Random Vibration of a Beam Column

The lateral displacement of a vertical cantilever beam subjected to an axial load acting at the free end and under a random horizontal motion of the clamped end is evaluated. This is one of the beam-column problems on which little work has been done for random loading on random boundary conditions. The axial load is assumed to be less than the fundamental buckling load of the column. For the random motion of the clamped end, a particular form of the random process is considered possibly appropriate for motion resulting from earthquake acceleration. Hence, the problem might be considered as a simplified model of the tower of a suspension bridge under horizontal earthquake acceleration.