scholarly journals Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Dinh Kien Nguyen ◽  
Van Tuyen Bui
Keyword(s):  
Dynamic Behaviour ◽  
Thermal Environment ◽  
Beam Element ◽  
Higher Order ◽  
Functionally Graded ◽  
Published Data ◽  
Timoshenko Beams ◽  
Material Inhomogeneity ◽  
Forced Vibration Analysis ◽  
Loading Parameter

A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

scholarly journals VIBRATION OF 2D-FGSW TIMOSHENKO BEAMS UNDER A MOVING HARMONIC LOAD

2020 ◽  
Vol 58 (6) ◽  
pp. 760
Author(s):  
Kien Dinh Nguyen
Keyword(s):  
Moving Load ◽  
Excitation Frequency ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Harmonic Load ◽  
Timoshenko Beams ◽  
Power Functions ◽  
Material Inhomogeneity ◽  
Moving Harmonic Load

Vibration of two-directional functionally graded sandwich (2D-FGSW) Timoshenko beams under a moving harmonic load is investigated. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with the material properties continuously varying in both the thickness and length directions by power functions. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The obtained numerical result reveals that the material inhomogeneity and the layer thickness ratio play an important role on the natural frequencies and dynamic response of the beams. A parametric study is carried out to highlight the effects of the power-law indexes, the moving load speed and excitation frequency on the vibration characteristics of the beams.  The influence of the beam aspect ratio on the vibration of the beams is also examined and discussed. 

Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 191-218 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Pham Hong Cong
Keyword(s):  
Dynamic Analysis ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Thermal Environment ◽  
Nonlinear Dynamic Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Sandwich Plates ◽  
Elastic Foundations

Used the Reddy's higher-order shear deformation plate theory, the nonlinear dynamic analysis and vibration of imperfect functionally graded sandwich plates in thermal environment with piezoelectric actuators (PFGM) on elastic foundations subjected to a combination of electrical, damping loadings and temperature are investigated in this article. One of the salient features of this work is the consideration of temperature on the piezoelectric layer, and the material properties of the PFGM sandwich plates are assumed to be temperature-dependent. The governing equations are established based on the stress function, the Galerkin method, and the Runge–Kutta method. In the numerical results, the effects of geometrical parameters; material properties; imperfections; elastic foundations; electrical, thermal, and damping loads on the vibration and nonlinear dynamic response of the PFGM sandwich plates are discussed. The obtained natural frequencies are verified with the known results in the literature.

scholarly journals FREE VIBRATION OF TAPERED FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE BEAMS USING A HIERARCHICAL BEAM ELEMENT

2020 ◽  
Vol 57 (6A) ◽  
pp. 107
Author(s):  
Trinh Thi Hien
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Longitudinal Direction ◽  
Beam Element ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Published Data ◽  
Reinforced Composite

Free vibration of tapered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams is investigated. The beams with four types of carbon nanotube distribution in the thickness, namely the uniform (UD-CNT), X-type (FGX-CNT), A-type (FGA-CNT) and O-type (FGO-CNT), are assumed to be linearly tapered in longitudinal direction by three different taper cases. Based on the first-order shear deformation theory, equations of motion with variable coefficients are derived from Hamilton’s principle. Using hierarchical functions to interpolate the displacement field, a two-node beam element with nine degrees of freedom is formulated and employed to compute frequencies of the beams. The accuracy of the derived formulation is confirmed by comparing frequencies obtained in the present work with the published data. The effects of the total CNT volume fraction, CNT distribution type, taper cases, taper ratio, aspect ratio, boundary conditions, etc., on the vibration characteristics of the beams are examined and discussed.

On the flexural and vibration behavior of imperfection sensitive higher order functionally graded material skew sandwich plates in thermal environment

2018 ◽  
Vol 233 (4) ◽  
pp. 1271-1288 ◽  
Author(s):  
Sanjay Singh Tomar ◽  
Mohammad Talha
Keyword(s):  
Functionally Graded Material ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Skew Angle ◽  
Vibration Behavior ◽  
Graded Material

This work presents an investigation on the flexural and vibration behavior of imperfection sensitive higher order functionally graded material skew sandwich plates in thermal environment. Material properties have been assumed to be temperature dependent and graded in transverse direction following the power law distribution. Reddy’s higher order shear deformation theory has been used to model displacement field kinematics of skew sandwich plate. Variational principle has been used for deriving the governing equations. Finite element methodology has been adopted to discretize plate domain. Convergence and comparison studies have been performed to demonstrate the reliability of present formulation. Effect of various system parameters such as thickness ratio, volume fraction index, skew angle, imperfection parameter, and boundary conditions on the flexural and vibration response have been investigated.

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