Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory

Hosseini-Hashemi, Shahrokh; Ilkhani, Mohammad Reza

doi:10.1016/j.compstruct.2016.08.019

Cited by 26 publications

(10 citation statements)

References 43 publications

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“…Eringen’s nonlocal theory describes the stress at a point as a function of the strain in its vicinity, which could be expressed as follows (Hosseini-Hashemi and Ilkhani, 2016)…”

Section: Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Shojaeefard

Googarchin

Mahinzare

et al. 2018

Journal of Intelligent Material Systems and Structures

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This article investigates free vibration of a functionally graded piezomagnetic material cylindrical nanoshell embedded in viscoelastic media under rotational, external electric and magnetic loadings. The governing equations of the nanoshell are derived based on Eringen’s nonlocal theory. It is found that, magnetic and piezoelectric properties of the structure change exponentially along the thickness. The rotational loading is calculated considering initial hoop tension. The results are obtained by applying generalized differential quadrature method to the governing equations and associated boundary conditions. Results also include those achieved for clamped-clamped and simply hinged-hinged boundary conditions. It is found that free vibration characteristics of functionally graded piezomagnetic material cylindrical nanoshell are influenced by several factors including angular velocity, length scale parameter, external voltage, external amperage, functionally graded power index, and viscoelastic media parameters.

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“…Eringen’s nonlocal theory describes the stress at a point as a function of the strain in its vicinity, which could be expressed as follows (Hosseini-Hashemi and Ilkhani, 2016)…”

Section: Formulationmentioning

confidence: 99%

“…where K 0 is the modified Bessel function. Inserting equation (4) into equation (3) leads to (Hosseini-Hashemi and Ilkhani, 2016)…”

Section: Formulationmentioning

confidence: 99%

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Shojaeefard

Googarchin

Mahinzare

et al. 2018

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

show abstract

“…. , exp(jk n,ns )} is the wave number matrix and n s is the number of the characteristics roots of Equation (17) and the value of it is 10. W n = {W n,1 , W n,2 , .…”

Section: Implementation Of the Wbmmentioning

confidence: 99%

“…According to the previously reported studies, there are three main shell theories that are usually known: classical shell theory (CST) [13][14][15][16], first-order shear deformation shell theory (FSDST) [17][18][19][20][21] and higher-order shear deformation shell theory (HSDST) [22][23][24][25][26]. The classical shell theory is the basic theory, the transverse normal and shear deformations are ignored.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Shi

Wang

et al. 2020

Materials

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A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.

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“…With the development of cylindrical shell theory in recent decades, more and more theories are put forward and developed. At present, the main shell theory related to free vibration of cylindrical shell mainly includes three types, namely, classical shell theory [1][2][3][4], first-order shear deformation shell theory [5][6][7][8], and high-order shear deformation shell theory [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

Pang

Huo

et al. 2019

Mathematical Problems in Engineering

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The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the governing equations. On the basis of the kinematic relationship between the force resultant and displacement vector, the overall matrix of the shell is established. Comparison studies of this paper with the solutions in the literatures were carried out to validate the accuracy of the present method. Furthermore, by analyzing some numerical examples, the free vibration characteristics of orthogonal anisotropic cylindrical shells under classical boundary conditions, elastic boundary conditions, and their combinations are studied. Also, the effects of the material parameter and geometric constant on the natural frequencies for the orthotropic circular cylindrical shell under general boundary conditions are discussed. The conclusions obtained can be used as data reference for future calculation methods.

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Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory

Cited by 26 publications

References 43 publications

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

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