Material Properties Of Functionally Graded Beam Research Articles

Implementation of numerical approximations in studying vibration of functionally graded beams

In this investigation, a brief review on three efficient computational techniques viz. Finite Element Method, Differential Quadrature Method and Rayleigh–Ritz Method along with their mathematical formulation to study free vibration of thin Functionally Graded (FG) beams subject to various classical boundary supports have been presented. The deformation of FG beam is based on the framework of classical beam theory. Three different FG beam constituents assumed in this study are Al/Al $$_{2}$$ O $$_{3}$$ , Al/ZrO $$_2$$ and SUS304/Si $$_3$$ N $$_4$$ , in which the first component is meant for the metal constituent and the second for ceramic constituent respectively. The material properties of FG beam are assumed to vary continuously along thickness direction in a power-law form. The objective is to outline exemplary works carried out by various researchers on the concerned problem and also to find the effect of volume fraction of FG constituents on natural frequencies. The natural frequencies of different FG beams under four sets of classical edge supports have been evaluated along with two-dimensional mode shapes after finding the convergence with reference to concerned numerical methods and validation with available literature.

Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities

In this article, static deflection and buckling of functionally graded (FG) nanoscale beams made of porous material are carried out based on the nonlocal Timoshenko beam model which captures the small scale influences. The exact position of neutral axis is fixed, to eliminate the stretching and bending coupling due to the unsymmetrical material change along the FG nanobeams thickness. The material properties of FG beam are graded through the thickness on the basis of the power-law form, which is modified to approximate the material properties with two models of porosity phases. By employing Hamilton's principle, the nonlocal governing equations of FG nanobeams are obtained and solved analytically for simply-supported boundary conditions via the Navier-type procedure. Numerical results for deflection and buckling of FG nanoscale beams are presented and validated with those existing in the literature. The influences of small scale parameter, power law index, porosity distribution and slenderness ratio on the static and stability responses of the FG nanobeams are all explored.

Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions

In this paper, free vibration of functionally graded (FG) beam subjected to all sets of boundary conditions has been investigated using Rayliegh-Ritz method. Different higher-order shear deformation beam theories (SDBTs) have also been incorporated, out of which three SDBTs are proposed in the form of inverse trigonometric functions. The proposed deformation theories satisfy the transverse shear stress conditions at the bottom and top surfaces of the beam. The material properties of FG beam are assumed to vary along thickness direction in power-law form and trial functions denoting the displacement components are expressed as linear combination of algebraic polynomials. Rayleigh–Ritz method is used to estimate frequency parameters in order to handle to all sorts of boundary conditions at the edges with ease. Comparison of frequency parameters is carried out with the available literature in special cases and new results are also provided after checking the convergence of frequency parameters.

Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton\'s principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

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

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.

Semi-analytical Vibration Characteristics of Rotating Timoshenko Beams Made of Functionally Graded Materials

Free vibration analysis of rotating functionally graded (FG) thick Timoshenko beams is presented. The material properties of FG beam vary along the thickness direction of the constituents according to power law model. Governing equations are derived through Hamilton's principle and they are solved applying differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The emphasis is placed on investigating the effect of several beam parameters such as constituent volume fractions, slenderness ratios, rotational speed and hub radius on natural frequencies and mode shapes of the rotating thick FG beam.

Effects of different shear deformation theories on free vibration of functionally graded beams

Abstract Free vibration of functionally graded (FG) beams subjected to different sets of boundary conditions is examined in the present paper. Different higher-order shear deformation beam theories (SDBTs) have been incorporated for the free vibration response of FG beam. The material properties of FG beam are taken in the thickness direction in power-law form and trial functions denoting the displacement components are expressed in algebraic polynomials. The Rayleigh–Ritz method is used to estimate frequency parameters in order to handle to various sets of boundary conditions at the edges in a simple way. Comparison of frequency parameters is carried out with the existing literature in special cases and new results are also provided after checking the convergence of frequency parameters.