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Dynamical Characterization of Plates Containing Plane Cracks with Functional Gradient Materials.
Gen Liu1, An Xi2,3, Yunchao Qi4
1School of Advanced Manufacturing Technology, Guangdong Mechanical and Electrical Polytechnic, Guangzhou 510550, China.
This study models functionally graded material (FGM) plates with cracks, revealing how crack length and material properties influence vibration frequencies and modes. Cracks alter vibration patterns and cause asymmetric displacements in FGM plates.
Area of Science:
- Solid Mechanics
- Materials Science
- Vibrational Analysis
Background:
- Functionally Graded Materials (FGM) offer tunable properties by varying composition through thickness.
- Cracks significantly impact structural integrity and dynamic behavior of materials.
- Understanding vibration characteristics is crucial for predicting material performance and failure.
Purpose of the Study:
- To develop a vibration model for functionally graded material (FGM) plates containing embedded planar cracks.
- To analyze the influence of crack parameters and material gradient distribution on the vibrational characteristics of FGM plates.
- To investigate the asymmetric displacement behavior induced by material gradients during vibration.
Main Methods:
- Application of thin plate theory and von Kármán geometric nonlinear strain assumptions.
- Derivation of kinetic and potential energies for different material regions.
- Utilizing the Ritz method with displacement field trial functions to determine natural frequencies and modes.
- Analysis of exponentially graded FGM plates with embedded planar cracks.
Main Results:
- Natural frequencies decrease as crack length increases.
- The presence of cracks modifies nodal line patterns and mode symmetry.
- Relative displacement occurs between the upper and lower crack surfaces during free vibration.
- Material gradient coefficients induce thickness-direction asymmetry and non-uniform displacements.
Conclusions:
- Crack characteristics and material gradient coefficients are critical factors affecting FGM plate vibration.
- Crack presence significantly alters the dynamic response and vibration modes.
- Thickness-wise material asymmetry in FGM plates leads to complex displacement patterns, especially near cracks.

