Providing a unified understanding of vibration analysis for graduate students and industry professionals, Advanced Vibration Analysis presents a comprehensive theory for the advanced analysis of vibrations. This book ties together the theories and analysis methods for vibrations of discrete systems and vibrations of continuous systems with a unified mathematical theory. It covers vibrations in single degree of freedom systems, calculus of variations, linear algebra, operators for vibration problems, free vibrations of conservative and non-conservative systems, forced response, and variational methods. It also includes recent applications such as vibrations of nanotubes.