A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads

Khalili, S.M.R.; Jafari, Ali; Eftekhari, S. A.

doi:10.1016/j.compstruct.2010.02.012

Cited by 150 publications

(57 citation statements)

References 43 publications

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“…Regardless of the grading index , the table shows a good agreement between the result of the present work with that obtained by using a semianalytical method in [39] and the different transformation method in [40]. In addition, the deflections evaluated by the present beam element are in excellent agreement with the finite element solution in [30], where the beam element based on Kosmatka's shape functions was used.…”

Section: Forcedsupporting

confidence: 75%

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

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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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.

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Section: Forcedsupporting

confidence: 75%

“…The beam is also assumed to be formed from SUS304 and Al 2 O 3 , and the moving load speed V is considered to be constant. The problem has been previously investigated by several authors, including Simsek and Kocatürk [39] and Khalili et al [40], for a FGM beam in room temperature.…”

Section: Forcedmentioning

confidence: 99%

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

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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“…Due to the importance of this problem, many papers have appeared in the literature. Compared with the problem of beams subjected to moving loads (see [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]), the number of studies related to the vibration of plates due to moving loads is rather limited. Gbadeyan and Oni [69] developed a theory related to the response of Rayleigh beams and plates under an arbitrary number of moving masses.…”

mentioning

confidence: 99%

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

et al. 2015

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This study deals with forced vibration analysis of a microplate subjected to a moving load. The formulation is developed based on the modified couple stress theory in conjunction with Kirchhoff-Love plate theory. The equations of motion of the problem are derived using Lagrange's equations. In order to obtain the response of the microplate, the trial function for the dynamic deflection is expressed in the polynomial form. The equations of motion are solved by using the implicit time integration Newmark-β method, and then displacements, velocities and accelerations of the microplate at the considered point and time are determined. Five different sets of boundary condition are considered. For this purpose, boundary conditions are satisfied by adding some auxiliary functions to the trial functions. A parametric study is conducted to study the effects of the material length scale parameter, plate aspect ratio, boundary conditions and the moving load velocity on the dynamic response of the microplate. Also, in order to validate the present formulation and solution method, some comparisons with those available in the literature are performed. Good agreement is found. The results show that the dynamic deflections are significantly affected by the scale parameter and the load velocity.

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“…Simsek and Kocaturk [6] investigated free vibration characteristics and the dynamic behavior of simply-supported FG beam under a concentrated moving harmonic load. Khalili et al [7] combined the Rayleigh-Ritz method and the differential quadrature method to solve forced vibration analysis of FG beams subjected to moving loads. Alshorbagy et al [8] presented the dynamic characteristics of FG beams with material graduation in axially or transversally through the thickness.…”

Section: Introductionmentioning

confidence: 99%

Static and vibration analysis of functionally graded beams using refined shear deformation theory

et al. 2013

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Citation: Vo, Thuc, Thai, Huu-Tai, Nguyen, Trung-Kien and Inam, Fawad (2013) Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)Static and vibration analysis of functionally graded beams using refined shear deformation theory AbstractStatic and vibration analysis of functionally graded beams using refined shear deformation theory is

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A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads

Cited by 150 publications

References 43 publications

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

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

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

Static and vibration analysis of functionally graded beams using refined shear deformation theory

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