## 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.]