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WEEK-3: Free Vibration of SDOF systems

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

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WEEK-3: Free Vibration of SDOF systems

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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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