Mechanical Vibration/Prerequisites

Prerequisites

This book is intended to act as a guide for an undergraduate mechanical engineer. There will be references and explanation to core principles, regardless of whether or not they fall out of range in Vibrational Analysis. We will attempt to minimalize the amount of extraneous learning material within this text, but it is never a bad idea to offer a refresher lesson when working with all too often forgetable scientific and mathematical complexities.

Can you quickly recall the Taylor Series expansion for a function of two variables?

This textbook aims to offer a balance of both learned material and material to be learned, but what we must assume is that the reader has at minimum a good understanding of the following and all of the background that each would require to understand:

Matrices

• Basic Operations
• Inverse
• Determinant
• Eigenvalues & Eigenvectors

Taylor Series

• Linearization

Ordinary Differential Equations

• Linear Equations
• Homogenous Solutions
• Particular Solutions

Newtonian Physics

• Basic Velocitory and Aceleratory Understanding
• Inertia & Damping
• Hooke's Law

MATLAB

Microsoft Excel

Fluid Dynamics

Probability

• Distribution
• Density
• Basic Correlation

Electrical Engineering Basics

• Resistor/Capacitor Systems

Don't worry if you aren't entirely familiar with all of these; certainly some can be considered to follow after the study of Vibration or some may seem virtually unrelated. They have only been noted to suggest the best background possible for success in quickly and efficiently learning the material presented in this text.