An extended finite element framework for vibration analysis of cracked FGM shells

Nasirmanesh, Amir; Mohammadi, Soheil

doi:10.1016/j.compstruct.2017.08.019

Cited by 25 publications

(5 citation statements)

References 59 publications

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“…Substituting equation (4) in terms of n and g into equation (6) gives the quadratic shape function, and it is given for the flexural vibration of the plate (7)…”

Section: Out-of-plane Vibration Of Platesmentioning

confidence: 99%

“…4 Joshi et al 5 presented an analytical model for vibration analysis of a thin orthotropic plate containing a partial crack, which is parallel to one of the edges of the plate, located at the center of the plate using Classical Plate Theory. Given the widespread use of functionally graded material shell elements in numerous industrial fields and their extreme vulnerability to crack formation, Nasirmanesh and Mohammadi 6 presented work is directed towards investigating the vibrational behaviors of cracked functionally graded material shells. Nguyen et al 7 investigated the vibration behaviors of functionally graded microplates with cracks, using a simple yet rigorous version of Mindlin's generalized continuum and the extended isogeometric analysis.…”

Section: Introductionmentioning

confidence: 99%

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Effect of crack on free vibration of a pre-stressed curved plate

Gönenli

Öztürk

Daş

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

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“…Substituting equation (4) in terms of n and g into equation (6) gives the quadratic shape function, and it is given for the flexural vibration of the plate (7)…”

Section: Out-of-plane Vibration Of Platesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of crack on free vibration of a pre-stressed curved plate

Gönenli

Öztürk

Daş

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…In 2018, Torabi and Ansari [4] presented a formulation of higher-order isoparametric supplement to study the free vibration of FGM shells, considering the structural effects of circular cylindrical, conical, spherical and toroid shells. In 2017, Baltacıoğlu and Civalek [5] used the extended FEM to obtain the frequency of the vibration of cracked FGM shells considering the structural effects of cylindrical * Corresponding author. E-mail address: cchong@mail.hust.edu.tw shell, conical shell and spherical on the vibrations.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Frequency of Thick FGM Circular Cylindrical Shells with Simply Homogeneous Equation by Using TSDT

Hong

2020

Adv. technol. innov.

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The objective of this study is to provide the frequency solutions of free vibration in thick FGM circular cylindrical shells by mainly considering both shear correction coefficient and nonlinear coefficient term. This paper investigates the effects of third-order shear deformation theory (TSDT) and the varied shear correction coefficient on the free vibration of thick functionally graded material (FGM), the circular cylindrical shells with simply homogeneous equation under thermal environment. The approach of derivations are given as follows, the varied value of shear correction coefficient is included in the simple homogeneous equation. The nonlinear term of displacement field of TSDT is also included to derive the simply homogeneous equation, some reasonable simplifications in the elements of homogeneous matrix under free vibration of thick FGM circular cylindrical shells are assumed, thus, the natural frequency can be found. Three parameters effect on the frequency of thick FGM circular cylindrical shells are computed and investigated, they are nonlinear coefficient c1 term, environment temperature and power law index. There are some main conclusions obtained, generally the natural frequency results are in decreasing value with the mode shape numbers for the thicker circular cylindrical shells. The values of natural frequencies are also affected by the nonlinear coefficient term.

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“…Chen et al (2017) studied the natural frequencies of sandwich doubly curved shallow FGM shells by using the new shear deformation theory based on Reddy's TSDT with transverse stretching effects. Nasirmanesh and Mohammadi (2017) studied the natural frequencies of cracked cylindrical FGM shells by using the general extended finite element formulation. Wali et al (2015) studied the natural frequencies of thick cylindrical FGM shells by using the discrete double directors shell model.…”

Section: Introductionmentioning

confidence: 99%

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

Hong

2020

Journal of Vibration and Control

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The effects of third-order shear deformation theory and varied shear correction coefficient on the vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation under thermal environment are investigated. The nonlinear coefficient term of displacement field of third-order shear deformation theory is included to derive the fully homogeneous equation under free vibration of functionally graded material cylindrical shells. The determinant of the coefficient matrix in dynamic equilibrium differential equations under free vibration can be represented into the fully fifth-order polynomial equation, thus the natural frequency can be found. Two parametric effects of environment temperature and functionally graded material power law index on the natural frequency of functionally graded material thick cylindrical shells with and without the nonlinear coefficient term of displacement fields are computed and investigated.

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An extended finite element framework for vibration analysis of cracked FGM shells

Cited by 25 publications

References 59 publications

Effect of crack on free vibration of a pre-stressed curved plate

Effect of crack on free vibration of a pre-stressed curved plate

Free Vibration Frequency of Thick FGM Circular Cylindrical Shells with Simply Homogeneous Equation by Using TSDT

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

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