Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells

Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells
Author: Yi-Yuan Yu
Publisher:
Total Pages: 56
Release: 1962
Genre: Elasticity
ISBN:

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An integrated procedure is presented for applying the variational equation of motion to the approximate analysis of nonlinear vibrations of homogeneous and layered plates and shells involving large deflections. The procedure consists of a sequence of variational approximations. The first of these involves an approximation in the thickness direction and yields a system of equations of motion and boundary conditions for the plate or shell. Subsequent variational approximations with respect to the remaining space coordinates and time, wherever needed, lead to a solution to the nonlinear vibration problem. The procedure is illustrated by a study of the nonlinear free vibrations of homogeneous and sandwich cylindrical shells, and it appears to be applicable to still many other homogeneous and composite elastic systems.

Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells

Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells
Author: Yi-Yuan Yu
Publisher:
Total Pages: 56
Release: 1962
Genre: Elasticity
ISBN:

Download Application of Variational Equation of Motion to the Nonlinear Vibration Analysis of Homogeneous and Layered Plates and Shells Book in PDF, Epub and Kindle

An integrated procedure is presented for applying the variational equation of motion to the approximate analysis of nonlinear vibrations of homogeneous and layered plates and shells involving large deflections. The procedure consists of a sequence of variational approximations. The first of these involves an approximation in the thickness direction and yields a system of equations of motion and boundary conditions for the plate or shell. Subsequent variational approximations with respect to the remaining space coordinates and time, wherever needed, lead to a solution to the nonlinear vibration problem. The procedure is illustrated by a study of the nonlinear free vibrations of homogeneous and sandwich cylindrical shells, and it appears to be applicable to still many other homogeneous and composite elastic systems.

AFOSR.

AFOSR.
Author: United States. Air Force. Office of Scientific Research
Publisher:
Total Pages: 968
Release: 1968
Genre: Research
ISBN:

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Nonlinear Analysis of Structures (1997)

Nonlinear Analysis of Structures (1997)
Author: Muthukrishnan Sathyamoorthy
Publisher: CRC Press
Total Pages: 548
Release: 2017-11-22
Genre: Mathematics
ISBN: 1351359819

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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.

Vibrations of Elastic Plates

Vibrations of Elastic Plates
Author: Yi-Yuan Yu
Publisher: Springer Science & Business Media
Total Pages: 234
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461223385

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This book is based on my experiences as a teacher and as a researcher for more than four decades. When I started teaching in the early 1950s, I became interested in the vibrations of plates and shells. Soon after I joined the Polytechnic Institute of Brooklyn as a professor, I began working busily on my research in vibrations of sandwich and layered plates and shells, and then teaching a graduate course on the same subject. Although I tried to put together my lecture notes into a book, I never finished it. Many years later, I came to the New Jersey Institute of Technology as the dean of engineering. When I went back to teaching and looked for some research areas to work on, I came upon laminated composites and piezoelectric layers, which appeared to be natural extensions of sandwiches. Working on these for the last several years has brought me a great deal of joy, since I still am able to find my work relevant. At least I can claim that I still am pursuing life-long learning as it is advocated by educators all over the country. This book is based on the research results I accumulated during these two periods of my work, the first on vibrations and dynamical model ing of sandwiches, and the second on laminated composites and piezoelec tric layers.

Vibrations of Elastic Plates

Vibrations of Elastic Plates
Author: Yi-Yuan Yu
Publisher: Springer Science & Business Media
Total Pages: 256
Release: 1996-04-25
Genre: Science
ISBN: 9780387945149

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This book deals with the dynamical modeling of thin elastic structures, such as beams, plates and shells - particularly, the linear and nonlinear vibrations in these structures. The approach makes systematic use of variational equations of motion.

Journal of Applied Mechanics

Journal of Applied Mechanics
Author:
Publisher:
Total Pages: 1134
Release: 1971
Genre: Mechanical engineering
ISBN:

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Publishes original research in all branches of mechanics including aerodynamics; aeroelasticity; boundary layers; computational mechanics; constitutive modeling of materials; dynamics; elasticity; flow and fracture; heat transfer; hydraulics; impact; internal flow; mechanical properties of materials; micromechanics; plasticity; stress analysis; structures; thermodynamics; turbulence; vibration; and wave propagation.

Nonlinear Oscillations

Nonlinear Oscillations
Author: Ali H. Nayfeh
Publisher: John Wiley & Sons
Total Pages: 720
Release: 2008-09-26
Genre: Science
ISBN: 3527617590

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Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.