... can lead to undesirable tube vibrations in the cross-flow direction, which in turn introduce vibration, noise, and additional loading on support structures; in extreme cases, catastrophic failure becomes a concern. external flows flow instability fluid oscillations Lyapunov methods noise...

... 2009 damping eigenvalues and eigenfunctions Lyapunov methods method of moments noise partial differential equations resonance stability stochastic processes parametric resonance moment Lyapunov exponents bounded noise The equations of motion for many engineering problems...

... ) ‖ and describes the almost-sure or sample stability of the system. When the largest Lyapunov exponent λ is negative, system 1 is asymptotically stable with probability 1. diffusion linear differential equations Lyapunov methods Monte Carlo methods numerical analysis stability stochastic...

... noises. The variations of the moment Lyapunov exponents with the change of different parameters are discussed. 09 06 2006 08 07 2007 25 02 2008 differential equations Lyapunov methods noise stability vibrations viscoelasticity Typical examples of engineering systems...

... stability is guaranteed by perturbation of the inverse. 03 12 2004 19 12 2005 kinematics mechanical contact state-space methods nonlinear control systems Lyapunov methods stability force feedback biomechanics legged locomotion Three problems associated with rigid body...

... after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 03 January 2004 17 September 2004 15 03 2005 Monte Carlo methods Lyapunov methods stochastic systems white noise stability Stochastic differential equations are encountered...

... processes asymptotic stability Lyapunov methods exponential distribution Dynamic stability of elastic systems under parametric stochastic excitation has been a subject of research for a few decades. Most of the papers on stochastic stability that have appeared deal with the systems under Gaussian...

... mechanical stability eigenvalues and eigenfunctions Lyapunov methods This paper is concerned with stochastic stability of two-degree-of-freedom (dof) systems in the presence of internal resonances . In linear multi-degree-of-freedom systems, resonances occur due to commensurability...

... and eigenfunctions feedback differential equations dynamic programming stochastic programming Lyapunov methods optimal control asymptotic stability The feedback stabilization of stochastic systems is an important problem in control theory. Although the basic formulation and fundamental equations...

.... Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 24 Apr 2001 02 Oct 2001 03 05 2002 Lyapunov...

... of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 15 May 2000 26 Feb 2001 mechanical stability noise stochastic processes Lyapunov methods oscillations classical mechanics In the study of stability of solutions of random dynamical systems, the exponential growth...

... Nov 1999 08 Nov 2000 bifurcation Lyapunov methods elasticity mechanical stability vibrations stochastic processes damping Investigations of the dynamic stability of elastic systems, such as the transverse vibration of columns and flat plates under randomly fluctuating axial...