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Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

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Abstract

In this paper, the strain gradient theory (SGT) and two-variable refined plate theory are implemented simultaneously to analyze bending and free vibration of micro-plate. The proposed theory is called two-variable strain gradient theory (TV-SGT). The TV-SGT, which can be used for both thin and moderately thick micro-plates, predicts parabolic variation of transverse shear stresses across the plate thickness and does not need the shear correction factor. The governing equations are obtained using a variational approach and solved analytically to find the deflection of simply supported micro-plate under uniformly distributed loading and natural frequency of this plate. Thereby, the effects of length scale parameters and dimensions on the bending deflection and natural frequency of the micro-plate are investigated. Results show that, strengthen micro-plate has higher shear rigidity. Moreover, it is inferred that TV-SGT is well defined to analyze the micro-plate.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran

    H. Farahmand

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  1. H. Farahmand
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Technical Editor: Paulo de Tarso Rocha de Mendonça, Ph.D.

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Farahmand, H. Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory. J Braz. Soc. Mech. Sci. Eng. 42, 251 (2020). https://doi.org/10.1007/s40430-020-02341-2

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