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WEEK-3: Free Vibration of SDOF systems
Assoc. Prof. Dr. Abdullah Seçgin
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Free vibration of SDOF systems
Assume following initial conditions Natural frequency Damping Ratio Equation of motion Standart form of equation of motion Assume a harmonic solution
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Free vibration of SDOF systems
Equation of motion Harmonic solution Types of Free Vibrations
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Free vibration of SDOF systems
General harmonic solution Applying initial conditions
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Example:
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Example:
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1.Underdamped vibration
By applying initial conditions and expand with cos and sine terms gives
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1.Underdamped vibration
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1.Underdamped vibration
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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 phase for the following initial conditions: e) Draw roughly the amplitude-time graphics of the response
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Example: Governing equation of motion of an underdamped single degree of freedom system shown below is given as Find all vibration parameters
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Solution:
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