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Random free vibration analysis of porous functionally graded cantilever plates

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Abstract

The present study outlines the stochastic framework to address the dynamic behavior of the porous functionally graded cantilever plates. The intrusive variability in the fundamental material properties of the porous structures composed of functionally graded materials (FGM) influences the system's desired operational behavior. This creates a strong rationale to quantify the extremes of the structural behavior of porous FGM subjected to practically relevant randomness in material properties. The conventional finite element (FE) analysis is carried out on the porous FGM plate which is imposed with the random material properties. The material properties of porous functionally graded plates are determined by using the power law distribution. The randomness in the inherent material properties (such as elastic young’s modulus, shear modulus, Poisson’s ratio and mass density) of the plates is enforced by implementing the Monte Carlo simulations (MCS). The randomly varied material properties are fed to the FE analysis to determine the first three natural frequencies of the cantilever FGM structure. The proposed stochastic framework is further extended to ascertain the effects of different parameters such as degree of randomness, thickness of the plate, working temperature, porosity index and power law exponent on the dynamic response of the FG plates. The present study also elucidates the comparative dynamic behavior of non-porous, evenly porous and unevenly porous FGM plates. Further, the statistical analysis is carried out to determine the material property with the relatively higher influence on the dynamic behavior of the FG plates. Such an MCS coupled with FE analysis reveals the detailed probabilistic dynamic behavior of the FG cantilever plates, which will aid in the bottom-up design of application-specific light weight structures.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Silchar, India

    H. P. Raturi & S. Dey

  2. Department of Mechanical Engineering, Parul Institute of Engineering and Technology, Parul University, Vadodara, India

    P. K. Karsh

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  1. H. P. Raturi
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  2. P. K. Karsh
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  3. S. Dey
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Correspondence to P. K. Karsh.

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Technical Editor: Andre T. Beck.

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Raturi, H.P., Karsh, P.K. & Dey, S. Random free vibration analysis of porous functionally graded cantilever plates. J Braz. Soc. Mech. Sci. Eng. 44, 598 (2022). https://doi.org/10.1007/s40430-022-03906-z

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  • DOI: https://doi.org/10.1007/s40430-022-03906-z

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