Fundamentals of Mechanical Vibrations

Fundamentals of Mechanical Vibrations covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, the book dedicates a chapter to each topic, which aligns the text with its five major objectives. It starts from a concise, rigorous, and yet accessible introduction to using Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single-degree-of-freedom systems. In the process, every example includes a section called "Exploring the Solution with MATLAB". This is intended to develop a student's affinity to symbolic calculations and to encourage curiosity-driven explorations. The third topic introduces lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple-degrees-of-freedom systems, with many examples suitable for hand calculation and a few computer-aided examples that bridge the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and use of commercial software for vibration analysis of real-world structures.

A primer on MATLAB is included in an appendix. In addition, a supplemental set of MATLAB code files is available for download.