New higher-order shear deformation theory for bending analysis of the two-dimensionally functionally graded nanoplates

Wang, Qikai; Ai-qin, Yao; Dindarloo, Mohammad Hassan

doi:10.1177/0954406220952816

Cited by 19 publications

(8 citation statements)

References 60 publications

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“…Considering the various shear deformation theories, the small linear displacements of u , v , and w of the face sheets along the x, y (longitudinal), and z (thickness) axes are expressed by the following formulae (1): In this study, a new shear strain functionis modeled after equation (2). This new higher-order shear deformation theory 28 guides the shape as an accurate combination of the exponential, trigonometric, and polynomial functions as presented below: where z i is the vertical coordinate of each face sheet ( i = t , b ), measured upward from the mid-plane of each face sheet. The strain-displacement relations based on the presented displacement field can be expressed by: where Despite the fact that earlier studies did not pay attention to surface tension in the core, the current study assumed that it can tolerate the tension and assessed this effect.…”

Section: Methodsmentioning

confidence: 99%

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Comparison of the application of smart electrorheological and magnetorheological fluid cores to damp sandwich panels’ vibration behavior, based on a novel higher-order shear deformation theory

Keshavarzian

Najafizadeh

Khorshidi

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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Background: Magnetorheological and electrorheological materials show variations in their rheological properties when subjected to magnetic and electric fields. We analyzed the vibration control behavior of a sandwich panel with elastic face sheets and an electrorheological or magnetorheological fluid core, using an improved higher-order theory. The theory was applied to the analysis of the structure's components as a combination of exponential, trigonometric, and polynomial functions. The core's flexibility was analyzed based on Frostig's second model, which has attracted material science researchers’ attention. Methods: Using the new theory, we analyzed the transverse shear and rotary inertia effects of the cover sheets. The governing equations and boundary conditions were derived by Hamilton's principle. The natural frequencies and loss factors were derived by solving the eigenvalue problem. The effects of changing the geometric parameters, the thickness of the magnetorheological or electrorheological layer, and thickness ratios on the vibration behavior of the panel were determined. Results: The panel's natural frequencies increased when the magnetic or electric field strength, and the panel's aspect ratio increased. It decreased when the core to panel thickness ratio increased. The magnetorheological material showed higher strength and lower sensitivity to external impurities than did the electrorheological material. Conclusions: We conclude that the magnetorheological materials minimize the structure's vibration at high-frequency operation, and the electrorheological materials are optimal for minimizing the structure's vibration at lower frequency operation. The findings of this study are useful to better understand the vibration behavior of sandwich panels with laminates under free vibration conditions.

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Section: Methodsmentioning

confidence: 99%

“…is modeled after equation (2). This new higher-order shear deformation theory 28 guides the shape as an accurate combination of the exponential, trigonometric, and polynomial functions as presented below:…”

Section: Kinematicsmentioning

confidence: 99%

Comparison of the application of smart electrorheological and magnetorheological fluid cores to damp sandwich panels’ vibration behavior, based on a novel higher-order shear deformation theory

Keshavarzian

Najafizadeh

Khorshidi

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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“…The variation of kinetic energy induced by spinning speed and fluid flow velocity of the system is defined as 53 …”

Section: Mathematical Formulationmentioning

confidence: 99%

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

Liu

Ruonan

Koochakianfard

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the present investigation, with the aim of performance improvement of size-dependent bi-gyroscopic structures, the vibrational behavior of spinning small-scale tunes conveying fluid embedded in various foundations subjected to distributed tangential load and hygro-thermo-magnetic environments by including gravitational effect is investigated. The modified couple stress theory is used to study the microscale tube, and the modified nonlocal theory is utilized to model the nanoscale tubes. A parametric investigation is also conducted to highlight the impacts of various key factors such as gravity, flow profile modification factor, fluid velocity, spinning speed, substrate coefficients, boundary conditions, size-dependent parameters, and environmental attacks on divergence and flutter thresholds of the structure. The dynamical equations are solved using Laplace transformation as well as Galerkin discretization techniques, and forward and backward frequencies are identified accordingly. Meanwhile, the instability borders of the system are obtained analytically. Campbell and stability diagrams, and the time history of the system, are acquired. The results revealed that contrary to influences of gravity, magnetization, and size-dependent parameters, the compressive tangential load and humidity have decreasing effects on the vibrational frequencies and make the system prone to experience static and dynamical instabilities. Moreover, it is determined that applying the viscous foundation eliminates the re-stabilization zone in the system stability evolution, and after the occurrence of the divergence phenomenon, the system immediately undergoes the flutter instability.

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“…Many researchers have also done various studies on FGM plates' vibration analysis to use it effectively and efficiently. Wang et al 18 proposed a new HSDT model for the flexure analysis of FGM plate via the Galerkin method. Aydogdu 19 introduced a new HSDT laminated composite plate theory using an inverse method for the structural response.…”

Section: Introductionmentioning

confidence: 99%

New HSDT for free vibration analysis of elastically supported porous bidirectional functionally graded sandwich plate using collocation method

Kumar

Bajaj

Singh

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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The present paper deals with the free vibration response of elastically supported porous bidirectional functionally graded soft-core sandwich rectangular plate with proposed new tangent shape function-based higher-order transverse shear deformation theory. The theory is accomplished to uphold the continuity of transverse shear stresses and zero shear stress conditions on both the extreme surfaces of a plate. The bidirectional gradation varies through the thickness ( z-axis) and length ( x-axis) directions. The effective material properties are calculated via the modified power-law. The governing differential equations (GDEs) of motion are acquired via the Hamilton principle. The inverse multi-quadric radial basis function-based Collocation method is implemented to discretize the GDEs obtained by strong form formulation. The current theory and method’s accuracy and efficacy are validated by comparing the present results with existing results in the literature. Studies show that the results of the proposed theory are in close agreement with 3D approach. Numerical results are obtained with a different scheme of sandwich layers for free vibration analysis. Effects of grading index, porosity fraction, two parameters foundation, different scheme, and the span to thickness ratio on free vibration response have been discussed. New results for free vibration response in porous media are presented with different skin materials.

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New higher-order shear deformation theory for bending analysis of the two-dimensionally functionally graded nanoplates

Cited by 19 publications

References 60 publications

Comparison of the application of smart electrorheological and magnetorheological fluid cores to damp sandwich panels’ vibration behavior, based on a novel higher-order shear deformation theory

Comparison of the application of smart electrorheological and magnetorheological fluid cores to damp sandwich panels’ vibration behavior, based on a novel higher-order shear deformation theory

Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

New HSDT for free vibration analysis of elastically supported porous bidirectional functionally graded sandwich plate using collocation method

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