A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Abstract

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

Effect of Corrosion on the Natural and Whirl Frequencies of a Functionally Graded Rotor-Bearing System Subjected to Thermal Gradients

“…They were used as super resistant materials to reduce the generation of thermal stress and improve thermal resistivity in the propulsion systems of spacecraft. Since then, functionally graded materials have gained much importance around the world for various engineering applications [ 1 , 2 , 3 , 4 , 5 ]. Given the wide range of applications, FGMs, when used in harsh environmental conditions at elevated temperatures for long durations of time, can undergo corrosion.…”

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

“…Akbas [31] explored the forced vibration analysis of FG porous deep beams under dynamic loads. Ebrahimi and Jafari [32] investigated the vibration analysis of porous FG beams subjected to various thermal loadings based on higher order shear deformation theory carried out by utilising the Navier solution method. Ebrahimi and Mokhtari [33] presented a transverse vibration analysis of rotating porous functionally graded beams using the differential transform method.…”

Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position

“…Atmane et al [7] presented a free vibrational analysis of FG beams considering porosities using computational shear displacement model. Vibration characteristics of Reddy's FG beams with porosity effect and various thermal loadings are investigated by Ebrahimi and Jafari [8]. Ebrahimi et al [9] analyzed vibration characteristics of temperature-dependent FG Euler's beams with porosity considering the effect of uniform, linear and nonlinear temperature distribution.…”