Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load

2012 ◽  
Vol 94 (9) ◽  
pp. 2861-2878 ◽  
Author(s):  
Mesut Şimşek ◽  
Sinan Cansız
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Functionally Graded Beam ◽  
Different Boundary Conditions ◽  
Moving Harmonic Load

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

2020 ◽  
Vol 20 (05) ◽  
pp. 2050068 ◽  
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Yong Chen
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Arbitrary Boundary Conditions ◽  
Porosity Coefficient

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.

FE Analysis of Functionally Graded Material Plate during Debonding Case with Different Boundary Conditions

2014 ◽  
Vol 627 ◽  
pp. 57-60 ◽  
Author(s):  
Wasim M.K. Helal ◽  
Dong Yan Shi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Von Mises Stress ◽  
Sigmoid Function ◽  
Different Boundary Conditions ◽  
Graded Material ◽  
The Relationship

Functionally graded materials (FGMs) have become helpful in our engineering applications. Analysis of functionally graded material (FGM) plate during debonding case with different boundary conditions is the main purpose of this investigation. Elastic modulus (E) of functionally graded (FG) plate is assumed to vary continuously throughout the height of the plate, according the volume fraction of the constituent materials based on a modified sigmoid function, but the value of Poisson coefficient is constant. In this research, the finite element method (FEM) is used in order to show the shape of a plate made of FGM during debonding case with different boundary conditions. In the present investigation, the displacement value applied to the FGM plate is changed in order to find the relationship between the maximum von Mises stress and the displacement. Also, the relationship between the maximum shear stress and the displacement is carried out in the present work. The material gradient indexes of the FGM plate are changed from 1 to 10. The stress distributions around the debonding zone with all the material gradient indexes of the FGM plate are investigated in this work.

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. 

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

2021 ◽  
pp. 095440622199068
Author(s):  
Ahmad Mamandi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Functionally Graded ◽  
Kantorovich Method ◽  
Different Boundary Conditions ◽  
Extended Kantorovich Method ◽  
Skew Plate ◽  
Pasternak Elastic Foundation ◽  
Graded Material

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

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