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Exploring Vibrations in Everyday Life

Learn how vibrations are present in various aspects of life such as in machines, the human body, and earthquakes. Discover the theory and fundamentals of vibrations, including single and multi-degree-of-freedom systems, spring-mass systems, and energy methods.

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Exploring Vibrations in Everyday Life

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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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