Author: Michele Ducceschi
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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.
Nonlinear Vibrations of Thin Rectangular Plates
Author: Michele Ducceschi
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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.
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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.
Nonlinear Vibrations and Stability of Shells and Plates
Author: Marco Amabili
Publisher: Cambridge University Press
ISBN: 1139469029
Category : Science
Languages : en
Pages : 391
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.
Publisher: Cambridge University Press
ISBN: 1139469029
Category : Science
Languages : en
Pages : 391
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.
Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
Author: Marco Amabili
Publisher: Cambridge University Press
ISBN: 1107129222
Category : Mathematics
Languages : en
Pages : 585
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.
Publisher: Cambridge University Press
ISBN: 1107129222
Category : Mathematics
Languages : en
Pages : 585
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.
Nonlinear Analysis of Structures (1997)
Author: Muthukrishnan Sathyamoorthy
Publisher: CRC Press
ISBN: 1351359819
Category : Mathematics
Languages : en
Pages : 548
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.
Publisher: CRC Press
ISBN: 1351359819
Category : Mathematics
Languages : en
Pages : 548
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.
Flow Induced Nonlinear Vibrations of Rectangular Plates
Author: Berk Geveci
Publisher:
ISBN:
Category : Plates, Aluminum
Languages : en
Pages : 564
Book Description
The response of two- and three-dimensional plates to the motion of a single recti-linear vortex in incompressible flow is studied for various physical parameters. It is shown that the passage of a vortex over the plate can induce complex vibrations and large deformations of the plate.
Publisher:
ISBN:
Category : Plates, Aluminum
Languages : en
Pages : 564
Book Description
The response of two- and three-dimensional plates to the motion of a single recti-linear vortex in incompressible flow is studied for various physical parameters. It is shown that the passage of a vortex over the plate can induce complex vibrations and large deformations of the plate.
Thin Plates and Shells
Author: Eduard Ventsel
Publisher: CRC Press
ISBN: 9780203908723
Category : Mathematics
Languages : en
Pages : 688
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
Publisher: CRC Press
ISBN: 9780203908723
Category : Mathematics
Languages : en
Pages : 688
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
Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials
Author: Marco Amabili
Publisher: Cambridge University Press
ISBN: 1108577636
Category : Science
Languages : en
Pages : 585
Book Description
This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.
Publisher: Cambridge University Press
ISBN: 1108577636
Category : Science
Languages : en
Pages : 585
Book Description
This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.
Nonlinear Vibration of Thin Plates
Author: Victor Chin-Po Kuo
Publisher:
ISBN:
Category : Plate
Languages : en
Pages : 190
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.
Publisher:
ISBN:
Category : Plate
Languages : en
Pages : 190
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.
Theories and Applications of Plate Analysis
Author: Rudolph Szilard
Publisher: John Wiley & Sons
ISBN: 9780471429890
Category : Technology & Engineering
Languages : en
Pages : 1062
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.
Publisher: John Wiley & Sons
ISBN: 9780471429890
Category : Technology & Engineering
Languages : en
Pages : 1062
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.
Vibration of Plates
Author: Arthur W. Leissa
Publisher:
ISBN:
Category : Plates (Engineering)
Languages : en
Pages : 380
Book Description
Publisher:
ISBN:
Category : Plates (Engineering)
Languages : en
Pages : 380
Book Description