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# Engineering Vibration I: Introduction: Single-Degree-of-Freedom Systems

### Overview

This course is an introduction to exploring the topic of engineering systems undergoing vibration. The methods taught in the course are used to predict the response of engineering structures to various types of input and to analyze the resulting vibratory motion. The free vibration of Single Degree-of-Freedom (SDOF) systems will be the focus of this course.

### Syllabus

Week 1 â€“ Vibration System Modeling Elements

• Module 1 â€“ Introduction and Importance of Vibrations
• Module 2 â€“ Vibrations Modeling System Elements - Mass
• Module 3 â€“ Vibrations Modeling System Elements â€“ Linear and Torsional Springs
• Module 4 â€“ Equivalent Spring Constants for Multiple Springs
• Module 5 â€“ Equivalent Spring Constants for Axially and Torsionally Loaded Members
• Module 6 â€“ Equivalent Spring Constants for Beam Structures
• Module 7 â€“ Vibrations Modeling System Elements â€“ Damper

Week 2 â€“ Vibration System Differential Equations of Motion

• Module 8 â€“ Generalized Coordinates and Degrees of Freedom
• Module 9 â€“ Model Real World Systems
• Module 10 â€“ Static Equilibrium â€“ SDOF
• Module 11 â€“ Derive Differential Equation of Motion â€“ SDOF translational motion
• Module 12 â€“ Solve Differential Equation of Motion â€“ SDOF translational motion

Week 3 â€“ Undamped Single Degree-of-Freedom Vibration Systems

• Module 13 â€“ Natural Frequency/Period of Oscillation
• Module 14 â€“ Transient Response Solution
• Module 15 â€“ Phase Angle Form of Solutions
• Module 16 â€“ Analyze Position, Velocity, Acceleration Solutions â€“ SDOF systems
• Module 17 â€“ Solve for Undamped, Free Vibration
• Module 18 â€“ Derive Differential Equation of Motion â€“ SDOF rotational motion
• Module 19 â€“ Derive Differential Equation of Motion â€“ SDOF rotational motion
• Module 20 â€“ Solve Differential Equation of Motion â€“ SDOF rotational motion/Stability
• Module 21 â€“ Solve Undamped, Free Vibration problems

Week 4 â€“ Damped, Single-Degree-of-Freedom Vibration Systems

• Module 22 â€“ Derive Differential Equation of Motion â€“ SDOF damped, free vibration
• Module 23 â€“ Cases of Damping/Critical Damping
• Module 24 â€“ Derive Differential Equation of Motion â€“ SDOF damped, free vibration
• Module 25 â€“ Plot and Interpret Transient Underdamped Vibration
• Module 26 â€“ Solve Differential Equation of Motion â€“ SDOF damped, free vibration

Week 5 â€“ Damped, Single-Degree-of-Freedom Vibration Systems

• Module 27 â€“ Logarithmic Decrement
• Module 28 â€“ Solve Differential Equation of Motion - SDOF rotational damped, free vibration
• Module 29 â€“ Solve for natural frequency, damping factor, and time to decay
• Module 30 â€“ Overdamped Vibration
• Module 31 â€“ Critically Damped Vibration
• Module 32 â€“ Course Conclusion

Wayne Whiteman

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