VIBRATION AND STABILITY OF A NON-PRISMATIC COLUMN COMPRESSED BY NON-CONSERVATIVE FORCES IN NON-LINEAR CREEP CONDITIONS

The paper deals with the problem of vibrations and stability of a non-prismatic column compressed by the follower force. The material of the column is characterized by Rabotnovʹs strain hardening non-linear creep law. It is assumed that the stress and strain in the basic state (e.g., pure compression) are subject to slight variation due to small vibrations. Thus, it is possible to linearize the creep law with respect to these variations so that the linear equations of motion can be obtained. They allow determination of the relationship between the real and imaginary parts of complex frequency and the compressive force (characteristic curves). The behaviour of characteristic curves for several types of non-prismatic columns have been examined and presented in numerous figures. Additionally, some parametrical optimization procedures have been performed.