Sub-tangentially loaded and damped Beck's columns on two-parameter elastic foundation

• Published in: Journal of sound and vibration Vol. 306; no. 3; pp. 766 - 789
• Main Authors: Lee, Jun-Seok, Kim, Nam-Il, Kim, Moon-Young
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 09.10.2007; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Stiffness matrix; Divergence; Internal friction; Vibration; Aeroelastic flutter; Newmark method; Hermite interpolation; Non conservative system; Modeling; Interval arithmetic; Frequency effect; Complex variable method; Natural frequency; Finite element method; Column; Dynamic stability; Hamiltonian mechanics; Follower force; Mass matrix; Aeroelasticity; Elastic foundations; Pasternak foundation
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2007.06.017

The dynamic stability of the damped Beck's column on two-parameter elastic foundation is investigated by using Hermitian beam elements. For this purpose, based on the extended Hamilton's principle, the dimensionless finite element (FE) formulation using the Hermitian interpolation function is presented. First, the mass matrix, the external and internal damping matrices, the elastic and the geometric stiffness matrices, Winkler and Pasternak foundation matrices, and the load correction stiffness matrix due to the sub-tangential follower force are obtained. Then, evaluation procedure for the flutter and divergence loads of the non-conservative system and the time history analysis using the Newmark- β method are shortly described. Finally, the influences of various parameters on the dynamic stability of non-conservative systems are newly addressed: (1) variation of the second flutter load due to sub-tangentiality, (2) influences of the external and the internal damping on flutter loads by analysis of complex natural frequencies, (3) the effect of the growth rate of motion in a finite time interval using time history analysis, and (4) fluctuation of divergence and flutter loads due to Winkler and Pasternak foundations.