Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler–Pasternak elastic foundations

Mechab, Boubaker; Mechab, Ismail; Benaissa, Samir; Ameri, Mohammed; Sérier, B.

doi:10.1016/j.apm.2015.09.093

Cited by 58 publications

(12 citation statements)

References 23 publications

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“…The effective material properties of the porous FGM-I piezoelectric plate are variables across the thickness direction based on the modified power-law model as [5,16]: …”

Section: The Materials Properties Of Porous Fg Piezoelectric Platesmentioning

confidence: 99%

“…They stated that the volume fraction of porosity has a notable effect on natural frequencies for every material graduation. Mechab et al [16] investigated the effects of porosities in functionally graded small scale plates resting on Winkler-Pasternak elastic foundations. Also, some papers dealing with mechanical behavior of plates made of saturated porous materials are carried out.…”

mentioning

confidence: 99%

“…Moreover, when the porosities are distributed around the cross section mid-zone and the amount of porosity diminishes at the top and bottom of the cross-section. In this case (FGM-II), the effective material properties can be defined by[5,16]:…”

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confidence: 99%

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Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Barati

Shahverdi

Zenkour

2016

Mechanics of Advanced Materials and Structures

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Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. Modified power-law model is adopted to describe the graded material properties of FG piezoelectric plate. Implementing an analytical approach which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters and boundary conditions on vibration of porous FGP plate are discussed. KEYWORDS Downloaded by [University of Cambridge] at 03:23

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“…The effective material properties of the porous FGM-I piezoelectric plate are variables across the thickness direction based on the modified power-law model as [5,16]: …”

Section: The Materials Properties Of Porous Fg Piezoelectric Platesmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Barati

Shahverdi

Zenkour

2016

Mechanics of Advanced Materials and Structures

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“…Similar analysis was developed for porous FG nanoplates with considering size effects by Mechab et al. 63 Ebrahimi et al. 64 analyzed the thermal effect on the free vibration of nanobeams made of nanoporous materials.…”

Section: Introductionmentioning

confidence: 94%

Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field

Karami

Shahsavari

Karami

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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Flexural and longitudinal wave behaviors of nanobeams made of nanoporous-graded materials while surrounded by Winkler-Pasternak foundation, subjected to the longitudinal magnetic field and exposed to the hygrothermal environment are studied analytically. To this end, the governing equation derived by Euler–Bernoulli beam theory in conjunction with the nonlocal strain gradient theory is defined by employing Hamilton’s principle. By adopting an analytic model, the flexural and longitudinal dispersion relations between phase velocity and wave number are derived. The reliability of the present method is confirmed by comparing the obtained results with those stored in the literature. Finally, the effects of the power-law index, porosity volume fraction, nonlocal and material characteristic parameters, uniform temperature and moisture rise, elastic foundation parameters, magnetic field intensity, and wave number are also investigated in detail. It is found that the small-scale parameters are more influential in higher wave numbers where the wavelength is close to the length scale of nanostructures. However, foundation parameters, porosity volume fraction, and longitudinal magnetic field are more influential in lower wave numbers.

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“…The influence of the different parameters is analyzed. A more recent work is due to Mechaba et al [13] which used Monte Carlo method to predict the distribution function of the vibration response of a nanoplate resting on Winkler-Pasternak elastic foundations. The small scale effects were introduced using nonlocal elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Assessing the influence of material and geometrical uncertainty on the mechanical behavior of functionally graded material plates

Carvalho

Silva²,

Loja

et al. 2016

Mechanics of Advanced Materials and Structures

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Composite materials possessing a functional gradient are becoming strong candidates to enhance the performance of structures, when severe operating conditions are a reality. This type of conditions may for example, range from situations where a high thermal gradient is present to others where it is imperative to minimize abrupt stresses transitions between materials interfaces. The manufacturing achievement of the gradients determined for a specific application may in practice face some limitations which can be due, among other factors, to technological process constraints, eventual operating condition deterioration of production stages or to non-conforming raw materials. Regardless the origin of such limitations, the reality is that the uncertainty is always present to some extent, being this clearly reflected in the scattering of material and geometrical properties of these composites. The understanding that deterministic analyses are not enough to provide a complete prediction of the composite structures behavior emphasizes the crucial need to identify the effects that the variability in material and geometrical parameters will produce in the structural response. With the present work, one intends to study the influence of this variability in the static and free vibrations behavior of functionally graded plates. It is also an objective of this study the use of regression models to predict these responses, to characterize the contribution of each model parameter to the explanation of the response variability. To this purpose, a set of numerical results is presented and discussed.

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Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler–Pasternak elastic foundations

Cited by 58 publications

References 23 publications

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field

Assessing the influence of material and geometrical uncertainty on the mechanical behavior of functionally graded material plates

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