Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler–Pasternak foundation with different boundary conditions under thermal environment

Tú, Trần Minh; Nguyen, Van-Loi; Pham, Sy-Dong; Rungamornrat, Jaroon

doi:10.1007/s00707-020-02658-y

Cited by 33 publications

(6 citation statements)

References 43 publications

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“…Based on Donnell's thin shell theory and employing the Galerkin procedure, the free vibration behavior of gridstiffened composite truncated spherical shells was reported by Ansari, Hemmatnezhad and Taherkhani [14]. Tu Tran et al [15] employed FSDT, together with the Galerkin method and Lekhnitsky's smeared stiffener technique, to analyze natural frequencies of stiffened FG circular cylindrical shells supported by a Pasternak elastic foundation for various boundary conditions subjected to a thermal environment. The free vibration analysis of laminated stiffened cylindrical panels based on FSDT and utilizing FEM was surveyed by Tuan, Quoc and Tu, [16].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Zhou,

Zhang,

Nyasha Chirukam

et al. 2023

Mathematics

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In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, ring and stinger with GPLs is independently studied. Halpin–Tsai relations are employed to evaluate the mechanical properties of the shell panel, rings and stringers. The first-order shear deformation shell theory, accompanied by the Lekhnitsky smeared stiffener model, using the numerical finite element method and Hamilton principle, is employed to develop the governing motion equations of the shell panel. Four different types of GPL patterns, including FG-A, FG-X, FG-O and UD, are assumed across the thickness of the shell panel, rings and stringers. The effects of different factors, including various weight fractions and patterns of GPLs nanofillers, the geometry of the shell panel and stiffeners and two displacement boundary conditions, on the natural frequencies of the shell panel, have been studied.

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Section: Introductionmentioning

confidence: 99%

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Zhou,

Zhang,

Nyasha Chirukam

et al. 2023

Mathematics

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“…Free vibration analysis of functionally graded doubly curved shell panels resting on elastic foundation in thermal environment was researched by Tran et al [12]. Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler-Pasternak foundation with different boundary conditions under thermal environment was studied by Tran et al [13]. Vibrations of ribbed shallow rectangular shells on the Winkler and Pasternak Foundation was studied by Lugovoi et al [14].…”

Section: Introductionmentioning

confidence: 99%

An analytical method for shallow spherical shell free vibration on two-parameter foundation

Gan

Yuan

et al. 2021

Heliyon

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The free vibration control differential equation of shallow spherical shell on two-parameter foundation is a four order differential equation. Using the intermediate variable, the four order differential equation is reduced to two lower order differential equations. The first lower order differential equation is a Helmholtz equation. A new method of two-dimensional Helmholtz operator is proposed as shown in the paper in which the Bessel function included in Helmholtz equation needs to be treated appropriately to eliminate singularity. The first lower order differential equation is transformed into the integral equation using the proposed method in the paper. The second lower order differential equation which is a Laplace equation is transformed into the integral equation by existing methods. Then the two integral equations are discretized according to the middle rectangle formula, and the corresponding solutions can be obtained by MATLAB programming. In this paper, the R-function theory is used to select the appropriate boundary equation to eliminate the singularity. Based on the properties of Rfunction, the combined method of Helmholtz equation and Laplace equation can solve the free vibration problem of irregular shallow spherical shell on two-parameter foundation. Five examples are given to verify the feasibility of the method.

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“…Many works have been performed on the static and dynamic behaviors of FGM structural components in recent years. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] To apply the functionally graded (FG) beam structures widely into the engineering practice, an in-depth understanding of their both linear and nonlinear behaviors is essential. In the existing literature, it is found that many researchers have paid their attention to studying on linear behaviors of the FG beams.…”

Section: Introductionmentioning

confidence: 99%

“…Many works have been performed on the static and dynamic behaviors of FGM structural components in recent years. 1–14…”

Section: Introductionmentioning

confidence: 99%

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Long

Nguyen

Tú

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

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In this paper, an exact solution for nonlinear static behaviors of functionally graded (FG) beams with porosities resting on the elastic foundation is presented. The FG material properties with porosities are assumed to vary along the thickness of the beam, and two types of porosity distributions are considered. Actually, the geometrical middle surface of the FG beam selected in computations is very popular in the literature. By contrast, in this study, the physical neutral surface of the beam is utilized. Based on the Timoshenko beam theory, von Kármán nonlinear assumption, together with neutral surface concept, the nonlinear governing equations of the FG beam resting on the elastic foundation are derived. By using the physical neutral surface, the nonlinear governing equations have simple forms and can be solved directly. The exact solution for the problem with all immovable and moveable boundary conditions is conducted in detail. Some numerical investigations to show the effects of boundary conditions, material properties, length-to-thickness ratio, elastic foundation coefficients and several types of applied load on nonlinear static bending behaviors of the beam are given.

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Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler–Pasternak foundation with different boundary conditions under thermal environment

Cited by 33 publications

References 43 publications

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

An analytical method for shallow spherical shell free vibration on two-parameter foundation

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

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