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Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells

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Abstract

The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear deformation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh–Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.

Graphical Abstract

The free vibration of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations is investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. Shell motion is represented by first-order shear deformation theory. The governing equation is obtained using the Rayleigh–Ritz method. The fluid is described by classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.

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Abbreviations

\(b_\mathrm{e}\) :

Axial length of elastic foundation

\(K_\mathrm{W},\,K_\mathrm{P}\) :

Nondimensional stiffness of elastic foundation

\(L,\,R,\,h\) :

Length, radius, and thickness of shell

\(m,\,n\) :

Wave numbers in mode shape

p :

Volume fraction index

\(U,\,T\) :

Strain and kinetic energies of shell

\(U_\mathrm{EF}\) :

Strain energy due to elastic foundation

\(W_\mathrm{F}\) :

Work done by fluid

\({\varvec{K}}_{\mathrm{EF}}\) :

Added stiffness matrix by elastic foundation

\({\varvec{M}}_{\mathrm{F}}\) :

Added mass matrix by fluid pressure

\({\varvec{M}}_{\mathrm{S}},\,{\varvec{K}}_{\mathrm{S}}\) :

Mass and stiffness matrices of shell

\(\theta _{0}\) :

Contact angle of elastic foundation

\(\omega \) :

Angular natural frequency

\(\varOmega _\mathrm{NE}, \varOmega _\mathrm{NF}\) :

Nondimensional frequencies for empty (E), fluid-filled (F) shell without elastic foundation (N)

\(\varOmega _\mathrm{PE}, \varOmega _\mathrm{PF}\) :

Nondimensional frequencies for Pasternak model (P)

\(\varOmega _\mathrm{WE}, \varOmega _\mathrm{WF}\) :

Nondimensional frequencies for Winkler model (W)

\(\varOmega _\mathrm{S}, \varOmega _\mathrm{A}\) :

Nondimensional frequencies for symmetric and antisymmetric modes

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  1. Department of Mechanical Design Engineering, Chonnam National University, Yeosu, 550-749, Korea

    Young-Wann Kim

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Kim, YW. Effect of partial elastic foundation on free vibration of fluid-filled functionally graded cylindrical shells. Acta Mech. Sin. 31, 920–930 (2015). https://doi.org/10.1007/s10409-015-0442-5

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