Introduction to Structural Dynamics UNIT-I Introduction to Structural Dynamics

UNIT-I TOPICS COVERED

UNIT-I What are Vibrations?

Machines (large and small) Earth quake tremors Musical instruments ……. 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

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

UNIT-I

UNIT-I

UNIT-I

UNIT-I

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

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

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

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

1. Spring-mass system Newton’s Second Law of Motion 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

Single Degree-of-Freedom Systems UNIT-I 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

Single Degree of Freedom System UNIT-I Single Degree of Freedom System

UNIT-I

UNIT-I

Single degree of freedom system : UNIT-I 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)

UNIT-I

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

UNIT-I

UNIT-I

UNIT-I

UNIT-I DEFINITION OF FREE VIBRATION

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I

UNIT-I