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.]