Approximations to buckling loads and other eigenvalues via the least-squares method. (English) Zbl 0907.73031

Schmidt, Robert

Ind. Math. 47, No. 1, 11-17 (1997).

Summary: This paper traces the relations between the variational method and several approximate analytical techniques for estimating eigenvalues such as buckling loads and fundamental frequencies of vibration. A number of simple examples have been solved to corroborate some of the author’s statements concerning the upper and lower bounds. The numerical results obtained have been compared with the exact solutions.

MSC:

74G60	Bifurcation and buckling
74H55	Stability of dynamical problems in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
74P10	Optimization of other properties in solid mechanics

Keywords:

Sturm-Liouville eigenvalue problem; approximate analytical techniques; fundamental frequencies; upper and lower bounds