Introduction

This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis.

Mathematical Tools for 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 Exploring the Solution with MATLAB. This is intended to develop students' affinity to symbolic calculations, and to encourage curiosity-driven explorations.

Lumped-Parameter Modeling

The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs.

Mathematical Tools for Multiple Degrees of Freedom

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.

Finite Element Method

The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures.