Nonlinear Vibration of Thin Plates PDF Download

Author: Victor Chin-Po Kuo
Publisher:
ISBN:
Category : Plate
Languages : en
Pages : 190

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Book Description
Nonlinear analysis of the vibration of thin plates considering in-plane motion, is investigated. The coupled nonlinear differential equations are fully hyperbolic if strains are tensile. The one dimensional case is investigated by exact and approximate methods. All approximate results are consistent in period, which is a function of amplitude.

Author: Marco Amabili
Publisher: Cambridge University Press
ISBN: 1139469029
Category : Science
Languages : en
Pages : 391

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Book Description
This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

Author: Marco Amabili
Publisher: Cambridge University Press
ISBN: 1107129222
Category : Mathematics
Languages : en
Pages : 585

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Book Description
This book guides the reader into the modelling of shell structures in applications where advanced composite materials or complex biological materials must be described with great accuracy. A valuable resource for researchers, professionals and graduate students, it presents a variety of practical concepts, diagrams and numerical results.

Author: Eduard Ventsel
Publisher: CRC Press
ISBN: 9780203908723
Category : Mathematics
Languages : en
Pages : 688

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Book Description
Presenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering appli

Author: Michele Ducceschi
Publisher:
ISBN:
Category :
Languages : en
Pages : 154

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Book Description
Thin plate vibrations display a rich and complex dynamics that ranges from linear to strongly nonlinear regimes when increasing the vibration amplitude with respect to the thickness. This thesis is concerned with the development of a numerical code able to simulate without restrictions this large spectrum of dynamical features, described by the von Kármán equations, in the case of flat, homogeneous plates presenting a rectangular geometry. The main application of such a code is to produce gong-like sounds, in the context of sound synthesis by physical modelling. For that, a modal approach is used, in order to reduce the original Partial Differential Equations to a set of couped Ordinary Differential Equations. An energy-conserving, second-order accurate time integration scheme is developed in order to yield a stability condition. The most appealing features of the modal scheme are its accuracy and the possibility of implementing a rich loss mechanism by selecting an appropriate damping factor for each one of the modes. The sound produced by the numerical code is systematically compared to another numerical technique based on Finite Difference techniques. Fundamental aspects of the physics of nonlinear vibrations are also considered in the course of this work. When a plate vibrates in a weakly nonlinear regime, modal couplings produce amplitude-dependent vibrations, internal resonances, instabilities, jumps and bifurcations. The modal scheme is used to construct and analyse the nonlinear response of the plate in the vicinity of its first eigenfrequencies, both in free and forced-damped vibrations, showing as a result the effect of damping and forcing on the nonlinear normal modes of the underlying Hamiltonian system. When plates vibrate in a strongly nonlinear regime, the most appropriate description of the dynamics is given in terms of the statistical properties of the system, because of the vast number of interacting degrees-of-freedom. Theoretically, this framework is offered by the Wave Turbulence theory. Given the large amount of modes activated in such vibrations, a Finite Difference, energy-conserving code is preferred over the modal scheme. Such a scheme allows to produce a cascade of energy including thousands of modes when the plate is forced sinusoidally around one of its lowest eigenfrequencies. A statistical interpretation of the outcome of the simulation is offered, along with a comparison with experimental data and other numerical results found in the literature. In particular, the effect of the pointwise forcing as well as geometrical imperfections of the plates are analysed.

Author: Rudolph Szilard
Publisher: John Wiley & Sons
ISBN: 9780471429890
Category : Technology & Engineering
Languages : en
Pages : 1062

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Book Description
This book by a renowned structural engineer offers comprehensive coverage of both static and dynamic analysis of plate behavior, including classical, numerical, and engineering solutions. It contains more than 100 worked examples showing step by step how the various types of analysis are performed.

Author: Muthukrishnan Sathyamoorthy
Publisher: CRC Press
ISBN: 1351359819
Category : Mathematics
Languages : en
Pages : 548

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Book Description
Nonlinear Analysis of Structures presents a complete evaluation of the nonlinear static and dynamic behavior of beams, rods, plates, trusses, frames, mechanisms, stiffened structures, sandwich plates, and shells. These elements are important components in a wide variety of structures and vehicles such as spacecraft and missiles, underwater vessels and structures, and modern housing. Today's engineers and designers must understand these elements and their behavior when they are subjected to various types of loads. Coverage includes the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. This complete guide includes both mathematical treatment and real-world applications, with a wealth of problems and examples to support the text. Special topics include a useful and informative chapter on nonlinear analysis of composite structures, and another on recent developments in symbolic computation. Designed for both self-study and classroom instruction, Nonlinear Analysis of Structures is also an authoritative reference for practicing engineers and scientists. One of the world's leaders in the study of nonlinear structural analysis, Professor Sathyamoorthy has made significant research contributions to the field of nonlinear mechanics for twenty-seven years. His foremost contribution to date has been the development of a unique transverse shear deformation theory for plates undergoing large amplitude vibrations and the examination of multiple mode solutions for plates. In addition to his notable research, Professor Sathyamoorthy has also developed and taught courses in the field at universities in India, Canada, and the United States.

Author: Evangelos J. Sapountzakis
Publisher: Springer Nature
ISBN: 9811580499
Category : Technology & Engineering
Languages : en
Pages : 1203

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Book Description
This book presents the select proceedings of the 14th International Conference on Vibration Problems (ICOVP 2019) held in Crete, Greece. The volume brings together contributions from researchers working on vibration related problems in a wide variety of engineering disciplines such as mechanical engineering, wind and earthquake engineering, nuclear engineering, aeronautics, robotics, and transport systems. The focus is on latest developments and cutting-edge methods in wave mechanics and vibrations, and includes theoretical, experimental, as well as applied studies. The range of topics and the up-to-date results covered in this volume make this interesting for students, researchers, and professionals alike.

Author: Peter Hagedorn
Publisher: John Wiley & Sons
ISBN: 9780470518427
Category : Science
Languages : en
Pages : 396

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Book Description
The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.

Author: Malte Krack
Publisher: Springer
ISBN: 3030140237
Category : Technology & Engineering
Languages : en
Pages : 159

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Book Description
This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.