Response of a Buckled Beam Constrained by a Tensionless Elastic Foundation

Abstract

In this paper, we study the deformation and stability of a pinned buckled beam under a point force. The buckled beam is constrained by a tensionless elastic foundation, which is flat before deformation. From static analysis, we found a total of five different deformation patterns: (1) noncontact, (2) full contact, (3) one-sided contact, (4) isolated contact in the middle, and (5) two-sided contact. For a specified set of parameters, there may coexist multiple equilibria. To predict the response of the buckled beam foundation system as the point force moves from one end to the other, we have to determine the stability of these equilibrium configurations. To achieve this, a vibration method is adopted to calculate the natural frequencies of the system, taking into account the slight variation of the contact range between the buckled beam and the tensionless foundation during vibration. It is concluded that among all five deformation patterns, Deformations 1, 2, 3, and 4 may become stable for certain loading parameters. In the extreme case in which the foundation is rigid, on the other hand, only Deformations 1 and 3 are stable.