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Intermediate Strain Rate Material Characterization with Digital Image Correlation
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Vibration analysis of structural elements using differential quadrature method.

Mohamed Nassar1, Mohamed S Matbuly2, Ola Ragb2

  • 1Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt.

Journal of Advanced Research
|February 17, 2015
PubMed
Summary

This study analyzes free vibration in cracked cantilever beams using the differential quadrature method. Results validated against prior research, offering insights into vibration frequencies influenced by material and foundation properties.

Keywords:
CrackDifferential quadratureIrregular boundariesVibration

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Area of Science:

  • Mechanical Engineering
  • Structural Dynamics
  • Materials Science

Background:

  • Free vibration analysis is crucial for understanding structural integrity.
  • Functionally graded materials (FGMs) offer tailored mechanical properties.
  • Cracks significantly alter a structure's dynamic behavior.

Purpose of the Study:

  • To investigate the free vibration of a cracked cantilever beam made of FGM on an elastic foundation.
  • To apply the differential quadrature method (DQM) for analyzing complex structural dynamics.
  • To explore the influence of cracks and foundation models on natural frequencies.

Main Methods:

  • Employing the differential quadrature method (DQM) for free vibration analysis.
  • Simulating crack effects using a line spring model.
  • Utilizing a Winkler-Pasternak foundation model for elastic support.
  • Applying geometric mapping with DQM for irregular geometries.

Main Results:

  • The DQM accurately predicts natural frequencies for cracked FGM beams on elastic foundations.
  • Results show good agreement with existing literature, validating the proposed methodology.
  • Parametric studies reveal the impact of geometric and elastic properties on vibration frequencies.

Conclusions:

  • The DQM is an effective numerical tool for analyzing free vibrations of cracked FGM structures.
  • Crack presence and foundation characteristics substantially influence the dynamic response.
  • The study provides a foundation for designing more resilient FGM structures.