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Stochastic stability of a compound column. (English) Zbl 0776.73027

Summary: The dynamic stability of an axially-loaded, geometrically perfect compound column with simply supported ends is analyzed. The column is constructed from coaxial prismatic bars joined together at their ends. Two different kinds of stability are considered. First, under the assumption that the axial excitation is a stationary ergodic process, the almost certain asymptotic stability is examined. In the second case, when the parametric excitation is a wide-band Gaussian process mathematically modelled by white-noise, the uniform stochastic stability is investigated. The stability criteria are derived using Lyapunov’s method. The relation between the stability of nonlinear equations and linearized ones is analyzed.

MSC:

74H55 Stability of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H50 Random vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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