Free Vibration of Size-Dependent Functionally Graded Microbeams Based on the Strain Gradient Reddy Beam Theory

The microscale vibration characteristics of microbeams made of functionally graded materials (FGMs) are investigated based on the strain gradient Reddy beam theory capable of capturing the size effect. The non-classical governing differential equations, together with the corresponding boundary conditions, are obtained using Hamilton's principle. Then, the free vibration problem of simply supported FGM microbeams is solved using the Navier solution. The natural frequencies of FGM microbeams are calculated corresponding to a wide range of dimensionless length scale parameters, material property gradient indices, and aspect ratios to illustrate the influences of size effect on the vibrational response of FGM microbeams.