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Keywords: bifurcation
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Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. November 2010, 63(6): 060802.
Published Online: June 24, 2011
...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...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. May 2010, 63(3): 030801.
Published Online: April 27, 2010
... amplitude equations, 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...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. July 2008, 61(4): 040801.
Published Online: June 30, 2008
... 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 of...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. July 2006, 59(4): 230–248.
Published Online: July 1, 2006
... 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...
Journal Articles
Article Type: Article
Appl. Mech. Rev. March 2005, 58(2): 91–116.
Published Online: April 6, 2005
..., 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 and...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. November 2004, 57(6): 443–478.
Published Online: February 16, 2005
... 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...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. November 2004, 57(6): 515–549.
Published Online: February 16, 2005
... 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 that...
Journal Articles
Article Type: Review Articles
Appl. Mech. Rev. November 2004, 57(6): 479–514.
Published Online: February 16, 2005
... 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...
Journal Articles
Article Type: Book Reviews
Appl. Mech. Rev. September 2004, 57(5): B26.
Published Online: December 21, 2004
...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...
Journal Articles
Article Type: Book Reviews
Appl. Mech. Rev. September 2004, 57(5): B25–B26.
Published Online: December 21, 2004
...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...
Journal Articles
Article Type: Book Reviews
Appl. Mech. Rev. May 2003, 56(3): B40.
Published Online: May 2, 2003
...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...
Journal Articles
Article Type: Book Reviews
Appl. Mech. Rev. November 2002, 55(6): B107.
Published Online: October 16, 2002
...M Henon,, Author; FH Lutze,, Reviewer N-body problems celestial mechanics classical mechanics bifurcation reviews 16 10 2002 The first chapter (Ch 11) sets up the definitions (often times referring to Chs 1–10) and the governing equations. In addition, a general method...
Journal Articles
Article Type: Retrospectives
Appl. Mech. Rev. March 2002, 55(2): R5–R15.
Published Online: April 3, 2002
...Koncay Huseyin 03 04 2002 dynamics mechanical stability bifurcation buckling history 1 Stability boundary of shallow frame 2 Convexity of the characteristic surface and stability boundary 3 Characteristic curve of a gyroscopic system in ξ...