scholarly journals Vibration analysis of functionally graded materials for cylinder liner used in agricultural engine part

2019 ◽  
Vol 4 (1) ◽  
pp. 258-266
Author(s):  
Anand Prakash ◽  
Shiv Ranjan Kumar ◽  
Rahul Verma
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Vibration Analysis ◽  
Young's Modulus ◽  
Mass Density ◽  
Cylinder Liner ◽  
Functionally Graded ◽  
Power Exponent ◽  
Modulus Ratio ◽  
Engine Part

AbstractThe engine part is one of the major sources of vibration of agricultural machinery such as a tractor. Therefore, vibration analysis of agricultural engine part will improve the engine efficiency and agricultural performance. The main objective of present work was to study the dynamic behavior of functionally graded (FG) structural material for the application as cylinder liner as agricultural engine part. The vibration analysis of functionally graded (FG) beam was performed using Finite Element Method (FEM). A typical simply-supported FG beam was modeled in COMSOL Software, where the upper portion of the beam was alumina and the lower portion was steel. The basic properties of material such as Young’s Modulus and mass density were varied along the thickness according to the power law. The boundary conditions were also modeled, and parametric study was carried out with mass density and young’s modulus. Eigen value problem was solved and in turn natural frequency and mode shapes were obtained. The frequency ratio was calculated and compared for various boundary conditions. The finding of the results indicated that when power exponent was increased from 0 to 5, the nonlinear reduction in frequency was occurred but when power exponent was increased from 5 to 10, linear reduction in frequency was occurred. Also, the increase in power exponent caused the increase in frequency for Young’s Modulus ratio of 0.25 and 0.5, decrease in frequency for Young’s Modulus ratio of 2 and 4 and no change occurred for Young’s Modulus ratio of 1. The first non-dimensional frequency for Clamped-Clamped boundary condition was comparatively more than other boundary conditions and lowest frequency is obtained for Clamped –Free boundary conditions.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

2009 ◽  
Vol 44 (4) ◽  
pp. 249-261 ◽  
Author(s):  
Y P Xu ◽  
D Zhou
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Lower Surface ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Line ◽  
Simply Supported ◽  
Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Manufacturing and Measuring Mechanical Properties of Continuous Functionally Graded Beam

2021 ◽  
Vol 21 (2) ◽  
pp. 7-11
Author(s):  
Ahmed Mansoor Abbood ◽  
Haider K. Mehbes ◽  
Abdulkareem. F. Hasan
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
High Concentration ◽  
Functionally Graded Beam ◽  
Low Concentration ◽  
Graded Material ◽  
Vertical Gravity

In this study, glass-filled epoxy functionally graded material (FGM) was prepared by adopting the hand lay-up method. The vertical gravity casting was used to produce a continuous variation in elastic properties. A 30 % volume fraction of glass ingredients that have mean diameter 90 μm was spread in epoxy resin (ρ = 1050 kg/m3). The mechanical properties of FGM were evaluated according to ASTM D638. Experimental results showed that a gradually relationship between Young’s modulus and volume fraction of glass particles, where the value of Young’s modulus at high concentration of glass particles was greater than that at low concentration, while the value of Poisson’s ratio at high concentration of glass particles was lower than that at low concentration. The manufacture of this FG beam is particularly important and useful in order to benefit from it in the field of various fracture tests under dynamic or cyclic loads.

Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation

2017 ◽  
Vol 21 (8) ◽  
pp. 2700-2734 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
MH Zamani
Keyword(s):  
Young’S Modulus ◽  
Silica Aerogel ◽  
Young's Modulus ◽  
Nonlocal Parameter ◽  
Core Layer ◽  
Functionally Graded ◽  
Electric Field Effect ◽  
Governing Equations ◽  
Model Foundation ◽  
Mechanical Bending

In the present research electro-mechanical bending behavior of sandwich nanoplate with functionally graded porous core and piezoelectric face sheets is carried out. Vlasov’s model foundation is utilized to model the silica Aerogel foundation. Two functions are considered for nonuniform variation of material properties of the core layer along the thickness direction such as Young’s modulus, shear modulus, and density. The governing equations are deduced from Hamilton’s principle based on sinusoidal shear and normal deformation theory. In order to solve seven governing equations, an iterative technique is accomplished. After all, deflection and stresses are verified with corresponding literatures. Eventually, the numerical results reveal that applied voltage, plate aspect ratio, thickness ratio, nonlocal parameter, porosity index, Young’s modulus, and height of silica Aerogel foundation have substantial effects on the electro-mechanical bending response of functionally graded porous sandwich nanoplate.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

scholarly journals Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Shi ◽  
Shuai Zha ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shallow Shell ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
General Boundary ◽  
Volume Distribution ◽  
General Boundary Conditions

The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and Rayleigh-Ritz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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