The Dynamic Response of Columns Under Short Duration Axial Loads

Coupled nonlinear equations of motion in the axial and transverse directions are derived for a column under dynamic end load. Material dissipation is included by employing a Kelvin model for the material behavior. The dynamic response of the column in the presence of small transverse perturbations is investigated for short duration of axial loads. For certain geometric configurations, the inclusion of axial inertia permits parametric resonance of transverse modes due to the transient axial motion after the load is removed. The parametric effects are studied in detail. It is found that the usual simplified theory which neglects axial inertia adequately describes the column response provided the material dissipation is sufficiently large and/or the duration of loading is sufficiently long. For given dissipation parametric excitation becomes important as the load duration decreases. It becomes the dominant effect for very short duration loads.