free vibration...
TRANSCRIPT
Free Vibration - SDOF
EQUATION OF MOTION
• กฎขอ้ทีส่องของนิวตนั (Newton’s second law)• วธิงีาน-พลงังาน (Work-Energy method)• วธิขีอง Rayleigh• สมการลากรานจ์ (Lagrange equation)
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กฎขอ้ทีส่องของนิวตนั
NEWTON’S SECOND LAW
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กฎขอ้ทีส่องของนิวตนั
NEWTON’S SECOND LAW
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วธิีงาน-พลงังาน
WORK-ENERGY METHOD
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วธิีงาน-พลงังาน
WORK-ENERGY METHOD
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UNDAMPED FREE VIBRATION
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UNDAMPED FREE VIBRATION
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UNDAMPED FREE VIBRATION
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UNDAMPED FREE VIBRATION
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DAMPED FREE VIBRATION
DAMPED FREE VIBRATION
DAMPED FREE VIBRATION
DAMPED FREE VIBRATION
•Overdamped – free vibration•Critically damped – free vibration•Underdamped – free vibration
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CRITICALLY DAMPED – FREE VIBRATION
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OVERDAMPED – FREE VIBRATION
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OVERDAMPED – FREE VIBRATION
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UNDERDAMPED – FREE VIBRATION
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UNDERDAMPED – FREE VIBRATION
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UNDERDAMPED – FREE VIBRATION
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UNDERDAMPED – FREE VIBRATION
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การลดลงอย่างลอการิท่ึม
(LOGARITHMIC DECREMENT)
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การลดลงอย่างลอการิท่ึม
(LOGARITHMIC DECREMENT)
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การลดลงอย่างลอการิท่ึม
(LOGARITHMIC DECREMENT)
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EX: LOGARITHMIC DECREMENT
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EX: LOGARITHMIC DECREMENT
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EX: LOGARITHMIC DECREMENT
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CHAPTER SUMMARIES
• Equation of motion for SDOF undamped system
• Equation of motion for SDOF damped system
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CHAPTER SUMMARIES
• Undamped free vibration response
• Overdamped free vibration response
• Critically damped free vibration response
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CHAPTER SUMMARIES
• Underdamped free vibration response
• Logarithm decrement
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HOME WORK - 1
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Determine the differential equation of motion andthe equivalent stiffness for the system (N/m) of Figure
HOME WORK - 2
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For free vibration of underdamped system(ζ = 0.8) as shown in Figure.Determine stiffness of system
HOME WORK - 3
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The free response of the undamped system of Figure. Determine- Natural frequency, Initial velocity and Initial displacement
HOME WORK - 4
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The free response of the underdamped system in Figure.Calculate the damping ratio