Abstract A theory of free vibration for orthotropic shells of revolution including the effects of transverse shear and rotary inertia is formulated. Derived equilibrium equations are expressed in terms of the displacement vector, which is written as a truncated power series expansion in the thickness coordinate. The partition method, in conjunction with piecewise polynomials, is used to obtain a solution. The effect of transverse shear for non-axisymmetric, transverse vibrations of a cylinder and of a torus segment is indicated in several examples. Results show that transverse shear significantly affects the natural frequencies of these shells.
[1]
H. Langhaar.
Energy Methods in Applied Mechanics
,
1962
.
[2]
F. B. Hildebrand,et al.
Notes on the foundations of the theory of small displacements of orthotropic shells
,
1949
.
[3]
A. Love,et al.
The Mathematical Theory of Elasticity.
,
1928
.
[4]
P. M. Naghdi,et al.
ON THE THEORY OF THIN ELASTIC SHELLS
,
1957
.
[5]
E. Reissner,et al.
Stress Strain Relations in the Theory of Thin Elastic Shells
,
1952
.
[6]
D. Faddeev,et al.
Computational Methods of Linear Algebra
,
1959
.