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

2020 ◽  
Vol 10 (22) ◽  
pp. 8197
Author(s):  
Prabhakar Sathujoda ◽  
Aneesh Batchu ◽  
Bharath Obalareddy ◽  
Giacomo Canale ◽  
Angelo Maligno ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Power Law ◽  
Inner Core ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Linear Temperature ◽  
Volume Fractions ◽  
Rotor Bearing ◽  
Bearing System

The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Finite Element Analysis for Dynamic Response of Rotor-Bearing System With Cracked Functionally Graded Turbine Shaft

2017 ◽  
Author(s):  
Debabrata Gayen ◽  
Debabrata Chakraborty ◽  
Rajiv Tiwari
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Natural Frequencies ◽  
Crack Size ◽  
Fe Analysis ◽  
Functionally Graded ◽  
Gradient Index ◽  
Crack Orientation ◽  
Rotor Bearing ◽  
Bearing System

This paper describes finite element (FE) analysis of a rotor-bearing system having a functionally graded (FG) shaft with a transverse breathing crack. Two nodded Timoshenko beam element with four degrees of freedom (DOFs) per node has been considered and effects of translational and rotary inertia, transverse shear deformations, and gyroscopic moments are also considered. The FG shaft is considered to be composed of zirconia (ZrO2) and stainless steel (SS) with the volume fraction of SS increasing towards the inner radius of the shaft. Thermo-elastic material properties are considered in the radial direction of the FG shaft following power law gradation. Local flexibility coefficients (LFCs) of the cracked FG shaft are determined analytically as a function of crack size, power law gradient index (k), and temperature with crack orientation using the Castigliano’s theorem and Paris’s equations which are used to compute the stiffness matrix in the FE analysis. The FE formulation has been validated with the analytical and FE solutions reported in the literatures, and then natural frequencies and whirling (forward and backward) frequencies are determined. Influences of crack size, power law gradient index, slenderness ratio, and temperature gradient with crack orientation, on the dynamic responses of the rotor-bearing system with an FG shaft are studied. Results show that the power law gradient index has significant influence on the natural frequencies and whirling frequencies for the rotor-bearing system with the breathing cracked FG shaft and the choice of power law index could play an important role in design of FG shafts under thermo-mechanical environment from the view point of damage tolerant design.

A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness

2016 ◽  
Vol 232 (9) ◽  
pp. 769-784 ◽  
Author(s):  
Aritra Majumdar ◽  
Debabrata Das
Keyword(s):  
Stainless Steel ◽  
Temperature Distribution ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Mathematical Formulation ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Linear Temperature ◽  
Buckling Loads ◽  
Finite Element Software

The present work aims at the determination of thermal buckling loads of various functionally graded material beams with both ends clamped. Thermal loading is applied by applying linear temperature distribution and nonlinear temperature distribution at steady state heat conduction condition, across the beam thickness. Temperature dependences of the material properties, considered in the formulation, make the present problem physically nonlinear. Also, the effect of limit thermal load at which the effective elastic modulus and/or thermal expansion coefficient become theoretically zero is considered. The mathematical formulation is based on Euler–Bernoulli beam theory. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The solution of the governing equation is obtained using an iterative method. The validation of the present work is carried out with the available results in the literature and with the results generated by finite element software ANSYS. Four different functionally materials are considered, namely, stainless steel/silicon nitride, stainless steel/alumina, stainless steel/zirconia, and titanium alloy/zirconia. Comparative results are presented to show the effects of variations of volume fraction index, length–thickness ratio, and material constituents on nondimensional thermal buckling loads.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

scholarly journals Optimum response of functionally graded piezoelectric plates in thermal environments

2017 ◽  
Vol 35 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Hossein Nourmohammadi ◽  
Bashir Behjat
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Sensors And Actuators ◽  
Thermal Environments ◽  
Functionally Graded Piezoelectric ◽  
Power Law Index

AbstractIn this article, the static response of the functionally graded piezoelectric (FGP) plates with piezoelectric layers (sandwich FGPM) is studied based on the first order shear deformation plate theory. The plate is under mechanical, electrical and thermal loadings and finite element method is employed to obtain the solution of the equation. All mechanical, thermal and piezoelectric properties, except Poisson ratio, obey the power law distribution through the thickness. By solving the governing equation, optimum value of power law index is investigated in each type of loading. The effects of different volume fraction index, layer arrangements, various boundary conditions and different loading types, are studied on the deflection of FGPM plate. It is inferred that, the correlations between the deflection, power law index and layer arrangement are completely different in the mechanical and thermal loading and the optimum value of the power law index should be selected in each case separately. This optimum values can be used as a design criterion to build a reliable sensors and actuators in thermal environments.

A Comprehensive Analysis on the Structural–Acoustic Aspects of Various Functionally Graded Plates

2015 ◽  
Vol 07 (05) ◽  
pp. 1550072 ◽  
Author(s):  
N. Chandra ◽  
S. Raja ◽  
K. V. N. Gopal
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Transmission Loss ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Radiation Efficiency ◽  
Sound Power ◽  
Acoustic Behavior ◽  
Acoustic Response ◽  
Plate Velocity

The vibration, sound radiation and transmission characteristics of plates with various functionally graded materials (FGM) are explored and a detailed investigation is presented on the influence of specific material properties on structural–acoustic behavior. An improved model based on a simplified first order shear deformation theory along with a near-field elemental radiator approach is used to predict the radiated acoustic field associated with a given vibration and acoustic excitation. Various ceramic materials suitable for engineering applications are considered with aluminum as the base metal. A power law is used for the volume fraction distribution of the two constitutive materials and the effective modulus is obtained using the Mori–Tanaka homogenization scheme. The structural–acoustic response of these FGM plates is presented in terms of the plate velocity, radiated sound power, sound radiation efficiency for point and uniformly distributed load cases. Increase in both vibration and acoustic response with increase in power law index is observed for the lower order modes. The vibro–acoustic metrics such as root-mean-squared plate velocity, overall sound power, frequency averaged radiation efficiency and transmission loss, are used to rank these materials for vibro–acoustically efficient combination. Detailed analysis has been made on the factors influencing the structural–acoustic behavior of various FGM plates and relative ranking of particular ceramic/metal combinations.

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