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.