The document discusses the theory of vibration systems, covering concepts like static and dynamic behavior, as well as lumped and continuous models. It explains degrees of freedom, detailing the six types related to both rotational and translational movements. Additionally, it differentiates between forced vibrations, influenced by continuous external forces, and free vibrations, which occur when a system vibrates at its natural frequency after an initial input.

1. THEORY OF VIBRATION

2. SYSTEMS
combination of elements intended to act together
• STATIC (memory less)
• DYNAMIC (with memory)
• LUMPED OR DISCRETE (have finite number of storage elements)
• CONTINUOUS (infinite number of states)

3. BASIC CONCEPTS
• Model
• Analytical Techniques
• Parameters
• Lumping
• Lumped parameter model
• Distributed Parameter model

4. Vibrating systems
linear or non linear

5. DEGREE OF FREEDOM
DOF defines the number of directions a body can move
• There are six total degrees of freedom. Three correspond to
rotational movement around the x, y, and z axes, commonly termed
pitch, yaw, and roll. The other three correspond to translational
movement along those axes, which can be thought of as moving
forward or backward, moving left or right, and moving up or down.

6. Forced Vibration: under the influence of excitations
• Forced vibrations occur if a system is continuously driven by an
external agency
• Deterministic : magnitude of force exerting is known
• Random : magnitude of force unknown

7. Free vibration is a type of vibration in which a force is applied
once and the structure or part is allowed to vibrate at its
natural frequency. A plucked guitar string is an example of free
vibration. Free vibration occurs when a mechanical system is
set off with an initial input and then allowed to vibrate freely.