Free vibration analysis of a cylindrical micro-shell based on MCST

Rao, Li; Lin, Chao; Zhang, Chenglin; Arefi, Mohammad

doi:10.1016/j.aej.2021.11.058

Cited by 7 publications

(3 citation statements)

References 38 publications

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“…Mazur et al [33] incorporated the kinematic model of Kirchhoff-Love plate theory into the MCST to study the free vibration and static buckling behaviors of orthotropic small-scale plates with complex shapes. Incorporating the displacement model of the TSDT into the MCST, Rao et al [34] investigated the size-dependent free vibration characteristics of cylindrical microshells. Yuan et al [35] combined the MCST with the HSDT model to examine the size-dependent nonlinear instability behavior of FG conical microshells.…”

Section: Introductionmentioning

confidence: 99%

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A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

Wu,

Hsu

2023

Z Angew Math Mech

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Within the framework of the consistent couple stress theory (CCST), we develop a Hermitian Cn (n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into nl microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian Cn FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian Cn polynomials. The accuracy and the convergence rate of our Hermitian Cn FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.

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Section: Introductionmentioning

confidence: 99%

“…Incorporating the displacement model of the TSDT into the MCST, Rao et al. [34] investigated the size‐dependent free vibration characteristics of cylindrical microshells. Yuan et al.…”

Section: Introductionmentioning

confidence: 99%

A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

Wu,

Hsu

2023

Z Angew Math Mech

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“…Cylindrical micro-and nano-shells, including mesh ones, are among the typical sensing elements of MEMS and NEMS often operating in wide temperature ranges. Therefore, the need to study the behavior of such mechanical objects as cylindrical micro-and nano-shells under various external influences does not weaken [1][2][3][4][5][6]. Many authors rely on mathematical models based on linear theory; however, experimental data indicate the need to take nonlinearity into account when modelling the behaviour of the objects in question [7].…”

Section: Introductionmentioning

confidence: 99%

Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems

Krylova,

Sinichkina

2023

E3S Web Conf.

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A new mathematical model of a non-linear mesh cylindrical shell behaviour in the temperature field under normal distributed load is constructed. The construction of the mathematical model takes into account the Kirchhoff-Love kinematic model and the Duhamel-Neumann hypothesis. The scaling effect is taken into account by the modified moment theory of elasticity. It is assumed that the displacement and rotation fields are not independent. Geometric nonlinearity is taken into account according to T. von Karman's theory. The equations of motion of the smooth shell, boundary and initial conditions are derived from the variational Ostrogradsky-Hamiltonian principle. The lattice structure of the shell was modelled by the continuum theory of G. I. Pshenichny. This allowed us to replace the regular rib system by a continuous layer. The equilibrium conditions of a rectangular element were used to write down the relations connecting stresses occurring in an equivalent smooth shell with stresses in the ribs. The Lagrange multiplier method has been used to determine the physical relationships for the mesh shell. By means of the method of establishment the study of features of the shell's plasticity has been carried out and the frequencies of natural linear vibrations depending on the mesh geometry have been obtained.

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Effect of Folding Process on the More Accurate Vibrational Characteristics of G-ori Composite Shell

Yaxin

2024

J. Vib. Eng. Technol.

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Free vibration analysis of a cylindrical micro-shell based on MCST

Cited by 7 publications

References 38 publications

A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems

Effect of Folding Process on the More Accurate Vibrational Characteristics of G-ori Composite Shell

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Free vibration analysis of a cylindrical micro-shell based on MCST

Cited by 7 publications

References 38 publications

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems

Effect of Folding Process on the More Accurate Vibrational Characteristics of G-ori Composite Shell

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A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages