
Accession Number : AD0687012
Title : BOUNDARY PROBLEMS AND EIGENVALUES OF THE GENERALIZED BIHARMONIC EQUATION,
Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHTPATTERSON 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 Ptransformation 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 boundaryvalue 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