Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators
Artikel i vetenskaplig tidskrift, 2017

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.

Acoustics

hollow sphere

Mechanics

layers

Eigenfrequency

rods

Shell equations

Spherical shell

Surface differential operators

elastic-waves

Engineering

Författare

Reza Okhovat

Chalmers, Tillämpad mekanik, Dynamik

Anders E Boström

Chalmers, Tillämpad mekanik, Dynamik

Journal of Sound and Vibration

0022-460X (ISSN) 1095-8568 (eISSN)

Vol. 393 415-424

Ämneskategorier

Maskinteknik

Beräkningsmatematik

Geometri

DOI

10.1016/j.jsv.2017.01.025