PSI - Issue 79

Pranaw Parihar et al. / Procedia Structural Integrity 79 (2026) 404–412

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(a)

(b)

Fig. 5: (a) E ff ect of crack length at di ff erent normalized natural frequency vs modes (b) E ff ect of crack orientation in di ff erent boundary conditions.

in moderate sti ff ness and frequency. The SFSF plate, which has two free and two simply supported edges, is the most flexible case and is seen in Fig. 5(a) the lowest natural frequency. From the above data it is seen that reducing boundary restraint decreases sti ff ness and leads to a corresponding reduction in natural frequency.

6. Conclusions

• This study developed an HSDT-based XIGA framework for vibration analysis of cracked bi-directional func tionally graded plates. • The higher-order continuity requirement of HSDT e ffi ciently represents geometric features with NURBS, and models cracks using enrichment functions. • The normalized natural frequencies increase as the plate thickness decreases, following the trend b / h = 100 > 50 > 20 > 5. • Boundary conditions significantly influence the dynamic response, with frequencies ordered as CCCC > SSSS > CFCF > SFSF. • The presence of cracks reduces the natural frequencies. Frequencies decrease as crack length increases, for instance, d / a = 0 . 5 > 0 . 7. Overall, the combination of XIGA and HSDT provides a robust and reliable framework for analyzing the vibrational characteristics of cracked FGM plates under various geometrical, extended to thermal e ff ects and boundary conditions.

Acknowledgements

The corresponding author gratefully acknowledges the Anusandhan National Research Foundation for financial support under the International Travel Support Scheme (Grant No. ITS / 2025 / 003293) to present this work at the IGF28-MedFract3 Conference. The authors also thank the Indian Institute of Technology Patna for partial financial support.