Aspects of the Stability of Nonconservative Structural Systems

Julia F. Genovesi¹; Raul R. Silva¹

¹ Pontifical Catholic University of Rio de Janeiro (PUC-Rio)

doi:10.20906/CPS/CILAMCE2017-0340

Resumo

The stability of structures with non-conservative loads has been studied since 1930 by Nicolai for torsion in bars and 1952 by Beck for bending in beams. The loss of stability in these systems can be either by divergence, a static response, or by flutter, a dynamic response with amplitude oscillations increasing exponentially. Several aspects concerning the dynamic stability of beams were analyzed over the years, including paradoxical results such as the indifference of the flutter load of the Beck problem to the rigidity of a Winkler foundation. Such results have been criticized because of the difficulty in obtaining idealized follower loads in experiments. The aim of this work is to clarify some of these results and explore different examples evaluating the influence of certain parameters in classical problems and the actual application of nonconservative loads. A computer program has been developed in MATLAB R2016b based on the Rayleigh-Ritz method, using nodal shape functions enriched with internal additional functions. The dynamic method for determination of critical loads employed is based on a matrix formulation which includes symmetric elastic stiffness, damping, Coriolis and geometric matrices, while the contribution of non-conservative loads is incorporated in additional non-symmetric load matrices. Algorithms for determination of frequencies of vibration are used to evaluate their variation in an incremental load process. Validation examples are presented and novel results are introduced to clarify some of the issues raised in the recent literature.

Palavras-chave: Dynamic stability; Nonconservative; Follower force; Finite element method