Vibration Theory and Applications with Finite Elements provides extensive coverage of vibration-related topics, with particular emphasis on the three basic areas of modeling, analysis and applications.  The author recognizes that a thorough understanding of mathematical and modeling techniques is essential before progressing to methods of analysis, and there is a complete section covering the relevant math and programming techniques in MATLAB and MAPLE.  By using a wide range of practical examples and exercises, the author demonstrates how the math relates to engineering and its applications, connecting theory to engineering practice and problem solving.  Based on many years of research and teaching, this book brings together all the important topics in linear vibration theory, including failure models, kinematics and modeling, unstable vibrating systems, rotordynamics, model reduction methods, and finite element methods utilizing truss, beam, membrane and solid elements. It also explores in detail active vibration control, instability and modal analysis. The book provides the modeling skills and knowledge required for modern engineering practice, plus the tools needed to identify, formulate and solve engineering problems effectively.