Membrane Stress Field and Eigenvalue Problems at Rotating Circular Plates of Small Thickness, in Thermal Regime

摘要

From the analytical equations study of the disks behavior, some very important issues yield, issues which will be analyzed and solved in the following research. In the present paper one takes into account the fact that the study of the static and dynamical bending subjected disks, most be done mostly under the existence of a membrane stresses field (rotational motion, temperature field with a nonuniform distribution along the radius etc.). In the case of a plate of constant thickness, one uses the equation below: DΔ~2w + ζ(w) + ρh((partial deriv)~2w)/((partial deriv)t~2) = q, (1) where: w - the displacement measured normal to the plate's plane; q - the distributed force, normal to the plate's plane; D = Eh~3/12(1-v~2) - cylindrical modulus of elasticity, at bending of the plate; Δ - Laplace's operator; v - Poisson's ratio; h - the thickness of the plate; ρ - the material density.