scholarly journals Vibration analysis of functionally graded tapered rotor shaft system

2019 ◽  
Vol 23 (1) ◽  
pp. 241-245
Author(s):  
Abdelhak Elhannani ◽  
Kaddour Refassi ◽  
Abbes Elmeiche ◽  
Mohamed Bouamama
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Functionally Graded ◽  
Taper Angle ◽  
Hollow Shaft ◽  
Exponential Law ◽  
Shaft System ◽  
Graded Material ◽  
Extreme Materials

Abstract This investigation deals with the vibration analysis of a rotating tapered shaft in Functionally Graded Material (FGM). The dynamic system is modeled using the Timoshenko beam theory (FSDBT) with consideration of gyroscopic effect and rotary inertia. The equations of motion are expressed by the hierarchical finite element method based on bi-articulated boundary conditions. The material properties are continuously varied in the thickness direction of a hollow shaft according to the exponential law function (E-FGM). The presented model is validated by comparing the numerical results found with the available literature. Various analyses are carried out to determine the influence of taper angle and material distribution of the two extreme materials on the dynamic behavior of FGM conical rotors system.

scholarly journals FREE VIBRATION OF TWO-DIRECTIONAL FGM BEAMS USING A HIGHER-ORDER TIMOSHENKO BEAM ELEMENT

2018 ◽  
Vol 56 (3) ◽  
pp. 380 ◽  
Author(s):  
Tran Thi Thom ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Beam Element ◽  
Higher Order ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Power Law Distribution ◽  
Graded Material

Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

2017 ◽  
Vol 14 (02) ◽  
pp. 1750011 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Rabczuk ◽  
V. Ho-Huu ◽  
L. Le-Anh ◽  
H. Dang-Trung ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Plate Element ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Graded Material ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

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