Review of research on the vibration and buckling of the FGM conical shells

Sofiyev, A.H.

doi:10.1016/j.compstruct.2018.12.047

Cited by 146 publications

(24 citation statements)

References 146 publications

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“…A number of papers have reported the investigations of the vibrational characteristics of conical shell structures. A review on the buckling and vibrational characteristics of functionally graded material (FGM) conical shells was published by Sofiyev [22] . Song et al [23] studied the free vibration of the conical shells subject to an elastic constraint and inertia force under arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

Yang

Hao

Zhang

et al. 2021

Appl. Math. Mech.-Engl. Ed.

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In this study, the first-order shear deformation theory (FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite (FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets (GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young’s modulus. Hamilton’s principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

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Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

Yang

Hao

Zhang

et al. 2021

Appl. Math. Mech.-Engl. Ed.

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“…Babaei et al [17,18] obtained the linear/nonlinear free vibration responses of FG shallow arches with circular cross section using perturbation method. For more researches on the dynamic response and vibration analysis of FG structures in the shape of plates and shells with/without elastic foundation, one may refer to [19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Babaei

Eslami

2021

Eur. Phys. J. Plus

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A nonlocal strain gradient theory is developed in this paper to study the large amplitude vibrations of arches made of functionally graded (FG) porous material. The case of shallow arches resting on nonlinear elastic foundation is modeled via a general higherorder shear deformation theory. The third-order model of Reddy, the first-order model of Timoshenko, and the classical model of Euler-Bernoulli are analyzed. Thermomechanical properties of the arch exposed to the uniform thermal field are assumed to be temperature dependent. The nonlinear motion equations of the arch are established by employing Hamilton's principle and the von Kármán type of geometric nonlinearity. The two-step perturbation technique and the Galerkin method are utilized to solve the nonlinear governing equations. The size-dependent linear and nonlinear frequencies of the arch are obtained for the immovable pinned-pinned boundary conditions. The comparison studies are performed to verify the present solution method with the provided data in the literature, and a good agreement is observed. The novel parametric studies covered in this research include the effects of several parameters such as elastic foundation, nonlocal and length scale parameters, porosity, temperature field, power law index, and geometrical parameters on the frequencies of FG porous arches in detail.

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“…Functionally graded materials (FGMs) have continuously varying material properties along the structure dimension according to a certain law (Gupta and Talha, 2015;Koizumi, 1997;Sofiyev, 2019). The advantages of two or more materials can be designed into one FGM structure to achieve desired performance, for example, the FGM made of ceramics and metals, which combine the high tenacity of metals and temperature resistance of ceramics.…”

Section: Introductionmentioning

confidence: 99%

Vibration response and band gap characteristics of functionally graded frame structure

Liu

Yuan³

et al. 2020

Journal of Vibration and Control

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Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.

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Review of research on the vibration and buckling of the FGM conical shells

Cited by 146 publications

References 146 publications

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Vibration response and band gap characteristics of functionally graded frame structure

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