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Effect of porosity inclusions on the natural frequencies of the FGM plates using dynamic stiffness method

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Abstract

In the present article, an exact solution has been given to investigate the influence of porosity inclusion, boundary conditions, and volume fraction index on the vibration response of functionally graded material (FGM) plates using the dynamic stiffness method (DSM). The material properties of FGM are continuously changing along the thickness direction of plates according to the power law with even porosity inclusion. Classical plate theory (CPT) along with the concept of a physical neutral surface is employed to develop the governing differential equation of motion by using Hamilton's principle. The levy type (closed form) solution is used to develop the dynamic stiffness matrix. The Wittrick-Williams algorithm has been employed to compute the exact natural frequency of the FGM plates with porosity inclusion. The efficacy and authenticity of the present formulation have been ascertained by comparing the present results with those of the literature. A comprehensive parametric study has been performed to compute the influence of various geometric and boundary configurations on the vibration response of the FGM plates.

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Authors and Affiliations

  1. School of Engineering, Shiv Nadar University, Gautam Buddha Nagar, Noida, 201314, India

    Saurabh Rai & Ankit gupta

  2. Department of Mechanical Engineering, SR University, Warangal, 506371, India

    Subodh Kumar

  3. Division of Research and Innovation, Uttaranchal University, Dehradun, Uttarakhand, India

    Rajesh Singh

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  1. Saurabh Rai
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  2. Subodh Kumar
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Correspondence to Ankit gupta.

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Rai, S., Kumar, S., Singh, R. et al. Effect of porosity inclusions on the natural frequencies of the FGM plates using dynamic stiffness method. Int J Interact Des Manuf 17, 2723–2730 (2023). https://doi.org/10.1007/s12008-022-01170-y

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