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Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support

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Abstract

This paper presents the influence of randomness in material properties on the vibration response of functionally graded (FG) nanoplates using the nonlocal continuum model. Material properties such as Elastic modulus, Poisson’s ratio, and volume fraction index are modeled as independent random variables. A trigonometric shear-strain shape function-based refined shear deformation theory in conjunction with non-local theory has been presented for the first time to investigate the stochastic vibrational response of FG nanoplate. An efficient stochastic finite element formulation has been documented to capture the first- and second-order statistics of natural frequency. The first-order perturbation technique has been used to accommodate the effect of various material uncertainties parameters. The effective material properties have been computed using the recently developed modified rule of mixture to incorporate the porosity inclusion. The influence of conventional and unconventional (partial support) boundary constraints, porosity inclusion, small-scale effects, and material uncertainties on the vibration response of FG plates has been investigated in detail. In addition to this, the sensitivity of the functionally graded nanoplate has been observed in response to initial geometrical imperfection. It is observed that the variations in elastic modulus have a significant influence on the stochastic characteristics compared to Poisson’s ratio.

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    Yogesh Kumar & Ankit Gupta

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Kumar, Y., Gupta, A. Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support. Arch Appl Mech 92, 1053–1081 (2022). https://doi.org/10.1007/s00419-021-02092-z

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