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Introduction to Structural Dynamics

UNIT-I. Introduction to Structural Dynamics. UNIT-I. TOPICS COVERED. UNIT-I. What are Vibrations?. UNIT-I. Vibrations are present everywhere in life ------ Atomic vibrations (temperature) Human body (heart) Machines (large and small) Earth quake tremors Musical instruments …….

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Introduction to Structural Dynamics

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  1. UNIT-I Introduction to Structural Dynamics

  2. UNIT-I TOPICS COVERED

  3. UNIT-I What are Vibrations?

  4. UNIT-I Vibrations are present everywhere in life ------ Atomic vibrations (temperature) Human body (heart) Machines (large and small) Earth quake tremors Musical instruments ……. So we live in a world of vibrations…. Let us , from now onwards look at the world from this view point

  5. Everyday examples where vibrations are involved : UNIT-I Cars Bikes

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  10. Theory of vibrations UNIT-I Fundamentals of Linear Vibrations • Single Degree-of-Freedom Systems • Two Degree-of-Freedom Systems • Multi-DOF Systems • Continuous Systems

  11. UNIT-I What is a spring-mass system and why it is important? (Hooke’s Law)

  12. UNIT-I 1. Spring-mass system Dynamic problem: What is motion of the mass when acted by an external force or is initially displaced?

  13. UNIT-I Spring-mass system Forces acting on the mass Net force acting on the mass

  14. UNIT-I 1. Spring-mass system Newton’s Second Law of Motion the acceleration of an object due to an applied force is in the direction of the force and given by: For our spring-mass system

  15. Single Degree-of-Freedom Systems UNIT-I • A spring-mass system • General solution for any simple oscillator • General approach • Examples • Equivalent springs • Spring in series and in parallel • Examples • Energy Methods • Strain energy & kinetic energy • Work-energy statement • Conservation of energy and example

  16. Single Degree of Freedom System UNIT-I

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  18. m x(t) k Equation of motion : is an equivalent static force (‘inertial’ force) UNIT-I Damper removed : • Single degree of freedom system : Undamped natural frequency : Period of vibration, T :

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  20. UNIT-I Time solution for undamped SDOF subjected to free vibrations

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  24. UNIT-I DEFINITION OF FREE VIBRATION

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