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Mastering Free Vibration of SDOF Systems with Dr. Abdullah Seçgin

Dive into the world of free vibration of Single Degree of Freedom (SDOF) systems with Associate Professor Dr. Abdullah Seçgin. Learn about equations of motion, natural frequency, damping ratio, and the standard form of the equation of motion. Explore topics such as harmonic solutions, types of free vibrations, general harmonic solutions, and applying initial conditions. Through examples of underdamped vibrations, discover how to find natural frequencies, damping ratios, damped natural frequencies, free vibration response amplitudes, phases, and visualize amplitude-time graphics. Enhance your understanding of the governing equations and vibration parameters of underdamped SDOF systems.

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Mastering Free Vibration of SDOF Systems with Dr. Abdullah Seçgin

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  1. WEEK-3: Free Vibration of SDOF systems Assoc. Prof. Dr. Abdullah Seçgin

  2. Equation of motion • Natural frequency • Damping Ratio • Standart form of equation of motion Free vibration of SDOF systems • Assume following initial conditions • Assume a harmonic solution

  3. Free vibration of SDOF systems • Equation of motion • Harmonic solution • Types of Free Vibrations

  4. Free vibration of SDOF systems • General harmonic solution • Applying initial conditions

  5. Example:

  6. Example:

  7. 1.Underdamped vibration • By applying initial conditions and expand with cos and sine terms gives

  8. 1.Underdamped vibration

  9. 1.Underdamped vibration

  10. Example: Governing equation of motion of an underdamped single degree of freedom system is given as • Find the natural frequency • Find the damping ratio • Find the damped natural frequency of the system • Find the free vibration response amplitude • and its phasefor the following initial conditions: • e) Draw roughly the amplitude-time graphics of the response

  11. Example: Governing equation of motion of an underdamped single degree of freedom system shown below is given as • Find all vibration parameters

  12. Solution:

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