Dynamic equations for an isotropic spherical shell using power series method and surface differential operators
Paper i proceeding, 2015

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.

Surface differential operators

Dynamic

Power series

Eigenfrequency

Shell equations

Spherical shell

Författare

Reza Okhovat

Dynamik

Anders E Boström

Dynamik

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

2191-5652 (eISSN)

Vol. 6 29-36

Ämneskategorier

Maskinteknik

DOI

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

ISBN

978-3-319-06988-3

Mer information

Skapat

2017-10-07