Vibration and Buckling of Shear Deformable Functionally Graded Nanoporous Metal Foam Nanoshells

Zhang, Yufei; Zhang, Fei

doi:10.3390/nano9020271

Cited by 24 publications

(5 citation statements)

References 99 publications

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“…Liu and Wang [54] studied free vibration of FG piezoelectric material cylindrical nanoshells with porosites under thermo-electro-mechanical loading in considering small scale effect according to the Love's shell theory and the nonlocal elasticity theory. Also, Zhang and Zhang [55] investigated free vibration and buckling responses of FG nanoporous metal foam nanoshells by using the first-order shear deformation shell theory and Mindlin's most general strain gradient theory.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak’s Foundations in the Thermal Environment

Do Quang Chan,

Bui Gia Phi,

Nguyen Thi Thu Nga

et al. 2024

AAMM

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In this article, the effects of temperature and size-dependent on the buckling behavior of functionally graded (FG) cylindrical nanopanels resting on elastic foundation using nonlocal strain gradient theory are investigated in detail analytical approach. According to a simple power-law distribution, the material properties of FG cylindrical nanopanels are assumed to vary continuously through the thickness direction. The Pasternak model is used to describe the reaction of the elastic foundation on the FG cylindrical nanopanels. The fundamental relations and stability equations are derived by applying the nonlocal strain gradient theory and the classical shell theory based on the adjacent equilibrium criterion. Using Galerkin's method, the mechanical buckling behavior of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment is solved. The reliability of the obtained results has been verified by comparison with the previous results in the literature. Based on the obtained results, the influences of the material length scale parameter, the nonlocal parameter, temperature increment, geometric parameters, material properties, and elastic foundation on buckling behaviors of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment are analyzed and discussed.

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Section: Introductionmentioning

confidence: 99%

An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak’s Foundations in the Thermal Environment

Do Quang Chan,

Bui Gia Phi,

Nguyen Thi Thu Nga

et al. 2024

AAMM

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“…There have been a lot of studies conducted recently to investigate and reveal the mechanical behavior of porous beams, [5][6][7][8][9] porous plates, [10][11][12] and porous shells. [13][14][15][16] Various problems still need to be dealt with extensive research effort before being extended to actual structures.…”

Section: Introductionmentioning

confidence: 99%

Static bending mesh-free analysis of smart piezoelectric porous beam reinforced with graphene platelets

Hung

Duc

Tú

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents static analysis and response of smart piezoelectric porous beams by mesh-free approach. The beam consists of a functionally graded porous core reinforced with graphene platelets (GPLs) and two piezoelectric face layers. The effective material properties of the core vary smoothly through the thickness direction, and they are estimated based upon Halpin–Tsai micromechanical model. The electric potential is assumed to vary linearly across the thickness of the piezoelectric layers. Polynomial basis function-based C1-Hermite interpolation for all displacement and electric potential variables of the problem is proposed for the mesh-free method to discretize the equilibrium equations. Parametric studies are carried out to investigate the effects of material parameters and boundary conditions on the deflection and stresses of the beam subjected to mechanical and/or electrical load(s). Furthermore, the study also highlights the piezoelectric effect on the static bending control of the proposed beam.

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“…For many decades, vibration analysis of mechanical structures was a major topic among scientists [1][2][3][4][5][6][7][8][9][10]. Over recent decades, a surge of interest in studying hyperelastic materials was shown.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

et al. 2021

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In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

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Vibration and Buckling of Shear Deformable Functionally Graded Nanoporous Metal Foam Nanoshells

Cited by 24 publications

References 99 publications

An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak’s Foundations in the Thermal Environment

An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak’s Foundations in the Thermal Environment

Static bending mesh-free analysis of smart piezoelectric porous beam reinforced with graphene platelets

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

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