An Authoritative Mathematical Procedure for Vibration Investigation of FG Saturated Porous Curved Microbeams Based on Modified Strain Gradient Theory

This study employs a rigorous mathematical method utilizing Fourier series functions to solve the derived differential motion equations of a curved microbeam (CMB) and determine its natural frequencies. The center layer of the CMB consists of functionally graded saturated porous (FGSP) materials, with the fluid pressure in the pores considered by the Skempton coefficient, and the facesheets are carbon nanotubes-reinforced composites (CNT-RC). The Timoshenko beam theory (TBT) and modified strain gradient theory (MSGT), which incorporates three material length scale parameters, are employed to account for shear deformation and scale effects. The findings are provided for various configurations upon validating the results by comparison with straightforward tasks, and the influence of different parameters on the results is examined. Beams, particularly curved ones, are extensively utilized throughout multiple industries, rendering the findings of this study beneficial for these sectors. Given the absence of comparable investigations on such CMBs in the existing literature, the present results can serve as benchmarks for future research.