Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

• Vibration characteristics of cracked isotropic and FGM microplates is presented.
• A single internal material length scale parameter captures the microstructure.
• Linear and nonlinear response curves are shown for cracked isotropic and FGM plates.
• Result shows that frequency of cracked plate is affected by the microstructure.

An analytical model for vibration analysis of partially cracked isotropic and functionally graded rectangular plates is presented based on a modified couple stress theory. A single internal material length scale parameter capturing the microstructure is incorporated in the equation of motion of cracked plates derived using the equilibrium principle. Two crack configurations (i) a single partial continuous line crack and (ii) two perpendicular continuous line cracks located at the centre of the plate are considered for analysis. The effect of the single and the two perpendicular partial cracks is incorporated in the form of moment and in-plane forces based on a simplified line spring model. Berger׳s formulation for the in-plane forces makes the model nonlinear and Galerkin׳s method is used for its solution. Results for the fundamental frequencies as affected by plate aspect ratio, crack length, internal material length scale parameter and gradient index are presented for various boundary conditions. It is found that the microstructure of the plate affects the fundamental frequencies.