### Skapa referens, olika format (klipp och klistra)

**Harvard**

Okhovat, R. och Boström, A. (2015) *Dynamic equations for an isotropic spherical shell using power series method and surface differential operators*.

** BibTeX **

@conference{

Okhovat2015,

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

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

booktitle={2014 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, 2014; Greenville; United States; 2 June 2014 through 5 June 2014},

isbn={978-3-319-06988-3},

pages={29-36},

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 the shell 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 these 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 more compact form which can be represented explicitly in terms of the surface differential operators. The method is believed to be asymptotically correct to any order. The eigenfrequencies are compared to exact three-dimensional theory and membrane theory.},

year={2015},

keywords={Dynamic, Eigenfrequency, Power series, Shell equations, Spherical shell, Surface differential operators},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 213483

A1 Okhovat, Reza

A1 Boström, Anders

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

YR 2015

T2 2014 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, 2014; Greenville; United States; 2 June 2014 through 5 June 2014

SN 978-3-319-06988-3

SP 29

OP 36

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 the shell 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 these 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 more compact form which can be represented explicitly in terms of the surface differential operators. The method is believed to be asymptotically correct to any order. The eigenfrequencies are compared to exact three-dimensional theory and membrane theory.

LA eng

DO 10.1007/978-3-319-06989-0_4

LK http://dx.doi.org/10.1007/978-3-319-06989-0_4

OL 30