Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load

2009 ◽  
Vol 90 (4) ◽  
pp. 465-473 ◽  
Author(s):  
M. Şimşek ◽  
T. Kocatürk
Keyword(s):  
Forced Vibration ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Functionally Graded Beam ◽  
Moving Harmonic Load

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. 

Moving Element Method for Dynamic Analyses of Functionally Graded Plates Resting on Pasternak Foundation Subjected to Moving Harmonic Load

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003 ◽  
Author(s):  
Van Hai Luong ◽  
Tan Ngoc Than Cao ◽  
Qui X. Lieu ◽  
Xuan Vu Nguyen
Keyword(s):  
Volume Fraction ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Mindlin Plate ◽  
Harmonic Load ◽  
Pasternak Foundation ◽  
Fg Plates ◽  
Dynamic Analyses ◽  
Moving Harmonic Load ◽  
Element Method

This paper presents the moving element method (MEM) for dynamic analyses of functionally graded (FG) plates resting on Pasternak foundation under moving harmonic load. The Mindlin plate theory is used to model the FG plates. Macroscopic material properties of FG plates are assumed to continuously vary across the thickness direction by a simple power-law distribution. The governing equation of the FG plate is formulated in a coordinate system which moves along with the applied load. In addition, the method simply treats the moving load as “stationary” at the discretized node of plate to completely eliminate the update procedure of force vector due to the change of contact point with elements. To verify the accuracy of the computational paradigm, static and free vibration analyses of FG plates are examined first. Dynamic analyses of FG plates subjected to a moving harmonic load are then conducted to investigate the effects of various parameters such as volume fraction exponent, Young’ modulus, load velocity, foundation damping coefficient and load acceleration/deceleration on dynamic responses of the plate.

scholarly journals Geometrically Non-Linear Free and Forced Vibration of Clamped-Clamped Functionally Graded Beam with Discontinuities.

2017 ◽  
Vol 199 ◽  
pp. 1870-1875 ◽  
Author(s):  
Chajdi Mohcine ◽  
Merrimi El Bekkaye ◽  
El Bikri Khalid
Keyword(s):  
Forced Vibration ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Non Linear

scholarly journals Nonlinear Dynamic Response of an Axially Functionally Graded (AFG) Beam Resting on Nonlinear Elastic Foundation Subjected to Moving Load

2019 ◽  
Vol 8 (1) ◽  
pp. 250-260 ◽  
Author(s):  
Mehdi Alimoradzadeh ◽  
Mehdi Salehi ◽  
Sattar Mohammadi Esfarjani
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Nonlinear Dynamic ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Nonlinear Dynamic Response ◽  
Moving Harmonic Load

Abstract In recent years, structures made of Functionally Graded materials (FGMs) are used in industries due to the continuously compositional variation of the constituents in FGMs along different directions. In order to develop FGMs, nonlinear vibration analysis to study dynamic behavior is needed. This study proposes nonlinear vibration analysis of a simply supported axially functionally graded (AFG) beam subjected to a moving harmonic load as an Euler-Bernoulli beam utilizing Green’s strain tensor. Axial variation of material properties of the beam is based on the power law. The governing equations of motion are derived via Hamilton’s principle. The Galerkin’s method is implemented to reduce the nonlinear partial differential equations of the system to a number of nonlinear ordinary differential equations. He’s variational method is applied to obtain approximate analytical expressions for the nonlinear frequency and the nonlinear dynamic response of the AFG beam. The effect of some parameters such as the power index and stiffness coefficients, among others, on the nonlinear natural frequency has been investigated. The influence of above mentioned parameters as well as the velocity of the moving harmonic load on the nonlinear dynamic response has been studied. The results indicate that these parameters have a considerable effect on both nonlinear natural frequency and response amplitude.

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