NONLINEAR VIBRATION OF AN EXTENSIBLE ELASTIC BEAM

This paper is concerned with the large amplitude transverse, in-plane vibration of a hinged, initially prestressed, extensible elastic beam. The non-linear partial differential equations that take into account transverse and axial inertial forces, as well as the rotary inertial t erm, are derived. In deriving the equations the constitutive equations for an extensible elastic beam proposed by Pfluger are used. By modal expansion and spatial averaging, the equations of motion are reduced to a system of ordinary differential equations. The solution of this s ystem is studied both analytically and numerically. The general respon se and the frequency-amplitude relations are presented, and the relati ons to the static buckling problem are analyzed.