scholarly journals Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories

2021 ◽  
Vol 72 (4) ◽  
pp. 452-467
Author(s):  
Ninh Vu Thi An
Keyword(s):  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Height Ratio ◽  
Fundamental Frequencies ◽  
The Difference ◽  
Foundation Parameters ◽  
Material Gradation ◽  
Beam Theories

Investigation on the influence of beam theory and partial foundation support on natural frequencies play an important role in design of structures. In this paper, fundamental frequencies of a bidirectional functionally graded sandwich (BFGSW) beam partially supported by an elastic foundation are evaluated using various beam theories. The core of the sandwich beam is homogeneous while its two face sheets are made from three distinct materials with material properties varying in both the length and thickness directions by power gradation laws. The finite element method is employed to derive equation of motion and to compute the frequencies of the beam. The effects of the material gradation, the foundation parameters and the span to height ratio on the frequencies are studied in detail and highlighted. The difference of the frequencies obtained by different beam theories is also examined and discussed. The numerical results of the paper are useful in designing BFGSW beams with desired fundamantal frequencies.

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.

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%.

Bi-Directional Functionally Graded Nanotubes: Fluid Conveying Dynamics

2018 ◽  
Vol 10 (04) ◽  
pp. 1850041 ◽  
Author(s):  
Ye Tang ◽  
Tianzhi Yang
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Graded Materials ◽  
Critical Flow Velocity ◽  
Dynamic Behaviors ◽  
Fundamental Frequencies ◽  
Material Gradation

In the paper, a novel model of fluid-conveying nanotubes made of bi-directional functionally graded materials is presented for investigating the dynamic behaviors and stability. For the first time, the material properties of the nanotubes along both radical and axial directions are under consideration. Based on Euler–Bernoulli beam and Eringen’s nonlocal elasticity theories, the governing equation of the nanotubes and associated boundary conditions are developed using Hamilton’s principle. Differential quadrature method (DQM) is applied for discretizing the equation to determine the numerical solutions of the nanotubes with different boundary conditions. Numerical examples are presented to examine the effects of the material gradation, nonlocal parameter, and mode order on the dynamics and stability. It is shown that the two-directional materials distribution can significantly change the critical flow velocity, fundamental frequencies and stability. Comparing with traditional one-directional distribution, such 2D is more flexible to tune overall dynamic behaviors, this may provide new avenues for smart pipes.

scholarly journals Effect of Corrosion on the Natural and Whirl Frequencies of a Functionally Graded Rotor-Bearing System Subjected to Thermal Gradients

Materials ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 4546 ◽  
Author(s):  
Prabhakar Sathujoda ◽  
Bharath Obalareddy ◽  
Aneesh Batchu ◽  
Giacomo Canale ◽  
Angelo Maligno ◽  
...  
Keyword(s):  
Finite Element ◽  
Dynamic Characteristics ◽  
Beam Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Thermal Gradients ◽  
The Finite Element Method ◽  
Fourier Law ◽  
Corrosion Defect ◽  
Nonlinear Temperature

Corrosion causes a loss of material resulting in the reduction of mass and stiffness of a component, which consequently affects the dynamic characteristics of any system. Fundamental frequency analysis of a corroded functionally graded (FG) rotor system, using the finite element method based on the Timoshenko beam theory, was investigated in the present paper. The functionally graded shaft consisting of an inner metallic core and an outer ceramic layer was considered with the radial gradation of material properties based on the power law. Nonlinear temperature distribution (NLTD) based on the Fourier law of heat conduction was used to simulate the thermal gradient through the cross-section of the FG rotor. The finite element formulation for a functionally graded shaft with a corrosion defect was developed and the dynamic characteristics were investigated, which is the novelty of the present work. The corrosion parameters such as length, depth and position of the corrosion defect in the shaft were varied and a parametric study was performed to investigate changes in the natural and whirl frequencies. An analysis was carried out for different power indexes and temperature gradients of the functionally graded shaft. The effects of corrosion were analysed and important conclusions are drawn from the investigations.

scholarly journals Bending Analysis of Sandwich Beam with Functionally Graded Face Sheets Using Various Beam Theories by Meshfree Method

10.29007/9nvf ◽  
2020 ◽  
Author(s):  
Minh Duc Do ◽  
Minh Tu Tran ◽  
Hoai Chinh Truong
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Virtual Work ◽  
Axial Stress ◽  
Sandwich Beam ◽  
Meshfree Method ◽  
Functionally Graded ◽  
Skin Thickness ◽  
Material Volume ◽  
Beam Theories

An interpolation technique-based meshfree method using polynomial functions is employed to analyze the static behavior of sandwich beams with functionally graded face sheets and homogenous softcore. Various beam theories are expressed in general form and taken into account both shear deformation and normal deformation effects. The governing equation is derived from the principle of virtual work. The obtained results have been verified with the previously published works and a good agreement is found. The effects of skin-core-skin thickness ratios, material volume fraction indices, slenderness ratios, shear deformation, and thickness stretching effect on deflection and axial stress are investigated and discussed.

scholarly journals Free vibration analysis of sandwich beams with FG porous core and FGM faces resting on Winkler elastic foundation by various shear deformation theories

2018 ◽  
Vol 12 (3) ◽  
pp. 23-33 ◽  
Author(s):  
Dang Xuan Hung ◽  
Huong Quy Truong
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Porous Core ◽  
Winkler Elastic Foundation ◽  
Beam Theories ◽  
Good Agreement

