Nonlinear vibration of beams in an axial force field

Abstract

The nonlinear vibrational characteristics of beams with variable axial restraint at the boundary, and with an axial force applied at any intermediate station of the beam are studied. The behavior of the system at the time of maximum amplitude is determined by the use of successive integration and iteration scheme. Numerical results are presented for a uniform, simply supported beam, for the cases of movable and immovable hinges. For the case of an immovable hinge, the nonlinearity is always of the hardening type. In the case of a movable hinge, for low values of the imposed axial force, the nonlinearity is of the softening type. But, the softening behavior changes to a hardening one when the axial force approaches the value of the buckling load. When the results are particularized for the linear case, the agreement is very good with those available in the literature.