Post on 22-Dec-2015
WEEK-3: WEEK-3: Free Vibration of SDOF Free Vibration of SDOF
systemssystemsAssoc. Prof. Dr. Abdullah Assoc. Prof. Dr. Abdullah SeçginSeçgin
Free vibration of SDOF systems
•Natural frequency
•Damping Ratio
•Equation of motion
•Standart form of equation of motion
•Assume following initial conditions
•Assume a harmonic solution
Free vibration of SDOF systems•Equation of motion •Harmonic solution
• Types of Free Vibrations
Free vibration of SDOF systems•General harmonic solution
•Applying initial conditions
Example:
Example:
1.Underdamped vibration
•By applying initial conditions and expand with cos and sine terms gives
1.Underdamped vibration
1.Underdamped vibration
Example: Governing equation of motion of an underdamped single degree of freedom system is given as
a) Find the natural frequencyb) Find the damping ratioc) Find the damped natural frequency of the systemd) Find the free vibration response amplitude and its phase for the following initial conditions:
e) Draw roughly the amplitude-time graphics of the response
0)0(,15.0)0( xmx
Example: Governing equation of motion of an underdamped single degree of freedom system shown below is given as
a) Find all vibration parameters
Solution: