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A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

Published online by Cambridge University Press:  30 April 2020

Ankur Gupta Open the ORCID record for Ankur Gupta [Opens in a new window] ,
Shashank Soni  and
N. K. Jain
Ankur Gupta*
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Raipur, Chhattisgarh492010, India.
Shashank Soni
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Raipur, Chhattisgarh492010, India.
N. K. Jain
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Raipur, Chhattisgarh492010, India.
*
*Corresponding author (ankurgupta1729@gmail.com)
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Abstract

A non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

Keywords

Star CrackMicro-PlateMultiple CrackFrequency
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 4 , August 2020 , pp. 465 - 484
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

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