The destabilizing effect of damping on both linear and nonlinear behavior of the Ziegler column is discussed. The paper addresses classical and non-classical aspects related to the ‘Ziegler paradox’. First, the linear problem is illustrated in a new perspective, according to which no discontinuities in the critical load exist between undamped and damped systems. Second, it furnishes a first overview of the mechanical behavior of the system in the post-critical range. The equations of motion for the system are derived via the extended Hamilton’s principle. Then a linear stability analysis is performed via a perturbation approach, in which, however, simple and not double eigenvalues are perturbed, in contrast with a commonly pursued strategy in the literature. According to this idea, a series expansion around the distinct purely imaginary eigenvalues of the undamped and under-critically loaded system is carried out, with the load kept as a fixed, although unknown, parameter. By pursuing the same idea, an algorithm based on the Multiple Scale Method is developed to investigate the post-critical behavior of the system. The role played by the nonlinear damping on the existence of limit-cycles is discussed.
|Titolo:||Linear and nonlinear damping effects on the stability of the Ziegler column|
|Data di pubblicazione:||2015|
|Appare nelle tipologie:||2.1 Contributo in volume (Capitolo o Saggio)|