A new Hamiltonian-based approach for free vibration of a functionally graded orthotropic circular cylindrical shell embedded in an elastic medium

Ni, Yiwen; Tong, Zhenzhen; Rong, Dalun; Zhou, Zhenhuan; Xü, Xinsheng

doi:10.1016/j.tws.2017.09.003

Cited by 26 publications

(10 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a better illustration of the influence of geometrical parameters, the vibration mode shapes of a S-S porous METE-FG cylindrical shell for various L/R and h/R are displayed in Figure 4. The phenomenon for porous METE-FG cylindrical shells is similar to those for a classical elastic cylindrical shell (Leissa, 1973;Ni et al, 2017).…”

Section: Parametric Study (A) Effect Of Boundary Conditions Lengths and Thicknesses Of Shellssupporting

confidence: 54%

“…With reference to l and m (Ni et al, 2017), the eigenfunctions (39) can be grouped into seven categories as presented in Table 1 where 1 are determined by equation ( 38). In addition, it is significant to note that the eigenfunctions h n can be divided into two groups: (1) zero eigenfunctions with m = 0 and (2) non-zero eigenfunctions with m 6 ¼ 0.…”

Section: Symplectic Eigenvalue Problem and Exact Frequency Solutionmentioning

confidence: 99%

“…The physical insight of porosities in the shells is revealed by the porosity volume fraction and porosity distribution profiles. Some studies that presented exact solutions for other focuses using the Hamiltonian system have been reported (Chen and Zhao, 2009;Kattimani and Ray, 2018;Lim and Xu, 2010;Ni et al, 2017;Sun et al, 2013Sun et al, , 2014aSun et al, , 2014bWang and Qin, 2007;Yao et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An accurate model for free vibration of porous magneto-electro-thermo-elastic functionally graded cylindrical shells subjected to multi-field coupled loadings

Zhu

Sun

et al. 2021

Journal of Intelligent Material Systems and Structures

Self Cite

View full text Add to dashboard Cite

An accurate model for vibration of a porous magneto-electro-thermo-elastic functionally graded (METE-FG) cylindrical shell made of barium titanate (BaTiO3) and cobalt diiron tetraoxide (CoFe2O4) with magneto-electro-thermal loadings is proposed within the framework of Hamiltonian system. Four types of porosity distribution profiles in the thickness direction are considered. By introducing a new total eigenvector, the higher-order governing differential equations are transformed into a set of lower-order equations. The exact solution for free vibration of METE-FG shells can be expanded in terms of specific symplectic eigenfunctions having seven possible explicit forms. Subsequently, analytical frequency equations and vibration mode shapes for METE-FG shells with various boundary conditions are derived simultaneously. A comparison study is presented to demonstrate the accuracy of the proposed model and very good agreement is observed. The effects of material properties and magneto-electro-thermal loadings on free vibration characteristics of METE-FG cylindrical shells are analyzed and discussed in detail.

show abstract

Section: Parametric Study (A) Effect Of Boundary Conditions Lengths and Thicknesses Of Shellssupporting

confidence: 54%

Section: Symplectic Eigenvalue Problem and Exact Frequency Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An accurate model for free vibration of porous magneto-electro-thermo-elastic functionally graded cylindrical shells subjected to multi-field coupled loadings

Zhu

Sun

et al. 2021

Journal of Intelligent Material Systems and Structures

Self Cite

View full text Add to dashboard Cite

show abstract

“…The circular cylinders have stainless steel on their inner surface and nickel on their outer surface. Table 3 shows comparisons of the natural frequencies of clamped-clamped FGM cylindrical shells made with those of Iqbal et al [21] and Ni et al [31]. The circular cylinders have stainless steel on their outer surface and nickel on their inner surface.…”

Section: Validation Studiesmentioning

confidence: 99%

“…Then, the natural frequencies of the FGM cylinders were attained by solving algebraic equations. Ni et al [31] used the Hamiltonian approach to find the exact solution for the free vibration of FGM circular cylindrical shells embedded in an elastic medium. Based on the Reissner shell theory and symplectic mathematics, solutions were determined analytically.…”

Section: Introductionmentioning

confidence: 99%

Natural frequencies analysis of functionally graded circular cylindrical shells

Alshabatat

Zannon

2021

ACM

View full text Add to dashboard Cite

In the present work, a study on natural frequencies of functionally graded materials (FGM) circular cylindrical shells is presented. TheFGM is considered to be a mixture of two materials. The volumetric fractions are considered to vary in the radial direction (i.e., through the thickness) in compliance with a conventional power-law distribution. The equivalent material properties are estimated based on the Voigt model. The analysis of the FGM cylindrical shells is performed using the third-order shear deformation shell theory and the principle of virtual displacements. Moreover, the third-order shear deformation shell theory coupled with Carrera’s unified formulation is applied for the derivation of the governing equations associated with the free vibration of circular cylindrical shells. The accuracy of this method is examined by comparing the obtained numerical results with other previously published results. Additionally, parametric studies are performed for FGM cylindrical shells with several boundary conditions in order to show the effect of several design variables on the natural frequencies such as the power-law exponent, the circumferential wave number, the length to radius ratio and the thickness to radius ratio.

show abstract

An analytical method for free vibrations of functionally graded cylindrical shells with arbitrary intermediate ring supports

Xie

Chen

2021

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

A new Hamiltonian-based approach for free vibration of a functionally graded orthotropic circular cylindrical shell embedded in an elastic medium

Cited by 26 publications

References 49 publications

An accurate model for free vibration of porous magneto-electro-thermo-elastic functionally graded cylindrical shells subjected to multi-field coupled loadings

An accurate model for free vibration of porous magneto-electro-thermo-elastic functionally graded cylindrical shells subjected to multi-field coupled loadings

Natural frequencies analysis of functionally graded circular cylindrical shells

An analytical method for free vibrations of functionally graded cylindrical shells with arbitrary intermediate ring supports

Contact Info

Product

Resources

About