Dynamic analysis on axially functionally graded plates resting on elastic foundation

Kumar, Saurabh; Das, Subhankar; Gayen, Debabrata; Joshi, Ankita

doi:10.1016/j.matpr.2022.08.478

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…Coskun et al [14] analyzed the elastic stability of variable cross-section columns by means of some analytical approximation techniques. Kumar [15] analysed the dynamic behaviour of axially functionally graded beams resting on variable elastic foundations. Jorge et al [16] developed a FEM program to analyze the dynamic response of simply supported beams on a non-uniform nonlinear foundation subjected to moving loads.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Huang,

Liu,

Zhao

2023

Applied Sciences

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Inhomogeneous materials, variable foundations, non-uniform cross-sections, and non-uniformly distributed loads are common in engineering structures and typically complicate their mechanical analysis considerably. This paper presents an accurate and efficient numerical method for the dynamic analysis of non-uniform functionally graded beams resting on inhomogeneous viscoelastic foundations subjected to non-uniformly distributed moving load and investigates the effects of non-uniformities and inhomogeneities on material, foundation, and load. Based on the Timoshenko beam theory and a Chebyshev spectral method, a consistent discrete dynamic model is derived, which can deal with all axially varying properties. A series of numerical experiments are carried out to validate the convergence and accuracy of the proposed method. The results are compared with those obtained through finite element analysis or in the literature, and excellent agreement is observed. Then, the dynamic response of an axially functionally graded beam resting on an inhomogeneous viscoelastic foundation and subjected to a non-uniformly distributed moving load is investigated. The results show that the material gradient and the inhomogeneous foundation can alter the vibration amplitudes and critical speeds of the beam significantly. Compared with more realistic non-uniformly distributed moving load models, idealized concentrated and uniformly distributed moving load models produce apparent computation errors in vibration amplitudes.

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Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Huang,

Liu,

Zhao

2023

Applied Sciences

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“…Yas et al [31] introduced the generalized differential quadrature method to observe the free vibrational characteristics of the FGM beam. Kumar [32] utilized the Rayleigh-Ritz principle to predict the vibrational frequency of the AFG beam.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

Lohar¹,

Mitra²

2022

FME Transactions

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The present work investigates the nonlinear free vibration of an axially functionally graded (AFG) beam supported on the variable foundation. The beam geometry is non-uniform, with a linear cross-section variation along the length. The beam material is graded along the axial direction following the power-law relation. A Winkler type of variable elastic foundation is taken, in which variation of stiffness is considered along the length of the foundation. Geometrical nonlinearity produced by the beam's large-amplitude deflection is also considered. To attain the desired objectives, the problem is divided into two parts. The static problem is solved first, then a subsequent free vibration analysis is executed on the statically deformed beam configuration. The governing differential equations of the system are derived using suitable energy methods. A numerical technique of direct substitution with relaxation is utilized to obtain the solution of the derived nonlinear differential equations. A suitable validation study is presented to ensure the appropriateness of the present methodology. Benchmark results are also presented by means of natural frequency, backbone curve, and mode shape plot to investigate the influences of elastic foundation, material gradation, and non-uniform geometry on nonlinear vibration.

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Dynamic analysis on axially functionally graded plates resting on elastic foundation

Cited by 2 publications

References 19 publications

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

Nonlinear free vibration analysis of non-uniform axially graded beam on variable elastic foundation

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