Free Vibrations and Stability of a New Slender System Subjected to a Conservative or Nonconservative Load

AbstractA slender system with different types of load (conservative and nonconservative) is considered in this paper. The conservative load is the specific load: a generalized load with the force directed toward the positive pole. The nonconservative load (Beck’s load) was generated by a reaction engine. A set of two bolts (characteristic for a specific load), with mutual rotation limited by a rotational spring with a linear characteristic, was taken into account in the system. The boundary problem of the considered systems was formulated on the basis of Hamilton’s principle. The critical loads, both divergence and flutter, the regions of divergence and flutter instability, and the characteristic curves in the plane: load – natural frequency were determined on the basis of the kinetic criterion of stability. Numerical computations were carried out for different values of the parameters of the considered system, such as the rigidity of a rotational spring, parameters connected to the length of the bolts, and the inertia parameters of the translational and rotational mass placed at the loaded end of a column.