Static and dynamic analyses of cracked functionally graded structural components: A review

Gayen, Debabrata; Tiwari, Rajiv; Chakraborty, Debabrata

doi:10.1016/j.compositesb.2019.106982

Cited by 78 publications

(20 citation statements)

References 135 publications

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“…Panigrahi and Pohit studied the non-linear dynamics of a FG cracked Timoshenko beam under an excitation force using the harmonic balance method in conjunction with an iterative technique [22]. The readers interested in more details on this topic can refer to [23]. The present article is an extension of our previous work [24], based on the single mode approach.…”

Section: Introductionmentioning

confidence: 94%

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

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Geometrically non-linear vibrations of functionally graded Euler-Bernoulli beams with multi-cracks, subjected to a harmonic distributed force, are examined in this paper using a theoretical model based on Hamilton's principle and spectral analysis. The homogenisation procedure is performed, based on the neutral surface approach, and reduces the FG beams analysis to that of an equivalent homogeneous multi-cracked beam. The so-called multidimensional Duffing equation obtained and solved using a simplified method (second formulation) previously applied to various non-linear structural vibration problems. The curvature distributions associated to the multi-cracked beam forced deflection shapes are obtained for each value of the excitation level and frequency. The parametric study performed in the case of a beam and the detailed numerical results are given in hand to demonstrate the effectiveness of the proposed procedure, and in the other hand conducted to analyse many effects such as the beam material property, the presence of crack, the vibration amplitudes and the applied harmonic force on the non-linear dynamic behaviour of FG beams.

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Section: Introductionmentioning

confidence: 94%

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

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“…Early application of gradation laws for composites was proposed in works of Bever and Duwez [8], and Shen and Bever [9] in 1972, but the work had limited impact due to restrictions in the knowledge of FGM production techniques. The first practical application of FGMs was carried out by Japanese material scientists at National Aerospace Laboratory of Japan in 1984 to prepare advanced ultra-high temperature resistance structural materials for using not only in space structures, fusion reactors, and future space-plane system but also in various functional (optic and electronic) materials [10]. Sankar provided an elasticity solution for FG beams using exponential law [11].…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Gradient on Vibration Characteristics of a Functionally Graded Shaft System

Bose¹,

Sathujoda²

2020

MMEP

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The study aims to investigate the vibration characteristics of ceramic-based functionally graded materials (FGM) when subjected to dynamic conditions. Effect of thermal gradients on natural frequencies of rotating FG shafts has been investigated using three dimensional (3D) solid elements which is rarely found in literature. The FG material used in the work has metal and ceramic as its constituents. Three-dimensional finite element modelling and analysis of the FG shaft system has been carried out using ANSYS software to determine the natural frequencies with proper validations. The study involves modelling of the shaft using two different material laws; power-law and exponential law. Continuous variation of material properties is achieved using a Python code that discretizes the shaft radially and applies the position-dependent material properties. The shaft has been subjected to different thermal environments by applying temperature gradients accordingly. Thermal gradation is achieved using two different methods, nonlinear temperature distribution (NLTD) and exponential temperature distribution (ETD). Effects of material gradation on the fundamental frequencies of the shaft is presented. The variations due to different material laws and thermal gradients are also identified. The whirl frequencies have been determined for the rotating shaft system. The effect of material gradation laws and temperature gradients on separation of the frequencies at rotating speeds is determined. Attempts have been made to obtain suitable reasons for the behaviours based on the material properties. The obtained results show the influence of material gradation methods, power-law index, and temperature gradients on vibration characteristics of the ceramic-based FG shaft system. Furthermore, the reasons of the variations are also discussed in detail.

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“…Consequently, FG materials are suitable for many engineering fields and considerable attention has been paid to the mechanical behaviors of FG structures [1][2][3] . Recently, with the advancement in micro-electro-mechanical systems (MEMSs), FG materials have been utilized to build various micro-structures in order to achieve high performance, which encourage researchers to investigate and predict the mechanical behaviors of FG micro-structures.…”

Section: Introductionmentioning

confidence: 99%

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

Wang

Sun

et al. 2020

Appl. Math. Mech.-Engl. Ed.

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A quasi-three dimensional model is proposed for the vibration analysis of functionally graded (FG) micro-beams with general boundary conditions based on the modified strain gradient theory. To consider the effects of transverse shear and normal deformations, a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness. The conventional beam theories including the classical beam theory, the first-order beam theory, and the higherorder beam theory are regarded as the special cases of this model. The material properties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme. The energy-based formulation is derived by a variational method integrated with the penalty function method, where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables. The formulation is validated by some comparative examples, and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

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Static and dynamic analyses of cracked functionally graded structural components: A review

Cited by 78 publications

References 135 publications

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Effect of Thermal Gradient on Vibration Characteristics of a Functionally Graded Shaft System

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

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