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Free Vibration Response of Porous FGM Plates Using Finite Element Analysis in Thermal Environment

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Abstract

Background

The functionally graded materials (FGM) have excellent properties that make them suited for mechanical, automobile and aerospace applications. However, the presence of insidious porosity inside the bulk of the FGMs significantly alters their vibration response especially when working under thermal environment as in aero-engines, turbine blades and nuclear power plants.

Purpose

The paper presents a detailed investigation of the thermomechanical response of porous FGM blades that is crucial in order to ensure the safe service life of the structural components. The randomly varying porosity distribution is modelled mathematically using a cosine law whilst the material properties of the FGM constituents (metal and ceramic) are assumed to vary with the absolute temperature.

Methods

A finite element method (FEM)-based model is developed to predict the influence of porosity distribution and thermal gradient on the free vibration response of rotating functionally graded porous FGM fan blades idealised as cantilever pre-twisted rotating plates and shells with varying metal and ceramic FGM constituent combinations. The present formulation is based on first-order shear deformation theory wherein the internal non-linear rotational and thermal strains are taken into account based on suitably derived geometric stiffness matrices.

Results

The non-dimensional frequencies are studied based on variations in crucial parameters like power index, pre-twist angle, plate aspect ratio, porosity distribution pattern, rotational speed, blade taper ratio and thermal gradient across the FGM plate. The natural frequencies for a tapered cylindrical fan blade composed of SUS304/Si3N4 FGM constituents are studied for different temperature and porosity type.

Conclusions

For all the FGM constituent combinations considered, the highest fundamental frequency is observed for Porosity Type 1 followed by no porosity, Porosity Type 3 and Porosity Type 2. For a certain value of the power index, the fundamental frequencies are found to increase with an increase in the rotational speed. On the other hand, there is a reduction in the frequency values with an increase in the thermal gradient for all porosity types owing to internal stresses and material property degradation. The tapering of the fan blades and the porosity gradient are found to have significant influence on their natural frequency in thermal environment.

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Authors and Affiliations

  1. Mechanical Engineering Department, Jadavpur University, Kolkata, 700032, India

    Twisha Dey & Tanmoy Bandyopadhyay

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  1. Twisha Dey
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Correspondence to Tanmoy Bandyopadhyay.

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Dey, T., Bandyopadhyay, T. Free Vibration Response of Porous FGM Plates Using Finite Element Analysis in Thermal Environment. J. Vib. Eng. Technol. 12, 4593–4615 (2024). https://doi.org/10.1007/s42417-023-01139-5

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