Vibration and Static Buckling of Rotating BDFGP Microbeams Resting on Variable Elastic Foundations

Abstract

For the first time, a two-node beam element with nine degrees of freedom (DOFs) was developed in this paper using a combination of modified couple stress and kth-order shear deformation beam theory to analyze the free vibration and static buckling responses of rotating bidirectional functionally graded porous (BDFGP) microbeams resting on variable elastic foundations, in which the whole structure was exposed to a magnetic field in the hygrothermal condition. The mechanical properties and the length-scale parameters varied in both the thickness and length directions, which in the novel porosity model and power-law indexes of the material were considered to be a function of the x- and z-coordinates. The present method’s accuracy was determined by comparing it with published findings. Additionally, extensive research was conducted to evaluate the effect of various parameters on the mechanical responses of the rotating BDFGP microbeam. The numerical results showed that porosity coefficient, elastic foundation parameters, and hygrothermal environment all significantly affect the rotating BDFGP microbeam’s free vibration and static buckling behavior.