### ASA 125th Meeting Ottawa 1993 May

## 3aSA8. An analytic model for the vibrations of rectangular shells of
variable curvature and thickness.

**Masahiko Okajima
**

**
Courtney B. Burroughs
**

**
**
*Grad. Prog. in Acoust., Penn State Univ., P.O. Box 30, University Park, PA
16804
*

*
*
A flexible and powerful model is developed for analyzing the vibration of
a rectangular platform shell whose curvature and thickness are arbitrary. The
shape of the shell can have almost any conceivable representation, since the
curvature and thickness are represented by bicubic polynomials of the
centerline arc length. The vibration model includes the effects of shear
deformation, rotary inertia, and centerline extension. The equations of motion
are solved by an alternative form of the Rayleigh--Ritz method. The resulting
integral formulas for the stiffness and mass matrix elements are evaluated by a
set of simple computer routines that do symbolic manipulations of algebra and
calculus. Predictions of the natural frequency for the several shell geometries
are compared to published data, with good agreement. A parameter study shows
the dependence of the resonance frequencies and mode shapes on the curvature
and the thickness of the shell.