1. Introduction to Structural Dynamics
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Introduction to Structural Dynamics

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TOPICS COVERED

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What are Vibrations?

4. Machines (large and small) Earth quake tremors Musical instruments …….
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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 :
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Everyday examples where vibrations are involved :
Cars Bikes

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

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

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

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

14. 1. Spring-mass system Newton’s Second Law of Motion
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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
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Single Degree-of-Freedom Systems
A spring-mass system
General solution for any simple oscillator
General approach
Examples
Equivalent springs
Spring in series and in parallel
Energy Methods
Strain energy & kinetic energy
Work-energy statement
Conservation of energy and example

16. Single Degree of Freedom System
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Single Degree of Freedom System

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

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21. Time solution for undamped SDOF subjected to free vibrations
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Time solution for undamped SDOF subjected to free vibrations

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DEFINITION OF FREE VIBRATION

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