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**Harvard**

Okhovat, R. och Boström, A. (2017) *Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators*.

** BibTeX **

@article{

Okhovat2017,

author={Okhovat, Reza and Boström, Anders},

title={Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators},

journal={Journal of Sound and Vibration},

issn={0022-460X},

volume={393},

pages={415-424},

abstract={Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be Used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.},

year={2017},

keywords={Spherical shell, Shell equations, Surface differential operators, Eigenfrequency, elastic-waves, hollow sphere, layers, rods, Acoustics, Engineering, Mechanics },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 248883

A1 Okhovat, Reza

A1 Boström, Anders

T1 Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

YR 2017

JF Journal of Sound and Vibration

SN 0022-460X

VO 393

SP 415

OP 424

AB Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be Used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.

LA eng

DO 10.1016/j.jsv.2017.01.025

LK http://dx.doi.org/10.1016/j.jsv.2017.01.025

OL 30