Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams

Arefi, Mohammad; Zenkour, Ashraf M.

doi:10.1007/s00339-017-0801-0

Cited by 53 publications

(31 citation statements)

References 34 publications

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“…Substituting (12) and (13) into (15) yields the following constitutive equations: Shock and Vibration 3…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Using strain gradient theory and shear deformation theory, Arefi and Zenkour [12] presented free vibration of a piezoelectric laminated microbeam. Based on nonlocal piezoelasticity theory, Arefi and Zenkour presented size-dependent bending and vibration response of a sandwich piezomagnetic nanobeam with curvature [13] and without curvature [14]. ey also investigated thermo-electro-magneto-mechanical bending behavior of a Sandwich nanoplate with simplysupported boundary conditions [15].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

Yuan

Zhang

Chen

2020

Shock and Vibration

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Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.

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“…Substituting (12) and (13) into (15) yields the following constitutive equations: Shock and Vibration 3…”

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

Yuan

Zhang

Chen

2020

Shock and Vibration

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“…But in present investigation the electric potential is assumed as the combination of a cosine function and a linear function along the thickness direction. The electric potential distribution is assumed by [39–41] and ψ0 is applied electric potentials. According to electric defined in equation (8), the electric fields are derived as …”

Section: Formulationmentioning

confidence: 99%

Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation

Arani

Zamani

2017

Jnl of Sandwich Structures & Materials

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In the present research electro-mechanical bending behavior of sandwich nanoplate with functionally graded porous core and piezoelectric face sheets is carried out. Vlasov’s model foundation is utilized to model the silica Aerogel foundation. Two functions are considered for nonuniform variation of material properties of the core layer along the thickness direction such as Young’s modulus, shear modulus, and density. The governing equations are deduced from Hamilton’s principle based on sinusoidal shear and normal deformation theory. In order to solve seven governing equations, an iterative technique is accomplished. After all, deflection and stresses are verified with corresponding literatures. Eventually, the numerical results reveal that applied voltage, plate aspect ratio, thickness ratio, nonlocal parameter, porosity index, Young’s modulus, and height of silica Aerogel foundation have substantial effects on the electro-mechanical bending response of functionally graded porous sandwich nanoplate.

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“…Yazdi et al [45] presented exact method for the vibrational behavior of nanorods by means of Eringen's theory. Arefi and Zenkour [46][47][48] presented the exact solutions for vibration and bending responses of size-dependent multilayer piezomagnetic curved nanobeams.…”

Section: Introductionmentioning

confidence: 99%

A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

Zenkour

2020

J Braz. Soc. Mech. Sci. Eng.

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The present article presents a simple nonlocal two-unknown shear and normal deformation beam theory to discuss the buckling response of nanorods. The theory uses two variables only and takes under consideration the small-scale impact as well as the inclusion of both shear and normal deformations. The equilibrium equations and end conditions are gained utilizing the principle of virtual work. Different end conditions like pinned, clamped and free are studied. The critical buckling loads are obtained for axially loaded nanorods with different end conditions. The significant of small-scale, shear and normal deformation parameters are investigated. Some validation examples are presented, and the sensitivity of all parameters on the critical and other buckling loads of nanorods may be observed.

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Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams

Cited by 53 publications

References 34 publications

Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation

A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

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