Thickness Shear Vibrations of an Ablating Rocket
Abstract
This paper presents an analytical study of the axial shear vibrations of a long hollow cylinder that is subjected to time dependent body forces in the axial direction. The outer surface of the cylinder is bonded to a rigid case, and the inner radius increases monotonically with time. An expression is determined for the shear stress at the bond-interface. It is shown that the frequency of the shear-bond stress increases, and that its amplitude decreases towards burnout time. The shear stress is studied for various ablation rates. Conventional methods of analysis, such as separation of variables and Fourier- Bessel analysis, are not directly applicable in this problem, since the boundary conditions are prescribed on a time dependent surface. A modified Fourier-Bessel mode is defined that satisfies the boundary conditions. By substituting this mode into the equation of motion, a solution is obtained by asymptotic methods in the vicinity of the bond-interface. The analysis is extended to include the axial shear vibrations of an ablating viscoelastic cylinder. Viscoelasticity is introduced by means of the relaxation function in shear.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1965
- Accession Number
- AD0624737
Entities
People
- Jan D. Achenbach
Organizations
- Northwestern University