A refined vibrational analysis of the FGM porous type beams resting on the silica aerogel substrate

Taking a look at the previously published papers, it is revealed that there is a porosity index limitation (around 0.35) for the mechanical behavior analysis of the functionally graded porous (FGP) structures. Over mentioned magnitude of the porosity index, the elastic modulus falls below zero for some parts of the structure thickness. Therefore, the current paper is presented to analyze the vibrational behavior of the FGP Timoshenko beams (FGPTBs) using a novel refined formulation regardless of the porosity index magnitude. The silica aerogel foundation and various hydrothermal loadings are assumed as the source of external forces. To obtain the FGPTB's properties, the power law is hired, and employing Hamilton's principle in conjunction with Navier's solution method, the governing equations are extracted and solved. In the end, the impact of the various variables as different beam materials, elastic foundation parameters, and porosity index is captured and displayed. It is revealed that changing hygrothermal loading from non-linear toward uniform configuration results in non-dimensional frequency and stiffness pushing up. Also, Al – Al2O3 as the material composition of the beam and the porosity presence with the O pattern, provide more rigidity in comparison with using other materials and other types of porosity dispersion. The presented computational model in this paper hopes to help add more accuracy to the structures' analysis in high-tech industries.