An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
Author: Raymond David Mindlin
Publisher: World Scientific
Total Pages: 211
Release: 2006
Genre: Technology & Engineering
ISBN: 9812703810

This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

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

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 Systems

Vibrations of Elastic Systems
Author: Edward B. Magrab
Publisher: Springer Science & Business Media
Total Pages: 499
Release: 2012-01-12
Genre: Technology & Engineering
ISBN: 9400726724

This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.

Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates, An - By R D Mindlin

Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates, An - By R D Mindlin
Author: Jiashi Yang
Publisher: World Scientific
Total Pages: 211
Release: 2006-12-29
Genre: Technology & Engineering
ISBN: 9814476544

This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

Vibrations of Shells and Plates

Vibrations of Shells and Plates
Author: Werner Soedel
Publisher: CRC Press
Total Pages: 594
Release: 2004-08-11
Genre: Mathematics
ISBN: 0203026306

With increasingly sophisticated structures involved in modern engineering, knowledge of the complex vibration behavior of plates, shells, curved membranes, rings, and other complex structures is essential for today‘s engineering students, since the behavior is fundamentally different than that of simple structures such as rods and beams. Now in its

Vibrations in Heterogeneous Elastic Plates

Vibrations in Heterogeneous Elastic Plates
Author: Peng-Chih Constance Yang
Publisher:
Total Pages: 93
Release: 1962
Genre: Elastic plates and shells
ISBN:

A two-dimensional heterogeneous dynamic plate theory was deduced from the three-dimensional dynamic equations of elasticity. The heterogeneity of the material was considered to be only along the thickness coordinate of the plate. Approximations of shear deformations and of rotary inertia were included. A tenth order differential equation was derived. Five boundary conditions and proper initial conditions were obtained to insure an unique solution. It was recognized that the fact of coupling between stretching and bending in the heterogeneous plate led to this higher order (tenth) differential equation. The heterogeneous plate theory was specialized to cases of symmetrically laminated aeolotropic, orthotropic and isotropic plates respectively. A heterogeneous plate theory neglecting shear deformations was also deduced from the three-dimensional dynamic equation of elasticity. It was shown that the method of solving the forced vibration of a homogeneous plate of finite length could be extended to a heterogeneous plate. (Author).