Stresses in rotating thin plates with curvilinear boundaries

✍ Scribed by G.M. Arkilic

• Publisher: Elsevier Science
• Year: 1958
• Tongue: English
• Weight: 615 KB
• Volume: 266
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(58)90474-5

✦ Synopsis

The problem of curvilinear plates rotating at constant speed about an axis in the plane of the plate is considered in this paper.

Stress components are expressed in terms of coordinates and in terms of certain potential functions.

It is shown that by suitable construction of these functions the stress components can be easily determined.

NOMENCLATURE

The following nomenclature is used in the paper :

x, Y = rectangular coordinates E, 11 = orthogonal curvilinear coordinates CO= angular velocity 02, u,, 7211 = stress components UE, utl, T10 = stress components in curvilinear coordinates y2 = x2 + y2 2= x + iy, 2=x--;y Re, Im = real and imaginary part of 020 = a harmonic function Q= uz + uy v2 = the Laplace's operator 5 + s 9, a., F1, Gr = F= f3= J= c, x = n= P= Q= conjugate harmonic functions 8Fl and G = 8G1 angle between (l = constant) and x-axis stretch ratio real positive constants a positive integer 1 + X2(lz + l)", P, = 1 + Az(n + 1) 2X(n + l), 91 = A(n + 2)