Accession Number : AD0687012

Title :   BOUNDARY PROBLEMS AND EIGENVALUES OF THE GENERALIZED BIHARMONIC EQUATION,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Polozhii,G. N. ; Bublik,B. N.

Report Date : 31 JAN 1969

Pagination or Media Count : 24

Abstract : The solution of boundary value and eigenvalue problems for a generalized biharmonic equation is analyzed utilizing the P-transformation methods developed by G. N. Polozhii. Two kinds of boundary conditions are defined and five cases are distinguished. The five cases are: (1) on one side of a rectangle the boundary conditions of the first kind are satisfied and on the other sides the boundary conditions of the second kind are satisfied; (2) on two opposite sides the boundary conditions of the first kind and on the other sides the boundary conditions of the second kind are satisfied; (3) on two adjacent sides the boundary conditions of the first kind, and on the other sides the boundary conditions of the second kind are satisfied; (4) on three sides the boundary conditions of the first kind and on one side the boundary conditions of the second kind are satisfied; (5) on all sides the boundary conditions of the first kind are satisfied. The formula of summary representations, written in the scaler form, establishes the basis for solving the boundary-value and eigenvalue problems for all five cases of boundary conditions.

Descriptors :   (*ELASTIC PROPERTIES, POTENTIAL THEORY), (*BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS), RECTANGULAR BODIES, TRANSFORMATIONS(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS, COMPLEX VARIABLES, DETERMINANTS(MATHEMATICS), USSR

Subject Categories : Theoretical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE