Nonlinear Vibrations and Stability of Shells and Plates

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.

Introduction. 1. Nonlinear theories of elasticity of plates and shells; 2. Nonlinear theories of doubly curved shells for conventional and advanced materials; 3. Introduction to nonlinear dynamics; 4. Vibrations of rectangular plates; 5. Vibrations of empty and fluid-filled circular cylindrical; 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes; 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells; 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells; 9. Vibrations of circular cylindrical panels with different boundary conditions; 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials; 11. Meshless discretization of plates and shells of complex shapes by using the R-functions; 12. Vibrations of circular plates and rotating disks; 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads; 14. Nonlinear stability and vibrations of circular shells conveying flow; 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

Marco Amabili is a professor and Director of the Laboratories in the Department of Industrial Engineering at the University of Parma. His main research is in vibrations of thin-walled structures and fluid-structure interaction. Professor Amabili is the winner of numerous awards in Italy and around the world including the 'Bourse québécoise d'excellence' from the Ministry of Education of Québec in 1999. He is Associate Editor of the Journal of Fluids and Structures, a member of the editorial board of Journal of Sound and Vibration, and editor of a special issue of the Journal of Computers and Structures. He is a co-organizer of 14 conferences or symposia, the Secretary of the ASME Technical Committee on Dynamics and Control of Structures and Systems (AMD Division), and a member of the ASME Technical Committees Vibration and Sound (DE Division) and Fluid-Structure Interaction (PVP Division). Professor Amabili is the author of more than 180 papers on vibrations and dynamics.