Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change

Jia, Xiaoli; Ke, Liao-Liang; Feng, Chun-Bo; Yang, Jie; Kitipornchai, S.

doi:10.1016/j.compstruct.2015.08.044

Cited by 41 publications

(17 citation statements)

References 41 publications

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“…It is assumed that material properties of the microbeam, such as Young's modulus (E) and mass density (ρ) vary linearly in the axial direction according to a power law function which can be described by [39]:…”

Section: Modeling Axially Functionally Graded Materialsmentioning

confidence: 99%

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Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

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In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

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Section: Modeling Axially Functionally Graded Materialsmentioning

confidence: 99%

“…Jia et al [39] examined the effect of length-scale parameters on the nonlinear vibration behavior of an FG microbeam. Ebrahimi and Zia [40] studied the large-amplitude nonlinear vibration of FG Timoshenko beams made of porous material.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Alimoradzadeh

Salehi

Esfarjani

2020

Period. Polytech. Mech. Eng.

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“…Using the modified couple stress theory and the Hamilton principle, the following non-dimensional governing equation of motion is obtained [ 33 ]:

where

for the clamped-clamped (C-C) boundary conditions and

for the clamped-free (C-F) boundary conditions. Some authors [ 45 , 46 , 47 ] studied the effects of curvature-related and inertial-related nonlinearities on the vibrational response for cantilever beams.…”

Section: Dynamic Modeling and Equations Of Motionmentioning

confidence: 99%

“…Uncontrolled variation of electrostatic voltage may lead to instability in the dynamical behavior. Jia et al [ 32 , 33 ] studied free vibration and the pull-in instability of functionally graded poly-SiGe micro-beams. Also, the free vibration characteristics of micro-switches under combined electrostatic, intermolecular forces and axial residual stress have been studied [ 34 ].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

et al. 2017

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Micro functionally graded material (FGM) structures are able to have proper functions in vast environments. In this paper, nonlinear governing equations of the size-dependent micro-switch are derived using modified couple stress theory. Effective external forces including fringing field of electrostatic force and Casimir force are considered. Two electrodes cooperate to track the in-plane motions of the micro continuous system by tuning the supply voltages of the electrostatic force. An adaptive projection law is proposed to compensate for the effect of error in the initial estimates of system parameters. To achieve more reliability, a robust active vibration strategy is presented to withstand external disturbances. At any time, just one electrode is operational, and optimization is performed to decrease the controller gains. The highly nonlinear inputs have a singularity in the dynamics of the system, which are known as pull-in instability, so for safety, the controller gains are chosen such that the pull-in voltage is avoided. The dynamic response of the system is simulated using a single mode or multiple modes to validate the effectiveness of the presented vibration control approaches. The effects of error of the initial estimate of system parameters, the effect of impulse and the influences of various volume fractions are studied.

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“…Yaghoobi and Fereidoon [7] carried out the bending analysis of simply supported FG beam under uniformly distributed load and commented on the influence of the neutral surface position on deflection. Jia et al [8] studied the size effect on the free vibration of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force based on Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. Ebrahimi and Salari [9] represented the thermal effect on buckling and free vibrational behaviours of functionally graded (FG) size-dependent Timoshenko nanobeams loaded to an in-plane thermal loading by implementing a Navier type solution.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Lohar¹,

Mitra

Sahoo³

2016

IFSL

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Abstract.A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton's principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change

Cited by 41 publications

References 41 publications

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

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