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Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

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The paper presents the studies on the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's thirdorder shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. |

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