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

• Students will model and analyze the free vibration of single-degree-of-freedom systems (SDOF)
• Students will apply analytical tools in the design of engineering systems and devices
• Students will derive equations of motion for SDOF systems using Newton/Euler laws
• Students will analyze the effects of viscous damping in the free vibration response
• Students will plot and interpret SDOF vibratory motion

Week 1 – Vibration System Modeling Elements

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

Week 2 – Vibration System Differential Equations of Motion

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

Week 3 – Undamped Single Degree-of-Freedom Vibration Systems

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

Week 4 – Damped, Single-Degree-of-Freedom Vibration Systems

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

Week 5 – Damped, Single-Degree-of-Freedom Vibration Systems

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

“Thank You to Georgia Tech and Dr. Wayne Whiteman in delivering these interactive engineering courses. I like the way the videos and the modules are created in such a way that they are understandable and helpful for the students taking the course.”

“This course was a really awesome experience. I recommend it to everyone who wants clear basic [engineering] concepts.”

"Excellent Course, I never thought that learning mechanics online would be so interesting and comfortable. The course plan was very good and Dr. Wayne Whiteman was very clear.”