Introduction to Engineering Nonlinear and Parametric Vibrations with MATLAB and Maple

Textbook on nonlinear and parametric vibrations discussing relevant terminology and analytical and computational tools for analysis, design, and troubleshooting

Introduction to Engineering Nonlinear and Parametric Vibrations with MATLAB and MAPLE is a comprehensive textbook that provides theoretical breadth and depth and analytical and computational tools needed to analyze, design, and troubleshoot related engineering problems.

The text begins by introducing and providing the required math and computer skills for understanding and simulating nonlinear vibration problems. This section also includes a thorough treatment of parametric vibrations. Many illustrative examples, including software examples, are included throughout the text. A companion website includes the MATLAB and MAPLE codes for examples in the textbook, and a theoretical development for a homoclinic path to chaos.

Introduction to Engineering Nonlinear and Parametric Vibrations with MATLAB and MAPLE provides information on:

• Natural frequencies and limit cycles of nonlinear autonomous systems, covering the multiple time scale, Krylov-Bogellubov, harmonic balance, and Lindstedt-Poincare methods
• Co-existing fixed point equilibrium states of nonlinear systems, covering location, type, and stability, domains of attraction, and phase plane plotting
• Parametric and autoparametric vibration including Floquet, Mathieu and Hill theory
• Numerical methods including shooting, time domain collocation, arc length continuation, and Poincare plotting
• Chaotic motion of nonlinear systems, covering iterated maps, period doubling and homoclinic paths to chaos, and discrete and continuous time Lyapunov exponents
• Extensive MATLAB and MAPLE coding for the examples presented

Introduction to Engineering Nonlinear and Parametric Vibrations with MATLAB and MAPLE is an essential up-to-date textbook on the subject for upper level undergraduate and graduate engineering students as well as practicing vibration engineers. Knowledge of differential equations and basic programming skills are requisites for reading.

Alan B. Palazzolo, James J. Cain Professor of Mechanical Engineering, Texas A&M University, USA. Professor Palazzolo has extensive industrial, research, and teaching experience in vibrations. He has taught graduate level courses in Nonlinear and Parametric Vibrations (MEEN 649) and Rotordynamics (MEEN 639). In addition, he has also held industrial positions at Bently Nevada, Southwest Research Institute, and Allis Chalmers Corporation in these areas, and has performed approximately $21M in funded research.

Dongil Shin, Lead Research Engineer at GE Vernova Advanced Research in Niskayuna, New York. Dongil has extensive experience in nonlinear vibration analysis of turbomachinery systems and has published multiple journal papers in this field. At GE Vernova, he specializes in tackling practical nonlinear vibration challenges in turbomachinery components, including blades, dampers, and bearings, with a focus on gas and steam turbine systems.

Jeffrey Falzarano, Professor of Ocean Engineering, Texas A&M University, USA. Professor Falzarano has extensive research, teaching, and industry/government experience. He has taught undergraduate and graduate courses in vibrations and ship dynamics (seakeeping and ship maneuvering). He has held engineering and research positions in both government and industry. He has performed research funded by the Office of Naval Research, National Science Foundation, and other government and industry entities. He is also the 2022 recipient of the Society of Naval Architects and Marine Engineers Davidson Medal for excellence in ship research.