...Yuri V. Mikhlin; Konstantin V. Avramov Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer–Rosenberg and Shaw–Pierre concepts, are analyzed. Properties of the NNMs and methods of their analysis are presented. NNMs stability and bifurcations are discussed...

..., which accurately describe the dynamics of the flow in the vicinity of the bifurcation threshold. These equations also enable us to analyze the mean flow induced by the nonlinearities as well as the stability properties of this flow. The open-loop control of unsteadiness is then studied by a sensitivity...

... element method and with group-theoretic bifurcation theory in nonlinear mathematics. The approaches serve as an efficient and insightful strategy to tackle probabilistic scatter of critical loads. We review, through the perspective of theoretical engineers, the historical development and recent revival...

... averaging method for quasi Hamiltonian systems, the stochastic stability, stochastic bifurcation, first-passage time and nonlinear stochastic optimal control of quasi Hamiltonian systems are summarized. Possible extension and applications of the theory are pointed out. This review article cites 158...

..., investigations are reported on modeling of damping mechanisms as viscoelastic materials, coupled vibration of power transmission systems, and bifurcation and chaos. The state of the art of active control of moving strings is surveyed on controllability and observability, the Laplace transform domain analysis...

... to predict nonzero mean response and underestimates the mean square response under white noise excitation. Complex response phenomena such as “on-off” intermittency, energy transfer, and stochastic bifurcation are reviewed. The dynamic behavior of suspended cables in still air is different from...

... systems theory are illustrated with reference to the single-degree-of-freedom model of cable, reporting on measures for diagnosis of nonlinear and chaotic response, as well as on techniques for local and global bifurcation analysis. The paper ends with a discussion on the main features and problems...

... have been presented, and different techniques for the analysis of nonlinear dynamics have been illustrated with reference to the suspended cable. Herein, we discuss the main features of system regular and complex response, and the associated bifurcational behavior. Nonlinear phenomena are considered...

...H Kielhofer,, Editor; HW Haslach,, Jr 21 12 2004 bifurcation partial differential equations reviews 9R3. Bifurcation Theory: An Introduction With Applications to PBEs (Applied Mathematical Sciences 156 Series). - Edited by H Kielhofer (Inst for Math, Univ of Augsburg...

...Shijun Liao,, Editor; SA Sherif,, Reviewer 21 12 2004 perturbation theory bibliographies boundary layers nonlinear equations bifurcation 9R2. Beyond Perturbation: Introduction to the Homotopy Analysis Method. - Edited by Shijun Liao (Shanghai Jiao Tong University...

...K Ikeda,, Author; K Murota,, Author; J Petrolito,, Reviewer 02 05 2003 mechanical stability bifurcation group theory reviews 5R19. Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory. Applied Mathematical Sciences, Vol...

...M Henon,, Author; FH Lutze,, Reviewer 16 10 2002 N-body problems celestial mechanics classical mechanics bifurcation reviews 11R10. Generating Families in the Restricted Three-Body Problem, II: Quantitative Study of Bifurcations. Lecture Notes in Physics, Vol m65. - M...

... concerning the nonlinear concepts of bifurcation and stability associated with general conservative systems which could be described by a total potential energy function in terms of generalized coordinates. Indeed, research was in progress in several directions when I joined the group: Chilver and WJ Supple...