Fundamentals of Mechanical Vibrations

By: Liang-Wu Cai

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Synopsis: This introductory book covers the most fundamental aspects of vibration analysis for mechanical engineers. Vibration studies small motions of a mechanical system around its equilibrium configuration. The book consists of five major topics, each in its own chapter. It starts from a concise introduction to Langrangian dynamics as a tool for obtaining the governing equation(s) of motion for a system. In the process, key concepts such as degrees of freedom are rigorously defined. The second topic introduces mathematical tools for different types of vibration analyses for single degree-of-freedom systems. In the process, mathematical software Matlab is used to explore every example in a symbolic way, and in a curiosity-driven manner. The third topic introduces the lumped-parameter modelling process: how to convert many simple engineering structures into models consisting of masses and springs so that the multiple degrees of freedom systems, with many examples suitable for hand calculations and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method. It is formally introduced by following the framework of Lagrangian dynamics, and followed by examples of vibration analyses using a commercial software package.