Nonlinear Vibrations and Stability of Shells and Plates (Hardcover)

In this impressively thorough work, Amabili (U. of Parma, Italy) utilizes nonlinear shell and plate theory to analyze shell stability in the presence of vibration, beginning the volume with an overview of the nonlinear theory of rectangular and circular plates and circular cylindrical and spherical shells. Nonclassical nonlinear theories are described in the second chapter, with attention to shear deformation and rotary inertia, and an overview of thermal stresses. Building on these foundations, Amabili turns to detailed discussion of nonlinear dynamics, stability, bifurcation analysis, and computational tools, with particular emphasis on the Galerkin method and Lagrange equations of motion and their applications to a variety of applications concerning discretizing plates and shells. Discussion of numerical techniques and various classical nonlinear shell theories follow, as these are applied for large amplitude vibrations of various shells and panels. Other chapters discuss stability under static and periodic loads, the methods for modeling aerodynamic loads, and problems arising from fluid-structure interaction, among other topics.