Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories

Xie, Ke; Wang, Yuewu; Fan, Xiang; Fu, Tairan

doi:10.1016/j.apm.2019.09.024

Cited by 33 publications

(7 citation statements)

References 46 publications

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“…Derivation for equations ( 16) and ( 17) 16). Substituting equation (A.12) into equation (A.13) obtains equation (17).…”

Section: Data Availability Statementmentioning

confidence: 99%

“…In the case of a functionally graded beam, the material properties may vary in the thickness direction [12][13][14][15][16][17], in the length direction [18][19][20][21][22][23][24][25] or in both directions referred to as bi-directional functionally graded beam (BDFGB) [26][27][28][29][30][31]. A considerable amount of literature has been published on the investigation of unidirectional functionally graded beams over the past decades [12][13][14][15][16][17][20][21][22][23][24][25]. The research devoted to BDFGB is relatively less but still noteworthy.…”

Section: Introductionmentioning

confidence: 99%

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A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

Zhang,

Liao,

Fan

et al. 2024

Smart Mater. Struct.

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This paper presents a novel semi-analytical simulation approach for analyzing the behaviour of bi-directional functionally graded cantilever beams subjected to arbitrary static loads, such as concentrated moments, concentrated forces, distributed force and their combinations applied at any location along the beam. The fundamental equations governing the cantilever beam’s response are derived, on the basis of which the proposed semi-analytical method is implemented using MATLAB programming language. The simulation results include field variables as well as stress contours, providing a compressive understanding of the beam’s behaviour. To validate the accuracy and reliability of the proposed method, a convergence study is conducted in comparison with the graded finite element method (GFEM) and analytical solutions. In the end, the developed method is applied to simulate the bending behaviour of bi-directional functionally graded cantilever beams under various loads individually and their combinations. The stress contours and deflection curves obtained from the simulation are compared with the solutions obtained using GFEM, revealing that the developed method possesses excellent capability in accurately simulating the bending behaviour of cantilever beams.

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“…Derivation for equations ( 16) and ( 17) 16). Substituting equation (A.12) into equation (A.13) obtains equation (17).…”

Section: Data Availability Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

Zhang,

Liao,

Fan

et al. 2024

Smart Mater. Struct.

View full text Add to dashboard Cite

show abstract

“…The force and frequency-amplitude diagrams of the AFG system are used to examine gradient index and tapered ratios. Ke Xie et al [ 37 ] performed a nonlinear free vibration analysis on functionally graded beams using a variety of shear deformation theories. In this study, the Ritz method and the Lagrange equation were employed to construct discrete formulations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear frequency analysis of porous Bi directional functionally graded beams utilizing reddy shear deformation theory

Forghani,

Bazarganlari,

Zahedinejad

et al. 2023

Heliyon

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“…Other nonlinear studies were conducted mostly based on Euler and Timoshenko beam theory using various approaches to obtain and solve the Governing Equations (Fallah and Agham, 2011; Malekzadeh and Shojaee, 2013; Panigrahi and Pohit, 2016; Simsek, 2010). Nonlinear free vibration analysis of functionally graded beams using different shear deformation theories was conducted by Xie et al(2020) utilizing Lagrange equation and Ritz method to yield the discrete formulations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear frequency behavior of cracked functionally graded porous beams resting on elastic foundation using Reddy shear deformation theory

Forghani

Bazargan-Lari

Zahedinejad

et al. 2022

Journal of Vibration and Control

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This paper presents the nonlinear frequency behavior of cracked functionally graded porous beams subjected to various boundary conditions using Reddy shear deformation theory and Green’s tensor together with the Von Karman geometric nonlinearity. The material properties of the beam vary exponentially in thickness direction. A generalized differential quadrature method (GDQM) in conjunction with a direct numerical iteration method is developed to solve the system of equations derived by means of Hamilton’s principle. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Euler and Timoshenko beam theory. The results for extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratios, porosity indexes, shear and elastic foundation parameters, and boundary conditions on the nonlinear frequency behavior. The location of crack plays the significant role on the nonlinear frequency ratios. The frequency ratios hit the minimum when the crack is located in mid-span of the beam. In this regard, the effect of shear stiffness of foundation is much more than that of Winkler one in the increasing mid-span value of nonlinear frequency ratio. It is also shown that the crack location results in decline of frequency ratios in the mid-span of beam specially for the cracks located closer to surface, the deeper ones lead to get nonlinear frequency ratios rise much more due to the fact that the deeper the crack is, the weaker the crack section becomes. The results of this paper and the effects of these parameters can be used in the optimal design of functionally graded beams and in crack prediction, detection, and monitoring techniques.

show abstract

Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories

Cited by 33 publications

References 46 publications

A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

Nonlinear frequency analysis of porous Bi directional functionally graded beams utilizing reddy shear deformation theory

Nonlinear frequency behavior of cracked functionally graded porous beams resting on elastic foundation using Reddy shear deformation theory

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