STRESS-WAVE PROPAGATION IN A THREE-REGION CYLINDRICAL COMPOSITE MEDIUM.
Abstract
A semi-analytical solution is developed for the steady-state pressure in a three-region cylindrical composite medium containing a point sinusoidal source. The geometry is such that conventional analytical methods are not applicable. The scalar wave equation for a viscous homogeneous fluid is solved by separation of variables in each region of the composite medium. Infinite series are set up from these solutions. A finite number of terms in the series are retained for each region, and the interface boundary conditions are applied at a selected finite number of interface boundary points, in order to produce a set of algebraic equations which are linear in the coefficients of the series. The solution of this set then leads to an analytical approximation to the solution of the boundary value problem. A central problem in this method is the specification of the eigenvalues in each region. There exist no general physically-based procedures for this purpose. In this paper an arbitrary Sturm-Liouville interface boundary condition is applied which enables a set of eigenvalues to be determined. The practical consequences of this step, in terms of numerical calculations, remain to be determined. These calculations are planned in subsequent work. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 21, 1968
- Accession Number
- AD0683342
Entities
People
- C. W. Tittle
- Danny R. Dixon
Organizations
- Southern Methodist University