Abstract
The vibrational equation of plate : [numerical formula] where E=Young's modulus, σ=Poisson's ratio, ρ=density, 2h=thickness varying along the radial direction, w=deflection and t=time, was led to ∇12 [κ3 (ζ) ∇12u (ζ)]-λ4κ (ζ) u (ζ)=0, under the substitution w=u (ζ) sin nθsin pt, ζ=r/a (a=outer radius of disc), h=h0κ (ζ), λ4=3/2×(1-σ2) ρp2 : Eh02/a4, ∇12=d2/dζ2+ζ-1d/dζ-n2ζ-2. Assuming [numerical formula], the general solution for u was determined, and the frequency equation, under generalized boundary conditions, such as, αj1u+αj2u'+αj3u+αj4u'''=0, (j=1, 2, 3, 4) was established. The frequency equation, here given, contains the Prescott's results as a special case. Finally the authors describes an application to a lens-formed section : h=h0 (1+αζ2), concave and convex corresponding to the sign of α, where |α| is very small, resulting λ4=104·2+113·8α, for the fundamental frequency of disc clamped at its circunference, and free at the centre.
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