Dynamic behaviors of tapered bi-directional functionally graded beams with various boundary conditions under action of a moving harmonic load

Yang, Yang; Kou, Kunpang; Lam, Chi Chiu; Iu, Vai Pan

doi:10.1016/j.enganabound.2019.03.022

Cited by 28 publications

(4 citation statements)

References 26 publications

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“…Utilizing finite element method (FEM) and Newmark method, the vibration of a BDFG Timoshenko beam under a moving load was investigated by [87] assuming that the material properties were varied in both thickness and length directions via power law functions. Yang et al [88] studied the vibration characteristics of a tapered BDFG Timoshenko beam subjected to a moving harmonic force employing the meshfree boundary-domain integral equation in conjunction with 2D elasticity theory. The exponential distribution was assumed for the variation of Young's modulus and mass density in transverse and axial directions.…”

Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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This paper presents an investigation of the dynamic behavior of bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in the context of the surface elasticity theory and the modified couple stress theory to incorporate the effects of surface energy and microstructure, respectively. Based on the generalized elasticity theory and the parabolic shear deformation beam theory, the nonclassical governing equations of the problem are obtained using Lagrange’s equation accounting for the physical neutral plane concept. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution, accounting for the gradation of the material length scale parameter and the surface parameters, i.e., residual surface stress, two surface elastic constants, and surface mass density. Using trigonometric Ritz method (TRM), the trial functions denoting transverse, axial deflections, and rotation of the cross sections of the beam are expressed in sinusoidal form. Then, with the aid of Lagrange’s equation, the system of equations of motion are derived. Finally, Newmark method is employed to find the dynamic responses of BDFG subjected to a moving harmonic load. To validate the present formulation and solution method, some comparisons of the obtained fundamental frequency and dynamic response with those available in the literature are performed. A parametric study is performed to extensively explore the impact of the key parameters such as the gradient indices in both directions, moving speed, and excitation frequency of the acting load on the dynamic response of BDFG nanobeams. The obtained results can serve as a guideline for assessing the multi-functional and optimal design of micro/nanobeams acted upon by a moving load.

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Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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“…From a computational point of view, the travelling load is usually applied as a simple massless force or an oscillator or an inertial force. Numerous historical studies concerning the moving load problem exist in the open literatures [20,[24][25][26][27]. Simsek [28] conducted a study on nonlocal vibration of a singlewalled carbon nanotube carrying a moving harmonic load.…”

Section: Introductionmentioning

confidence: 99%

Transient behavior of imperfect bi-directional functionally graded sandwich plates under moving loads

Esmaeilzadeh

Golmakani

Luo

et al. 2021

Engineering with Computers

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An investigation of dynamic behaviors of a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by two faces on a two-parameter elastic foundation and subjected to a moving load is carried out in this paper. The present sandwich solid is composed of a porous 2D-FG core covered by two homogenous layers. It is assumed that the middle layer has micro voids dispersed uniformly and unevenly through the layer thickness. The fundamental equations are governed within the framework of first-order-shear deformation theory by utilizing Hamilton’s principle, von-Karman geometrical nonlinearity and the principal of mixtures. Newmark direct integration procedure is implemented to transform the dynamic equations into a static form and then the kinetic dynamic relaxation numerical technique in conjunction with the finite difference discretization method are employed to solve the nonlinear partial differential governing equations. Finally, the effects of porosity fraction and scattering patterns, boundary constrains, the variation of materials’ grading indexes and elastic foundation constants on the transient performances of the plate are studied in detail.

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“…Yang and Wang [7] obtained the dynamical behaviour of an inclined beam under a moving vertical force and conducted stability analysis. Yang et al [8], for bi-directional functionally graded beams, conducted a dynamic response analysis using a boundary-domain integral equation technique and analysed the natural frequencies and forced vibrations. Sarparast and Ebrahimi-Mamaghani [9] conducted forced/free vibrations analysis due to moving loads on laminated curved beams via the Galerkin method and obtained the fundamental frequency and displacements.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear coupled moving-load excited dynamics of beam-mass structures

Ghayesh

Farokhi

Zhang

et al. 2020

Archiv.Civ.Mech.Eng

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Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton's principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.

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Dynamic behaviors of tapered bi-directional functionally graded beams with various boundary conditions under action of a moving harmonic load

Cited by 28 publications

References 26 publications

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Transient behavior of imperfect bi-directional functionally graded sandwich plates under moving loads

Nonlinear coupled moving-load excited dynamics of beam-mass structures

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