### ASA 124th Meeting New Orleans 1992 October

## 4pSA13. Vibration analysis of a thick plate using 3-D elasticity
equations.

**Satish Padiyar
**

**
J. M. Cuschieri
**

**
**
*Ctr. for Acoust. and Vib., Dept. of Ocean Eng., Florida Atlantic Univ.,
Boca Raton, FL 33431
*

*
*
Dynamic analysis of thick-plate structures are typically performed using
the approaches of Mindlin [J. Appl. Mech. 18, 31--38 (1951)] for out-of-plane
waves, and Mindlin and Medick [J. Appl. Mech. 26, 561--569 (1959)] for in-plane
waves. Using this type of analysis, approximations are included to simplify the
approach. The solution for the response of the thick plate is obtained for the
mid-plane of the plate. The response away from the mid-plane is then based on
an assumed set of orthogonal functions. With this formulation, the in-plane and
out-of-plane wave equations become uncoupled. One set of equations is obtained
that describes the in-plane wave motion and another set of equations is
obtained which describes the out-of-plane wave motion. An alternative approach
to study the behavior of a thick plate, is to use the full set of the
three-dimensional elasticity equations. This approach can lead to a complex
mathematical formulation even for such a simple structure as a plate with all
edges stress free. A solution for the free vibrations of a linearly elastic
rectangular slab with stress-free boundaries using the three-dimensional stress
equations has been developed by Hutchinson and Zillmer [J. Appl. Mech. 50(3),
123--130 (1983)]. In this case, the solution includes all the possible wave
types. A solution for the forced vibration of a plate using an approach based
on the method of Hutchinson and Zillmer is obtained, and compared to the
solution for the same plate obtained using the Mindlin approaches. The
differences and similarities between the two methods and the corresponding
results are investigated. The response obtained by either of the two techniques
can be used to analyze the scattering of wave energy from one wave type to
another in the presence of discontinuities. [Work sponsored by ONR.]