<p>This study presents a thorough mathematical analysis of poro-thermo-dependent vibrations in beams of varying thickness, whose core consists of functionally graded porous materials combined with agglomerated carbon nanotube-reinforced polymers. To improve the precision and dependability of the results, displacements are characterized using higher-order shear deformation theory, and the influence of rotation angle is taken into account to implement stress transformations at designated angles. After deriving the governing motion and boundary conditions differential equations, they are converted to algebraic ones with the aid of the generalized differential quadrature method, and then, a broad evaluation of the effects of various mechanical, physical, and geometrical parameters variations on natural frequencies is provided. As there is no comparable study in the literature, the results of this investigation can serve as standards for future research.</p>