A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory

In this research, we analyze size-dependent bending and vibration of microbeams made of porous metal foams. The porous microbeam model is developed based on the sinusoidal beam theory and the modified strain gradient theory. Hamilton’s principle is employed to obtain the governing equations and boundary conditions of the porous microbeam. Analytical solutions are presented for deflections and natural frequencies of the porous microbeam by using Navier’s method. The influences of the porosity distribution, the porosity coefficient, the slenderness ratio, and the microbeam thickness are clarified on the static bending and free vibration of porous microbeams. These findings can be applied to the design of metal foam microstructures in engineering.