This paper studies the free vibration behavior of a sandwich beam resting on Winkler elastic foundation. The sandwich beam is composed of two FGM face layers and a functionally graded (FG) porous core. A common general form of different beam theories is proposed and the equations of motion are formulated using Hamilton's principle. The result of the general form is validated against those of a particular case and shows a good agreement. The effect of different parameters on the fundamental natural frequency of the sandwich beam is investigated. Article history: Received 02 March 2018, Revised 26 March 2018, Accepted 27 April 2018

Dynamic Analysis of a Rotating Double-Tapered FGM Beam with Various Shear Models Using a Constrained Variational Method

2021 ◽  
Author(s):  
Zixuan Zhou ◽  
Xiuchang Huang ◽  
Hongxing Hua
Keyword(s):  
Variational Method ◽  
Shear Deformation ◽  
Power Law ◽  
Slenderness Ratio ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Geometrically Exact Beam ◽  
Beam Theories

A constrained variation modeling method for free vibration analysis of rotating double tapered functionally graded beams with different shear deformation beam theories is proposed in this paper. The material properties of the beam are supposed to continuously vary in the width direction with power-law exponent for different indexes. The mathematical formulation is developed based on the geometrically exact beam theory for each beam segment, the admissible functions denoting motion quantities are then expressed by a series of Chebyshev orthogonal polynomials. The governing equations are eventually derived using the constrained variational method to involve the continuity conditions of adjacent segments. Different shear deformation beam theories have been incorporated in the formulations, and the nonlinear effect of bending–stretching coupling vibration together with the Coriolis effect is taken into account. Comparison of dimensionless natural frequencies is performed with the existing literature to ensure the accuracy and reliability of the proposed method. Comparative discussions are performed on the vibration behaviors of the double tapered rotating functionally graded beam with first-order shear deformation beam theory and other higher-order shear deformation beam theories. The effect of material property graduation, power-law index, rotation speed, hub radius, slenderness ratio, and taper ratios is scrutinized via parametric studies, respectively.

On the Dynamic Model of a Functionally Graded Spinning Structural Element of an Aircraft Appendage

2014 ◽  
Vol 629 ◽  
pp. 89-94
Author(s):  
Khameel Bayo Mustapha
Keyword(s):  
Beam Theory ◽  
Primary Objective ◽  
Functionally Graded ◽  
Advanced Materials ◽  
Wave Mechanics ◽  
Dead Load ◽  
Structural Element ◽  
Propagation Behavior ◽  
Classical Models ◽  
Material Gradation

The use of advanced materials in automotive, aerospace and communication technologies has called for re-assessment of classical models of many structural elements. The primary objective of this study relates to the use of a higher-order continuum model for discerning the contribution of certain geometric and material properties on wave propagation behavior of a spinning appendage of an aircraft appendage. The spinning appendage is characterized by a through-thickness functional material gradation and subjected to an axial dead load. The foundation of the present model rests on the trio of the mechanics of functionally graded solid structures, the extended Hamilton’s principle and the thin beam theory. Numerical results from the wave mechanics analyses reveal the noticeable influence of axial dead load and attendant wave splitting effect caused by the gyroscopic moment of the system. The wave mechanics result paves the way for the non-destructive damage testing of the element.

Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: Magneto-electro-elastic vibration and buckling solution

2019 ◽  
Vol 25 (23-24) ◽  
pp. 2875-2893 ◽  
Author(s):  
M. Bamdad ◽  
M. Mohammadimehr ◽  
K. Alambeigi
Keyword(s):  
Timoshenko Beam ◽  
Material Properties ◽  
Vinylidene Fluoride ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Temperature Dependent

Vibration and buckling analysis of a magneto-electro-elastic sandwich Timoshenko beam with a porous core and poly-vinylidene fluoride (PVDF) matrix reinforced by carbon nanotubes (CNTs) is considered as face layers and material properties of CNTs and PVDF are assumed to be temperature-dependent. Different CNT distribution patterns including uniform distribution, AV (which top and bottom face sheets have functionally graded-A (FG-A) and functionally graded-V (FG-V) CNT distribution patterns, respectively) and VA patterns are employed. The governing equations of motion are derived based on Timoshenko beam theory, and Navier's solution is used to solve these equations. The sandwich beam resting on a Pasternak foundation and face layers are subjected to electric and magnetic potentials. The effect of different parameters such as porosity coefficient, electric and magnetic potential, parameters of foundation, and geometrical parameters are investigated on vibration and buckling behavior of the sandwich beam. Numerical results of this paper show that porosity distribution has a significant effect on the stiffness of the sandwich beam. The results can be used for future analysis of magneto-electro-mechanical sandwich systems as actuators and sensors.

scholarly journals Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

2021 ◽  
Vol 15 (4) ◽  
pp. 15-28
Author(s):  
Tran Quang Hung ◽  
Tran Minh Tu ◽  
Do Minh Duc
Keyword(s):  
Temperature Distribution ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Thermal Environment ◽  
Ritz Method ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Lagrange Equations ◽  
Linear Temperature

This paper aims to present thermo-electrical free vibration characteristics of functionally graded material (FGM) sandwich beam placed on the two-parameter elastic foundation. The beam is constructed of a foam core, two middle FGM layers, and two outer piezoelectric layers. It is assumed that the beam is subjected to a constant voltage and a uniform/linear temperature distribution. Physical properties of the core and two middle layers vary smoothly through the thickness according to the cosine and power-law forms, respectively. Lagrange equations in conjunction with the Reddy third-order beam theory is employed to derive the governing equations of motion. A simple polynomial trial function-based Ritz method is adopted for the approximation of the displacement field to obtain the vibration response. The correctness of the study is verified by comparisons with other authors’ published results. Influences of geometry parameters, material property distribution, applied voltage, elastic foundation, temperature distribution, temperature change, porosity coefficient, span-to-height ratio, and boundary conditions are investigated through parametric studies.

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