Mechanics Today, Volume 3 provides the advances in the fields of solid and fluid mechanics and applied mathematics. This volume is divided into six chapters that discuss the fundamentals and analytical and experimental results of dynamic behavior of linear and nonlinear systems. Chapter I provides a formulation of the effective stiffness theory with equations of motion and boundary conditions presented for the case of plain strain motion. Chapter II summarizes some of the analytical results that have been obtained in an effort to improve understanding of elastodynamic fracture processes. Chapter III presents the matrix difference equations used to formulate problems related to random vibration of periodic and almost periodic structures, taking advantage of the identical construction of the interconnecting units. Chapter IV describes a basic approach to the Oseen problem through the use of integral representations of the velocity and pressure fields. Chapter V deals with an analysis of nonlinear gyroscopic systems and the motions of high-order nongyroscopic systems. Chapter VI focuses on the application of the WKB perturbation method in the study of static deformation, vibration, wave propagation, and instability of elastic bodies. This volume is of great value to solid and fluid mechanics specialists and also to non-specialists with sufficient background of the field.