1.2. Basic Terminologies and Concepts

Vibration is defined as the oscillatory motion of a body about an equilibrium position. It can be:

• Free vibration: Occurs without external force after an initial disturbance.
• Forced vibration: Occurs due to continuous external excitation.

Vibration refers to the movement of an object back and forth around a central position. This movement can happen in two primary ways:

1. Free Vibration occurs when an object, after being moved from its position and then let go, continues to vibrate without additional forces acting on it. For example, if you pull a rubber band and let it go, it will oscillate until the energy is used up.
2. Forced Vibration happens when an ongoing external force constantly drives the motion of the object. For instance, if a loudspeaker vibrates as it produces sound, this is an example of forced vibration where the speaker is continually being prompted to move.

Think of a child on a swing. When they swing back and forth without pushing from a friend, that’s free vibration. But when their friend gives them consistent pushes to keep going, that’s forced vibration.

Types of Vibratory Systems:

• Single Degree of Freedom (SDOF) System: A system that requires only one coordinate to describe its motion.
• Multiple Degrees of Freedom (MDOF) System: Systems requiring two or more independent coordinates.
• Continuous Systems: Systems like beams or plates with infinite degrees of freedom.

Vibratory systems can be categorized based on how many dimensions they encompass and their complexity:

1. Single Degree of Freedom (SDOF) refers to a simple system, like a mass attached to a spring, where only one coordinate (like its position along the vertical axis) fully describes its motion.
2. Multiple Degrees of Freedom (MDOF) systems, on the other hand, involve more complex scenarios, like a building swaying in the wind, where multiple coordinates are necessary to describe the systems’ movements accurately.
3. Continuous Systems are even more advanced, like beams or plates that can vibrate in various directions, effectively needing infinite coordinates to capture all possible movements.

Imagine a pendulum for the SDOF (it breaks down perfectly to its central point of oscillation). In contrast, a tall building swaying during an earthquake exemplifies an MDOF system, as it experiences multiple simultaneous motion directions. Continuous Systems might be likened to a thick soup where each particle can move freely in numerous directions due to the fluidity.

Key Parameters of Vibration:

• Displacement (x): The distance moved from equilibrium.
• Velocity (ẋ): Rate of change of displacement.
• Acceleration (ẍ): Rate of change of velocity.
• Mass (m): Inertia of the vibrating body.
• Stiffness (k): Resistance to deformation.
• Damping (c): Energy dissipation mechanism.

Several key parameters help us understand and define vibrations:

1. Displacement (x) determines how far an object moves from its resting position (equilibrium).
2. Velocity (ẋ) measures how fast the displacement is changing over time. Essentially it's how quickly the object moves back and forth.
3. Acceleration (ẍ) tells us how quickly the velocity is changing, revealing if the object is speeding up or slowing down.
4. Mass (m) signifies the amount of matter in the body, affecting how much it resists acceleration.
5. Stiffness (k) reflects how much force is needed to deform an object, whether by stretching or compressing it.
6. Damping (c) refers to how energy is dissipated in the system over time, affecting how long oscillations last.

Imagine you're on a trampoline. Your displacement would be how high you jump from the ground. Your velocity would change as you go up and down—fastest at the lowest point. Your acceleration is high when you suddenly start going upward. The more mass you have, the harder it is to lift you (higher mass means greater resistance). The springs on a trampoline are an example of stiffness since they resist deformation. If you kept bouncing, you'd eventually slow down as you lose energy to air (that's damping).

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