scholarly journals FREE VIBRATION OF BFGSW BEAMS PARTIALLY RESTING ON PASTERNAK FOUNDATION BASED ON A SINUSOIDAL THEORY

2020 ◽  
Vol 58 (5) ◽  
pp. 635
Author(s):  
Ich Cong Le
Keyword(s):  
Free Vibration ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Pasternak Foundation ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
The Face

In this paper, free vibration of a bidirectional functionally graded sandwich (BFGSW) beams partially resting on a Pasternak foundation is studied. The beams with three layers, an axially functionally graded core and two bidirectional functionally graded face sheets, are made from a mixture of metal and ceramic. The material properties of the face sheets are considered to vary continuously in both the thickness and length directions by the power-law distributions, and they are estimated by Mori-Tanaka scheme. A sinusoidal shear deformation theory, in which the transverse displacement is split into bending and shear parts, is employed to derive energy expressions of the beam. A finite element formulation is formulated and employed to compute vibration characteristics. Numerical result reveals that the ratio of foundation support to the beam length plays an important role on the vibration behaviour, and the dependence of the frequencies upon the material grading indexes is governed by this ratio. Numerical investigation is carried out to highlight the effects of the material distribution, the layer thickness ratio, the foundation stiffness on the vibration characteristics of the beams. The influence of the aspect ratio on the frequencies of the beams and is also examined and discussed.

scholarly journals Free Vibration of FGSW Plates Partially Supported by Pasternak Foundation Based on Refined Shear Deformation Theories

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Cong Ich Le ◽  
Vu Nam Pham ◽  
Dinh Kien Nguyen
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Pasternak Foundation ◽  
Aspect Ratios ◽  
Hermitian Polynomials ◽  
Quadrilateral Finite Element

A refined third-order shear deformation theory (RTSDT), in which the transverse displacement is split into bending and shear parts, is employed to formulate a four-node quadrilateral finite element for free vibration analysis of functionally graded sandwich (FGSW) plates partially supported by a Pasternak foundation. An element based on the refined first-order shear deformation theory (RFSDT) which requires a shear correction factor is also derived for comparison purpose. The plates consist of a fully ceramic core and two functionally graded skin layers with material properties varying in the thickness direction by a power gradation law. The Mori–Tanaka scheme is employed to evaluate the effective moduli. The elements are derived using Lagrangian and Hermitian polynomials to interpolate the in-plane and transverse displacements, respectively. The numerical result reveals that the frequencies obtained by the RTSDT element are slightly higher than the ones using the RFSDT element. It is also shown that the foundation supporting area plays an important role on the vibration of the plates, and the effect of the material distribution on the frequencies is dependent on this parameter. A parametric study is carried out to highlight the effects of the material inhomogeneity, the foundation stiffness parameters, and the foundation supporting area on the frequencies and vibration modes. The influence of the layer thickness and aspect ratios on the frequencies is also examined and highlighted.

scholarly journals Free vibration of a 2D-FGSW beam based on a shear deformation theory

2020 ◽  
Author(s):  
Vu Thi An Ninh ◽  
Le Thi Ngoc Anh ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Length Direction

A two-dimensional functionally graded sandwich (2D-FGSW) beam model\break formed from three constituent materials is proposed and its free vibration is studied for the first time. The beam consists of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the length and thickness directions by power gradation laws. Based on a third-order shear deformation theory, a beam element using the transverse shear rotation as an independent variable is formulated and employed in the study.  The obtained numerical result reveals that the variation of the material properties in the length direction plays an important role on the natural frequencies and vibration modes  of the beam. The effects of the material distribution and layer thickness ratio on the vibration characteristics are investigated in detail. The influence of the aspect ratio on the frequencies is also examined and discussed.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

High-order free vibration analysis of FGM sandwich plates with non-monotonically graded flexible core

2016 ◽  
Vol 20 (6) ◽  
pp. 759-780 ◽  
Author(s):  
Ming Liu ◽  
Jun Liu ◽  
Yuansheng Cheng
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Core Layer ◽  
Functionally Graded ◽  
High Order ◽  
Sandwich Plates ◽  
The Face ◽  
Flexible Core

Free vibration analysis of sandwich plates with non-monotonically graded flexible core is studied using a high-order sandwich panel theory. The non-monotonically graded flexible core is considered as two monotonically graded flexible core layers. In this high-order theory, the first-order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for each single core layer. The laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Based on the continuity of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are derived by Hamilton’s principle. The accuracy of the present approach is validated by comparing with the numerical results obtained from finite element method and good agreements are reached. Parametric study is also conducted to investigate the effect of distribution of functionally graded material properties, the monotonically graded core thickness ratio, and the thickness-to-side ratio on the vibration frequency.

scholarly journals Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

2020 ◽  
Vol 14 (3) ◽  
pp. 136-150
Author(s):  
Le Thi Ngoc Anh ◽  
Vu Thi An Ninh ◽  
Tran Van Lang ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
First Order ◽  
Various Boundary Conditions

Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

scholarly journals Free vibration of FG sandwich plates partially supported by elastic foundation using a quasi-3D finite element formulation

2020 ◽  
Author(s):  
Le Cong Ich ◽  
Pham Vu Nam ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Layer Thickness ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Thickness Ratio ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Layer Thickness Ratio

Free vibration of functionally graded (FG) sandwich plates partially supported by a Pasternak elastic foundation is studied. The plates consist of three layers, namely a pure ceramic hardcore and two functionally graded skin layers. The effective material properties of the skin layers are considered to vary in the plate thickness by a power gradation law, and they are estimated by Mori--Tanaka scheme. The quasi-3D shear deformation theory, which takes the thickness stretching effect into account, is adopted to formulate a finite element formulation for computing vibration characteristics.  The accuracy of the derived formulation is confirmed through a comparison study. The numerical result reveals that the foundation supporting area plays an important role on the vibration behavior of the plates, and the effect of the layer thickness ratio on the frequencies is governed by the supporting area. A parametric study is carried out to highlight the effects of material distribution, layer thickness ratio, foundation stiffness and area of the foundation support on the frequencies and mode shapes of the plates. The influence of the side-to-thickness ratio on the frequencies of the plates is also examined and discussed.

