Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells surrounded by an elastic medium in thermal environments

Chan, Do Quang; Anh, Vu Thi Thuy; Duc, Nguyen Dinh

doi:10.1007/s00707-018-2282-4

Cited by 33 publications

(10 citation statements)

References 34 publications

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“…For natural frequency analysis, the transverse excitation f mn can be neglected. We assume the approximated periodic solution of the Duffing differential equation (26) as…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

“…Introducing Eq. (27) into the Duffing differential equation (26) and combining the coefficients of the cosine functions yield the following equation:…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

“…Ansari et al [25] employed the higher-order shear deformation shell theory to study the free vibrations and large-amplitude forced vibrations of a composite conical shell reinforced by FG carbon nanotubes. Chan et al [26][27] investigated the nonlinear dynamic behavior of the truncated eccentrically stiffened FG conical shell and truncated FG conical panel. The Haar wavelet method was used to derive the frequencies of a truncated rotating conical shell [28] .…”

Section: Introductionmentioning

confidence: 99%

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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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“…For natural frequency analysis, the transverse excitation f mn can be neglected. We assume the approximated periodic solution of the Duffing differential equation (26) as…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

“…Introducing Eq. (27) into the Duffing differential equation (26) and combining the coefficients of the cosine functions yield the following equation:…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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show abstract

“…Dung et al [18] solved the post-buckling problem of reinforced FG cylindrical shells under axial-compressive loads and on elastic foundations using the classical shell theory. Anh et al [19] studied the nonlinear vibration and dynamic response of stiffened FG cylindrical shells on elastic foundations in thermal environments. Recently, Liu et al presented a numerical model to predict compressive behavior of composite helical springs [20].…”

Section: Introductionmentioning

confidence: 99%

A numerical model for investigation of dynamic behavior and free vibration of functionally graded cylindrical helical springs

Bahri

Ebrahimi

Atibeh

2021

jcc

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“…Wang and Shen [41] presented the nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations. In addition, there were many other studies on FGM materials [42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Vibration and nonlinear dynamic analysis of variable thickness sandwich laminated composite panel in thermal environment

Nguyen

Kim

et al. 2020

Jnl of Sandwich Structures & Materials

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Based on the first-order shear deformation theory taking into account geometrical nonlinearity, initial geometrical imperfection, vibration and nonlinear dynamic analysis of the sandwich laminated composite panel characterized by a continuous thickness variation in thermal environment and resting on an elastic foundation are considered in this paper. Variable thickness could affect the design of composite panel since it allows to tailor the stiffness features in the most stressed areas within the domain, keeping the weight constant. As a consequence, an improved dynamic behavior of the structure may be exhibited. The motion equations of dynamic analysis are determined due to Galerkin method and the obtained equation is numerically solved by using Runge-Kutta method. In numerical results, the effects of initial geometrical imperfections and geometrical parameters, material properties, coefficients of foundation, mechanical loads, temperature and the variable thickness on the nonlinear dynamic response and vibration of the laminated composite panel are investigated.

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Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells surrounded by an elastic medium in thermal environments

Cited by 33 publications

References 34 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

A numerical model for investigation of dynamic behavior and free vibration of functionally graded cylindrical helical springs

Vibration and nonlinear dynamic analysis of variable thickness sandwich laminated composite panel in thermal environment

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