# Vibration Theory (425)

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## Chapter Outline

### Chapter 5.1 - Vibration Theory (Environmental Testing Procedures)

• Degrees of Freedom
• Mathematical Treatment of Vibration Forced Vibration
• Transmissibility
• Damping
• Isolation
• Random Vibration
• Definitions
• Spectral Density
• Calculating RMS
• Applications of Vibration Testing

## Video Outline

### Vibration Theory, part1

What is Vibration • Impact of Vibration • Vibration Terminology • Degrees of Freedom • Mathematical Treatment of Vibration • Mass-Spring Single-Degree-of-Freedom System • Free Periodic Motion: Mathematical Model • Undamped Vibrations in Single Degree of Freedom Systems • SDoF —Sinusoidal Relationships • Undamped Forced Periodic Motion, SDoF • Damped Forced Periodic Motion, SDoF • Amplitude Ratio –Application Example • Graph of Amplitude Ratio vs. Frequency Ratio • Transmissibility Ratio and Effect of Damping • Effect of Damping on Frequency of Max Response • Damping and Isolation • Applications of Dynamics & Vibration Testing • Overview of Mechanical Vibration Testing • Characterizing Periodic Vibration: Sine Sweep • Characterizing Random Vibration • Random Vibration Spectrum • Spectral Density Example • Special Definitions for Random Vibration • Applications: Characterizing Vibration Environment, Shaker Modal Testing System, Random Vibe Test –Launch Survivability, Product Environmental Vibration Screening, Transportation Vibration Testing

### Vibration Theory, part2

What is Vibration • Impact of Vibration • Vibration Terminology • Degrees of Freedom • Mathematical Treatment of Vibration • Mass-Spring Single-Degree-of-Freedom System • Free Periodic Motion: Mathematical Model • Undamped Vibrations in Single Degree of Freedom Systems • SDoF —Sinusoidal Relationships • Undamped Forced Periodic Motion, SDoF • Damped Forced Periodic Motion, SDoF • Amplitude Ratio –Application Example • Graph of Amplitude Ratio vs. Frequency Ratio • Transmissibility Ratio and Effect of Damping • Effect of Damping on Frequency of Max Response • Damping and Isolation • Applications of Dynamics & Vibration Testing • Overview of Mechanical Vibration Testing • Characterizing Periodic Vibration: Sine Sweep • Characterizing Random Vibration • Random Vibration Spectrum • Spectral Density Example • Special Definitions for Random Vibration • Applications: Characterizing Vibration Environment, Shaker Modal Testing System, Random Vibe Test –Launch Survivability, Product Environmental Vibration Screening, Transportation Vibration Testing