Vibrations of Elastic Plates : Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers

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. Front Matter....Pages i-xiii Nonlinear Elasticity Theory....Pages 1-30 Linear Vibrations of Plates Based on Elasticity Theory....Pages 31-55 Linear Modeling of Homogeneous Plates....Pages 57-89 Linear Modeling of Sandwich Plates....Pages 91-114 Linear Modeling of Laminated Composite Plates....Pages 115-129 Linear Vibrations Based on Plate Equations....Pages 131-149 Nonlinear Modeling for Large Deflections of Beams, Plates, and Shallow Shells....Pages 151-168 Nonlinear Modeling and Vibrations of Sandwiches and Laminated Composites....Pages 169-192 Chaotic Vibrations of Beams....Pages 193-207 Nonlinear Modeling of Piezoelectric Plates....Pages 209-225 Back Matter....Pages 227-228 Contents: Nonlinear Elasticity Theory Linear Vibrations of Plates Linear Dynamical Models of Homogeneous Plates Linear Dynamical Models of Sandwich Plates Linear Dynamical Models of Laminated Composite Plates Linear Vibrations of Plates Nonlinear Dynamical Models for Large Deflections of Beams, Plates, and Shells Nonlinear Dynamical Models of Vibrations in Sandwiches and Laminated Composite Plates Chaotic Vibrations of Beams Nonlinear Dynamical Models for Large Deflections of Piezoelectric Beams. 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.