scholarly journals Bending of Symmetric Sandwich FGM Beams with Shear Connectors

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Dung Nguyen Thai ◽  
Phung Van Minh ◽  
Cuong Phan Hoang ◽  
Tam Ta Duc ◽  
Nhung Nguyen Thi Cam ◽  
...  
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Beam Theory ◽  
Numerical Data ◽  
Functionally Graded ◽  
Engineering Practice ◽  
Graded Materials ◽  
Shear Connectors ◽  
The Impact

This paper carries out the static bending analysis of symmetric three-layer functionally graded sandwich beams, in which each layer is made from different functionally graded materials, and they are connected by shear connectors due to sliding movement. The finite element formulations are based on Timoshenko’s first-order shear deformation beam theory (FSDT) and the finite element method to establish the equilibrium equation of beams. The calculation program is coded in the MATLAB environment, and then verification examples are given out to compare the numerical data of present work with those of exact open sources. The impact of several geometrical and material parameters on the mechanical response of the structure, such as the height-to-length ratio, boundary conditions, volume fraction index, and especially the shear coefficient of connectors, is being explored. When designing and using these types of structures in engineering practice, the computed results can be utilized as a valid reference.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Flexural Sensitivity of a V-Shaped AFM Cantilever Made of Functionally Graded Materials

2010 ◽  
Author(s):  
M. Rahaeifard ◽  
M. H. Kahrobaiyan ◽  
S. A. Moeini ◽  
M. T. Ahmadian ◽  
M. Hoviattalab
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Contact Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Geometric Parameters ◽  
Graded Materials ◽  
Resonant Frequencies ◽  
Mass Distributions ◽  
Lateral Contact

In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of volume fraction of materials and geometric parameters on resonant frequencies and sensitivities is studied. Results show that natural frequencies and sensitivities are significantly affected by volume fraction of material constituents and geometric parameters. Using these results, optimum geometric parameters and mass distributions of material constituents can be chosen so that high resolution images could be obtained.

Nonlinear transient and thermal analysis of functionally graded shells using a seven-parameter shell finite element

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
Miguel Gutierrez Rivera ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Shell Element ◽  
Element Model ◽  
Functionally Graded ◽  
Plates And Shells ◽  
Shell Finite Element ◽  
Transient Thermal

AbstractIn this paper the thermo-mechanical response of functionally graded plates and shells is studied using a continuum shell finite element model with high-order spectral/hp basis functions. The shell element is based on the seven-parameter first-order shear deformation theory, and it does not utilize reduced integration or stabilization ideas and yet exhibits no locking. The static and dynamic response of functionally graded shells, with power-law variation of the constituents, under mechanical and thermal loads is investigated by varying the volume fraction of the constituents. Numerical results for deflections and stresses are presented and compared with available analytical and finite element results from the literature. The performance of the shell element for transient thermal problems is found to be excellent.

scholarly journals S1-ZGV Modes of a Linear and Nonlinear Profile for Functionally Graded Material Using Power Series Technique

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
M. Zagrouba ◽  
M. S. Bouhdima ◽  
M. H. Ben Ghozlen
Keyword(s):  
Power Series ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Zero Group ◽  
The Impact ◽  
Power Series Technique ◽  
Series Technique

The present work deals with functionally graded materials (FGM) isotropic plates in the neighborhood of the first-order symmetric zero group velocity (S1-ZGV) point. The mechanical properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate and obey a power law of the volume fraction of the constituents. Governing equations for the problem are derived, and the power series technique (PST) is employed to solve the recursive equations. The impact of the FGM basic materials properties on S1-ZGV frequency of FGM plate is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus. The gradient coefficient p does not affect the linear dependence of ZGV frequency fo as function of cut-off frequency fc; only the slope is slightly varied.

Sensitivity Analysis of Atomic Force Microscope Cantilever Made of Functionally Graded Materials

2009 ◽  
Author(s):  
M. Rahaeifard ◽  
M. H. Kahrobaiyan ◽  
M. T. Ahmadian
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Contact Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Graded Materials ◽  
Resonant Frequencies ◽  
Linear Spring ◽  
Fgm Beam ◽  
Micro Cantilever

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a simple power law of n. This variation is a function of the volume fraction of the beam material constituents. The interaction between AFM tip and surface is modeled by a linear spring which expresses the contact stiffness. Results show that, increasing the ceramic volume fraction increases the resonant frequencies of both modes 1 and 2. When contact stiffness is small, for both modes, as ceramic volume fraction increases, sensitivities decreases, while for large contact stiffness, as ceramic volume fraction increases the sensitivities will be increased. Results also show that at each contact stiffness, there is a unique value of n at which the sensitivity is maximized. Using these values for n, the high quality and high contrast images can be obtained.

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.

scholarly journals A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1422
Author(s):  
Youssef Boutahar ◽  
Nadhir Lebaal ◽  
David Bassir
Keyword(s):  
Beam Theory ◽  
Functionally Graded ◽  
Effective Characteristics ◽  
Hyperbolic Function ◽  
Transverse Displacement ◽  
Refined Theory ◽  
Distribution Law ◽  
Fg Beam ◽  
The Impact ◽  
Beam Theories

A refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams.

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