Influence of a viscoelastic foundation on the stability of Beck's column: An exact analysis

The stability of Beck's column supported by three different viscoelastic foundations, viz., the standard linear solid, the Maxwell and the Kelvin-Voigt, is investigated. Closed form stability criteria are obtained for the entire range of system parameters through an exact dynamic analysis for each foundation model. The results for the Kelvin-Voigt model show that for a given stiffness parameter of the foundation the critical load increases with an increase in damping and reaches a limiting value for large damping. Unlike the case of conservative loading, the Maxwell foundation is shown to have a positive influence on the stability of this non-conservative problem. Furthermore, for this model, an optimum combination of foundation parameters exists to yield the maximum flutter load. The standard linear solid foundation combines the characteristics of Maxwell and Kelvin-Voigt models, as expected.