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