Impact of pre-stress on stability and vibration of geometric nonlinear column at a load force directed to the positive pole

The subject of the results of theoretical and numerical studies measures to designate the effect of pre-stress on the vibration of geometrically non-linear column exposed to the load force directed to the positive pole. Considering the total mechanical energy of the system the equation of motion and the boundary conditions necessary to solve the boundary problem were determined. Based on the kinetic stability criterion the range of values of internal compression forces was determined in which the growth of critical load of the column above the local loss of stability was achieved. In the research the geometrically non-linear system was analysed with variable asymmetry of bending stiffness and at selected values of geometrical parameters of the head realizing the load