Mechanical Instability

Mechanical Instability

Author: Tomasz Krysinski

Publisher: John Wiley & Sons

Published: 2013-02-07

Total Pages: 282

ISBN-13: 1118600959

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This book presents a study of the stability of mechanical systems, i.e. their free response when they are removed from their position of equilibrium after a temporary disturbance. After reviewing the main analytical methods of the dynamical stability of systems, it highlights the fundamental difference in nature between the phenomena of forced resonance vibration of mechanical systems subjected to an imposed excitation and instabilities that characterize their free response. It specifically develops instabilities arising from the rotor–structure coupling, instability of control systems, the self-sustained instabilities associated with the presence of internal damping and instabilities related to the fluid–structure coupling for fixed and rotating structures. For an original approach following the analysis of instability phenomena, the book provides examples of solutions obtained by passive or active methods.


Lateral Ankle Instability

Lateral Ankle Instability

Author: Hélder Pereira

Publisher: Springer Nature

Published: 2021-04-28

Total Pages: 392

ISBN-13: 3662627639

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This superbly illustrated, up-to-date reference textbook covers all aspects of ankle instability and its management. Readers will find extensive information on biomechanics, injury prevention, current strategies for conservative treatment, and established and emerging surgical techniques. The most recent procedures, particularly those which are minimally invasive and arthroscopically assisted, are described and discussed in depth. Detailed attention is also devoted to controversies such as the indications and timing for conservative or surgical treatment, the current and future roles of arthroscopy, the definition of “anatomic” repair, and the upcoming concept of “anatomic reconstruction” (replication of anatomy by using a graft). The book is published in cooperation with ESSKA, and the chapter authors include clinicians and scientists working in the field of foot and ankle orthopaedics and sports medicine from across the world. All who are involved in the care of patients suffering from ankle instability, including amateur and high-level athletes, will find Lateral Ankle Instability to be an excellent source of knowledge and a valuable aid to clinical practice.


Mechanical Instability in Soft Materials

Mechanical Instability in Soft Materials

Author: Xudong Liang

Publisher:

Published: 2018

Total Pages: 134

ISBN-13:

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We are surrounded by soft materials in a variety of physical and chemical states, which can be easily deformed under external stimuli. When subjected to sufficiently large compression, electric voltage, gravity or impact, soft materials may undergo mechanical instabilities of various types. The instability modes can be either linear or nonlinear, depending on the form of perturbation when the instability set in. When the material is a pressurized dielectric elastomeric film under high voltage, snap-through instability is linear with finite change of volume, while the bulge-out mode is nonlinear with a localized deformation. In terms of surface instability, wrinkles are linear instability mode with undulations finite in space with infinitesimal strain deviating from the smooth state, while creases are localized nonlinear modes with large strain deviating from smooth state. If a soft material is subjected to high speed impact, both the viscoelastic behaviors of the material and inertial effect are involved, and the mechanical instability is coupled with the wave propagation, finally leading to highly nonlinear instability mode. We start with the instability analysis of a pressurized dielectric elastomeric film subjected to high voltage. By adopting ideal dielectric elastomer (DE) constitutive model, we show that linear perturbation analysis can capture the shape bifurcation in a spherical DE balloon. However, nonlinear bulge-out shape with a highly localized deformation appears as constraints of the boundaries of the film is applied. A competition between the surface instability modes between the wrinkle and crease is studied in both experiment and theoretical analysis under a deformation mode called eversion, and crease is shown to form prior to wrinkle with lower critical strain to set in. A transition between the wrinkle and crease instability happens when gravity becomes important. We measure the dynamics of soft elastomeric blocks with stiff surface films subjected to high-speed impact, and observe wrinkles forming along with, and riding upon, waves propagating through the system.


Multiparameter Stability Theory with Mechanical Applications

Multiparameter Stability Theory with Mechanical Applications

Author: Alexander P. Seyranian

Publisher: World Scientific

Published: 2003

Total Pages: 421

ISBN-13: 9812384065

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This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects of nonconservative stability problems, analysis of singularities of boundaries for the stability domains, stability analysis of multiparameter linear periodic systems, and optimization of structures under stability constraints. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems.A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed. Among these problems, the authors consider systems of rotating bodies, tubes conveying fluid, elastic columns under the action of periodic and follower forces, optimization problems for conservative systems, etc. The methods presented are constructive and easy to implement in computer programs.This book is addressed to graduate students, academics, researchers, and practitioners in aerospace, naval, civil, and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics.


Nonlinear Solid Mechanics

Nonlinear Solid Mechanics

Author: Davide Bigoni

Publisher: Cambridge University Press

Published: 2012-07-30

Total Pages: 549

ISBN-13: 1107025419

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Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.


Routes to Absolute Instability in Porous Media

Routes to Absolute Instability in Porous Media

Author: Antonio Barletta

Publisher: Springer

Published: 2019-01-02

Total Pages: 283

ISBN-13: 3030061949

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This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.


Stability Problems in Applied Mechanics

Stability Problems in Applied Mechanics

Author: Asok Kumar Mallik

Publisher: Alpha Science Int'l Ltd.

Published: 2005

Total Pages: 138

ISBN-13: 9781842653098

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"Stability Problems in Applied Mechanics starts with the stability problems in statics. The example of buckling of columns is studed through Euler method followed by the Energy method, based on Lagrange-Dirichlet theorem. Snap buckling, instability of shape, buckling due to follower load are also discussed. Insufficiency of static analysis for instability is clearly brought out and buckling problems are revisited from the point of view of dynamics. The theory of Dynamical System and the foundations of bifurcation theory and Floquet theory are developed and used to revisit the stability problems in the light of these unified mathematical concepts. This mathematical basis is then applied to investigate the stability problems encountered in dynamics of particle, rigid and flexible bodies. Finally the emergence of length scale and pattern formation as a consequence of instability in fluid, thermal and diffusion systems are discussed through a number of real-life problems. Different notions of stability and the analysis of nonlinear states are briefly included in two appendices."--BOOK JACKET.


Linear and Nonlinear Instabilities in Mechanical Systems

Linear and Nonlinear Instabilities in Mechanical Systems

Author: Hiroshi Yabuno

Publisher: John Wiley & Sons

Published: 2021-02-16

Total Pages: 324

ISBN-13: 1119066530

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LINEAR and NONLINEAR INSTABILITIES in MECHANICAL SYSTEMS An in-depth insight into nonlinear analysis and control As mechanical systems become lighter, faster, and more flexible, various nonlinear instability phenomena can occur in practical systems. The fundamental knowledge of nonlinear analysis and control is essential to engineers for analysing and controlling nonlinear instability phenomena. This book bridges the gap between the mathematical expressions of nonlinear dynamics and the corresponding practical phenomena. Linear and Nonlinear Instabilities in Mechanical Systems: Analysis, Control and Application provides a detailed and informed insight into the fundamental methods for analysis and control for nonlinear instabilities from the practical point of view. Key features: Refers to the behaviours of practical mechanical systems such as aircraft, railway vehicle, robot manipulator, micro/nano sensor Enhances the rigorous and practical understanding of mathematical methods from an engineering point of view The theoretical results obtained by nonlinear analysis are interpreted by using accompanying videos on the real nonlinear behaviors of nonlinear mechanical systems Linear and Nonlinear Instabilities in Mechanical Systems is an essential textbook for students on engineering courses, and can also be used for self-study or reference by engineers.