Mechanical Analysis

Most landslides are triggered by rainfall. In previous studies, slope stability is often evaluated based on the infiltration analysis. Hydro-mechanical coupling is significant to rainfall-caused landslide evolution. This book covers theoretical models of unsaturated infiltration, and provides hydro-mechanical models for rainfall-induced landslides. The influences of rainfall patterns, boundary conditions, layered structures, and SWCC hysteresis on the coupled unsaturated infiltration and deformation are discussed. Laboratory testing of rainfall-induced landslides is performed to study the developing process of landslide upon rainfall infiltration. The results provide a better understanding of rainfall-induced landslides.

This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale.
Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics.

The primary emphasis of this book is the modeling, analysis, and control of mechanical systems. The methods and results presented can be applied to a large class of mechanical control systems, including applications in robotics, autonomous vehicle control, and multi-body systems. The book is unique in that it presents a unified, rather than an inclusive, treatment of control theory for mechanical systems. A distinctive feature of the presentation is its reliance on techniques from differential and Riemannian geometry.

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.