### ASA 125th Meeting Ottawa 1993 May

## 3aSA1. Free vibration of a rotating annular plate including the effect of
bending, membrane, shear deformation, and rotatory inertia.

**Andre Cote
**

**
Noureddine Atalla
**

**
Jean Nicolas
**

**
**
*Dept. of Mech. Eng., Univ. de Sherbrooke, 2500 Boul. Univ., Sherbrooke PQ
J1K 2R1, Canada
*

*
*
Free response of an annular plate constrained at the inner radius is
investigated using a variational approach. In the method used here, special
attention has been taken to include all possible effects in linear theory: pure
bending, Mindlin's shear deformation, rotatory inertia, and membrane effect.
Membrane effect and bending (pure bending plus shear deformation) are then
shown to be independent, thus allowing a separated evaluation of the natural
frequencies. The influence of rotation is also investigated for both membrane
and bending movement. This general problem is solved using the Rayleigh--Ritz
method including symmetric and antisymmetric terms in the polynomials. Special
cases where symmetric and antisymmetric natural frequencies are not equivalent
can then be shown. The use of polynomials also produced stable results for a
future acoustic study. Finally, the critical speed of rotation is determined
for a nonrotating observer. Results are presented for every case. [Work
supported by N.S.E.R.C. and I.R.S.S.T.]