The bisection method for solving the nonlinear bar eigenvalue problem

Abstract

© Published under licence by IOP Publishing Ltd. In the present paper, the differential nonlinear eigenvalue problem describing longitudinal eigenvibrations of an elastic bar with elastically attached load to the bar end is considered. The original differential eigenvalue problem is approximated by a mesh scheme of the finite difference method on a uniform grid. The finite difference scheme is equivalent to the matrix nonlinear eigenvalue problem. To solve this matrix nonlinear eigenvalue problem, the bisection method is proposed and studied. Investigations of this paper can be generalized for the cases of more complicated and important problems on eigenvibrations of beams, plates and shells with elastically attached loads.