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Free vibration and buckling analyses of FG porous sandwich curved microbeams in thermal environment under magnetic field based on modified couple stress theory

Arshid Ehsan, Arshid Hossein, Amir Saeed, Mousavi S. Behnam

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 1

89--111

EN

Porous sandwich structures include different numbers of layers and are capable of demonstrating higher values of strength to weight ratio in comparison with traditional sandwich structures. Free vibration and mechanical buckling responses of a three-layered curved microbeam was investigated under the Lorentz magnetic load in the current study. A viscoelastic substrate was considered and the effect of the thermal environment on its mechanical properties was assessed. The core was composed of the functionally graded porous materials whose properties changed across the thickness based on some given functions. The face sheets were FG-carbon nanotube-reinforced composites and the influence of the placement of CNTs was evaluated on the behavior of the faces. Using the extended rule of mixture, their effective properties were determined. Modified couple stress theory was used to predict the results in the micro-dimension. While the governing equations were derived based on the higher order shear deformation theory and energy method, and mathematically solved via Navier’s method. The results were validated with the previously published works, considering the effects of various parameters. As comprehensively explained in the results section, natural frequencies and critical buckling loads were reduced by enhancing the central opening angle. Moreover, an increase in the porosity coefficient declined the mentioned values, but increasing the CNTs content showed the opposite effect. The outcomes of this study may help in the design and manufacturing of various equipment using such smart structures, making high stiffness to weight ratios more accessible.

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Response of thermoelastic microbeam with double porosity structure due to pulsed laser heating

Kumar Rajneesh, Vohra Richa

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

76--85

EN

The present investigation is concerned with vibration phenomenon of a homogeneous, isotropic thermoelastic microbeam with double porosity (TDP) structure induced by pulsed laser heating, in the context of Lord-Shulman theory of thermoelasticity with one relaxation time. Laplace transform technique has been applied to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field, and temperature distribution. The resulting quantities are recovered in the physical domain by a numerical inversion technique. Variations of axial displacement, axial stress, lateral deflection, volume fraction field, and temperature distribution with axial distance are depicted graphically to show the effect of porosity and laser intensity parameter. Some particular cases are also deduced.

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Modified Couple Stress Theory for Micro-Machined Beam Resonators with Linearly Varying Thickness and Various Boundary Conditions

Zenkour A. M.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 1

43--64

EN

This article employs the classical Euler–Bernoulli beam theory in connection with Green–Naghdi’s generalized thermoelasticity theory without energy dissipation to investigate the vibrating microbeam. The microbeam is considered with linearly varying thickness and subjected to various boundary conditions. The heat and motion equations are obtained using the modified couple stress analysis in terms of deflection with only one material length-scale parameter to capture the size-dependent behavior. Various combinations of free, simply-supported, and clamped boundary conditions are presented. The effect of length-to-thickness ratio, as well as the influence of both couple stress parameter and thermoelastic coupling, are all discussed. Furthermore, the effect of reference temperature on the eigenfrequency is also investigated. The vibration frequencies indicate that the tapered microbeam modeled by modified couple stress analysis causes more responses than that modeled by classical continuum beam theory, even the thermoelastic coupled is taken into account.