived. The equivalent boundary condition technique was applied to obtain the governing equation of the paddle-type actuator. Three distinct approaches, the DuanAdomian Method (DAM), Finite Di erence Method (FDM), and Lumped Parameter Model (LPM), were applied to solve the equation of motion of these two actuators. This study demonstrates the in uence of various parameters, i.e., the Casimir force, geometric characteristics, and the angular speed, on the pull-in performance.

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“…However, due to the nonlinearity of the electrostatic force and the neutral plane tension, MEMS resonators can exhibit typical nonlinear dynamic characteristics. So far, the effects of nonlinearities on the static and dynamic performances of MEMS devices have been discussed in many works of literature [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Mechanical Behaviors of Electrostatic Microbeams with Nonideal Supports

Chang

Zhang

Wang

et al. 2020

Shock and Vibration

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Deviation of the actual system from the ideal supporting conditions caused by micromachining errors and manufacturing defects or the requirement of innovative design and optimization of microelectromechanical systems (MEMS) make the nonideal boundary in the micro-/nanoresonator system receive wide attention. In this paper, we consider the neutral plane tension, fringing field, and nonideal boundary factors to establish a continuum model of electrostatically driven microbeam resonators. The convergent static solution with nine-order Galerkin decomposition is calculated. Then, based on the static solution, a 1-DOF dynamic equation of up to the fifth-order of the dynamic displacement using a Taylor expansion is derived. The method of multiple scales is used to study the effect of spring stiffness coefficients on the primary frequency response characteristics and hardening-softening conversion phenomena in four cases. The various law of the system’s static and dynamic performances with the spring stiffness coefficients is obtained. The conditions for judging the hardening-softening transition are derived. So, adjusting the support stiffness values can be a measure of optimizing the resonator performance.

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Micro-inertia effects on the dynamic characteristics of micro-beams considering the couple stress theory

Cited by 38 publications

References 21 publications

An analytical Solution for Bending Problem of micro Plate using New Displacement Potential Function

An analytical Solution for Bending Problem of micro Plate using New Displacement Potential Function

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

Mechanical Behaviors of Electrostatic Microbeams with Nonideal Supports

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