Bending Oscillations of the Vertical Rack

Abstract

The coordinate descent method has not been used. We consider the steady oscillations of the beam. No initial conditions are required. The boundary conditions depend on the ways the ends of the rod are supported and the perturbations acting here. We consider an elementary section of the rack. The Roman numeral and the strokes in the upper index denote the x derivatives. In this example, the frictional forces were not taken into account. The coordinate descent method is not used. The three eigenvalues of the table are directly taken from the graph displayed on the computer monitor. A three-dimensional vector process acts on the rod. Dynamic perturbations are represented by distributed loads, concentrated forces and moments. The hypothesis of flat sections is valid. The cross sections remain flat and perpendicular to the curved axis of the rod during deformation.