Transient vibration analysis of strain gradient multi-directional functionally graded microplates under a moving concentrated load

In the study, the modified strain gradient elasticity theory is used to investigate the transient vibrations of the multi-directional functionally graded square microplates subjected to a moving concentrated load by employing a normal and shear deformable plate theory with five unknowns based on the Newmark's method for the first time. In-plane displacement and thickness stretching component of the transverse displacement are approximated by using a rectangular four-noded element with 16 unknows satisfying C1 continuity requirement. In addition, bending and shear components of the transverse displacement are presented by employing a rectangular four-noded element with 24 unknows called as a higher order finite element model (HOFEM) is developed to analyse the dynamic amplification factors and time history analysis of strain gradient multi-directional functionally graded square microplates. The effects of the boundary condition, thickness to material length parameter, gradient index in three directions, aspect ratio, and dimensionless load velocity parameter are examined. It is exhibited based on the results that dynamic amplification factors and dynamic dimensionless center deflections of multi-directional functionally graded strain gradient microplates are significantly affected by the variation of the analysis parameters provided above.