Effects of damping on stability of elastic systems subjected to nonconservative forces

Abstract A question of the correlation between stability and quasistability regions of elastic and viscoelastic systems subjected to nonconservative forces is discussed. On the base of the method of expansion in fractional powers of parameters the more rigorous considerations are presented than the considerations used in the earlier papers where the semiintuitive assumptions, the arguments by analogy and the incomplete induction methods were applied widely. In the first part of the paper a number of general statements concerning both continuous and discrete systems are proved. It is shown that for real laws of damping a considerable part of the quasistability region belongs in fact to instability region. From this point of view a number of papers dealing with non-conservative stability problems (including panel flutter problems) must be reconsidered. To illustrate the general statements, in the second part of the paper a numerical examination of stability of cantilever bar made of the standard viscoelastic solid and subjected to follower and dead forces is presented. Some phenomena inherent to the nonconservative viscoelastic systems are discussed.