Thermo-Mechanical Vibration Analysis of Imperfect Inhomogeneous Beams Based on a Four-Variable Refined Shear Deformation Beam Theory Considering Neutral Surface Position

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of porous functionally graded (FG) beams by considering neutral surface position and different thermal loadings via a four-variable shear deformation refined beam theory. Four types of environmental conditions through the z-axis direction are supposed as: uniform (UTR), linear (LTR), nonlinear (NLTR) and sinusoidal (STR) temperature rises. Mechanical properties of porous FG beams are supposed to vary through the thickness direction and are modeled via the modified power-law. The modified power-law is formulated using the concept of even and uneven porosity distributions. Since the variation of pores along the thickness direction influences the mechanical properties, porosity plays a key role in the mechanical response of FG structures. The governing differential equations and related boundary conditions of porous FG beams are subjected to temperature field that is derived by Hamilton's principle based on a four-variable refined theory which verifies shear deformation regardless of any shear correction factor. The Navier-type solution procedure is used to achieve the natural frequencies of porous-FG beams supposed to various thermal loadings which satisfies the simply-simply boundary condition. A parametric study is led to carry out the effects of material graduation exponent, porosity volume fraction, different porosity distribution, and thermal effect on dimensionless frequencies of porous FG beams. It is concluded that these parameters play noticeable roles in the vibration behavior of imperfect FG beams. Presented numerical results can be applied as benchmarks for future designs of imperfect FG structures with porosity phases.