TY - JOUR

T1 - Three-dimensional sharp corner displacement functions for bodies of revolution

AU - Huang, Chiung-Shiann

AU - Leissa, A. W.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Sharp corner displacement functions have been well used in the past to accelerate the numerical solutions of two-dimensional free vibration problems, such as plates, to obtain accurate frequencies and mode shapes. The present analysis derives such functions for three-dimensional (3D) bodies of revolution where a sharp boundary discontinuity is present (e.g., a stepped shaft, or a circumferential V notch), undergoing arbitrary modes of deformation. The 3D equations of equilibrium in terms of displacement components, expressed in cylindrical coordinates, are transformed to a new coordinate system having its origin at the vertex of the corner. An asymptotic analysis in the vicinity of the sharp corner reduces the equations to a set of coupled, ordinary differential equations with variable coefficients. By a suitable transformation of variables the equations are simplified to a set of equations with constant coefficients. These are solved, the boundary conditions along the intersecting corner faces are applied, and the resulting eigenvalue problems are solved for the characteristic equations and corner functions.

AB - Sharp corner displacement functions have been well used in the past to accelerate the numerical solutions of two-dimensional free vibration problems, such as plates, to obtain accurate frequencies and mode shapes. The present analysis derives such functions for three-dimensional (3D) bodies of revolution where a sharp boundary discontinuity is present (e.g., a stepped shaft, or a circumferential V notch), undergoing arbitrary modes of deformation. The 3D equations of equilibrium in terms of displacement components, expressed in cylindrical coordinates, are transformed to a new coordinate system having its origin at the vertex of the corner. An asymptotic analysis in the vicinity of the sharp corner reduces the equations to a set of coupled, ordinary differential equations with variable coefficients. By a suitable transformation of variables the equations are simplified to a set of equations with constant coefficients. These are solved, the boundary conditions along the intersecting corner faces are applied, and the resulting eigenvalue problems are solved for the characteristic equations and corner functions.

UR - http://www.scopus.com/inward/record.url?scp=34248167021&partnerID=8YFLogxK

U2 - 10.1115/1.2178358

DO - 10.1115/1.2178358

M3 - Article

AN - SCOPUS:34248167021

SN - 0021-8936

VL - 74

SP - 41

EP - 46

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

IS - 1

ER -