Quadratic Eigenvalue Problems from a Nonlinear Structural Analysis.
CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF THE AEROSPACE AND MECHANICAL ENGINEERING SCIENCES
Pagination or Media Count:
In application of the previously developed modified structure method to the study of the nonlinear behavior of continuous elastic structures, including bifurcation and snap-through, one is generally led to an eigenvalue problem in which the enigen-parameter appears quadratically in the coeffieicnts of a linear differential equation. In the present study, the elementary example of a fixed-free column loaded both axially and laterally is considered as a continuum problem, an approach possible within the scope of the modified structure method. Earlier studies of this problem in finite element formulation showed non-existence of an eigenvalue for very slender columns. The present paper investigates the question of existence of a positive eigenvalue in a hierarchy of linearized quadratic eigenvalue problems which result from the retention of higher-order terms in the expansion of the potential energy functional. Non-existence of eigenvalues for columns of sufficiently high slenderness ratio rho is shown, and the Rayleigh Quotient method is used to bound the eigenvalue and give an approximation to the critical value of rho. Author
- Theoretical Mathematics