Influence of Material Uncertainty on Vibration Characteristics of Higher-Order Cracked Functionally Gradient Plates Using XFEM

2021 ◽  
Vol 13 (05) ◽  
Author(s):  
Ahmed Raza ◽  
Mohammad Talha ◽  
Himanshu Pathak
Keyword(s):  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Partition Of Unity ◽  
Higher Order ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Level Set Function

In this study, the influence of material uncertainty on the vibration characteristics of the cracked functionally graded materials (FGM) plates is investigated. Extended stochastic finite element formulation is implemented to model the cracked FGM plate with material uncertainty using higher-order shear deformation theory (HSDT). The level set function is employed to track the crack in the FGM domain. The concept of partition of unity technique is implemented to enrich the primary variable with additional functions. The gradation of the material properties along the thickness direction is done using the power-law distribution. The first-order perturbation technique (FOPT) is incorporated in the methodology for stochastic vibration analysis. The convergence and validation study has been performed to verify the efficacy and accuracy of the formulation. Numerical results are obtained to show the effects of various influential parameters like crack length, gradient index, thickness ratio, and boundary condition on the covariance of the square of natural frequencies. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of cracked FGM plates with material randomness.

scholarly journals VIBRATION OF FGSW BEAMS UNDER NONUNIFORM MOTION OF MOVING LOAD USING AN EFFICIENT THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 51
Author(s):  
Anh Thi Ngoc Le ◽  
Kien Dinh Nguyen
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Moving Load ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Nonuniform Motion

Vibration of functionally graded sandwich (FGSW) beams under nonuniform motion of a moving load is studied using a third-order shear deformation finite element formulation. The beams consists three layers, a homogeneous ceramic core and two functionally graded faces. Instead of the rotation, the finite element formulation is derived by using the transverse shear rotation as a unknown. Newmark method is used to compute the dynamic response of the beams. Numerical result reveals that the derived formulation is efficient, and it is capable to give accurate vibration characteristics by a small number of the elements. A parametric study is carried out to illustrate the effects of the material distribution, layer thickness ratio and moving load speed on the dynamic behavior of the beams. The influence of acceleration and deceleration of the moving load on the vibration of the beams is also examined and discussed.

scholarly journals Three new hybrid quasi-3D and 2D higher-order shear deformation theories for free vibration analysis of functionally graded material monolayer and sandwich plates with stretching effect

2020 ◽  
Vol 29 ◽  
pp. 096369352094186
Author(s):  
Y Belkhodja ◽  
D Ouinas ◽  
H Fekirini ◽  
JA Viña Olay ◽  
M Touahmia
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Functionally Graded Material ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Graded Material

The present investigation brings to the readers three new hybrid higher-order shear deformation theory (HSDT) models and analyses the functionally graded material (FGM) plates. The major objective of this work is to develop three HSDTs in a unique formulation by polynomial–hyperbolic–exponential and polynomial–trigonometric forms, propose the three new HSDT models, investigate the effect of thickness stretching by considering a quasi-three-dimensional theory and analyse the free vibration of isotropic and FGM monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) plates to demonstrate the models ability. Therefore, the Hamilton’s principle is exploited to develop equations of motion based on a displacement field of only five unknowns, of which three of them distinguished the transverse displacement membranes through the plate thickness (bending, shear and stretching displacements). In addition, the analytical solutions are found by applying the Navier approach for a simply supported boundary conditions type. The theory also considered that transverse shear deformation effect satisfied the stress-free boundary conditions on the plate-free surfaces without any requirement of shear correction factors. The used mechanical properties followed the power law and the Mori–Tanaka scheme distributions through the plate thickness. The determined results explained the effects of different non-dimensional parameters, and the proposed HSDTs predict the proper responses for monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) FGM plates in comparison with other different plates’ theories solutions found in the literature references, thus the reliability and accuracy of the present approach are ascertained. It is obtained that the present formulations of polynomial–hyperbolic–exponential and polynomial–trigonometric forms can be further extended to all existing HSDTs models, for numerous problems related to the shear deformable effect.

scholarly journals VIBRATION OF FGSW BEAMS UNDER NONUNIFORM MOTION OF MOVING LOAD USING AN EFFICIENT THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 51
Author(s):  
Anh Thi Ngoc Le ◽  
Kien Dinh Nguyen
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Moving Load ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Third Order ◽  
Layer Thickness Ratio ◽  
Numerical Result ◽  
Nonuniform Motion

Vibration of functionally graded sandwich (FGSW) beams under nonuniform motion of a moving load is studied using a third-order shear deformation finite element formulation. The beams consists three layers, a homogeneous ceramic core and two functionally graded faces. Instead of the rotation, the finite element formulation is derived by using the transverse shear rotation as a unknown. Newmark method is used to compute the dynamic response of the beams. Numerical result reveals that the derived formulation is efficient, and it is capable to give accurate vibration characteristics by a small number of the elements. A parametric study is carried out to illustrate the effects of the material distribution, layer thickness ratio and moving load speed on the dynamic behavior of the beams. The influence of acceleration and deceleration of the moving load on the vibration of the beams is also examined and discussed.

Sign in / Sign up

Export Citation Format

Share Document