Short Answer:

Transient vibration is a type of vibration that occurs for a short period of time when a mechanical system is suddenly disturbed by an external force or impact. It appears immediately after the disturbance and gradually dies out with time as the system returns to its normal state.

This vibration is temporary in nature and depends on the system’s natural frequency and damping. Transient vibration is commonly seen during machine startup, shutdown, or when a sudden shock or impact occurs. It is different from steady-state vibration, which continues as long as the external force acts on the system.

Detailed Explanation :

Transient Vibration

Transient vibration refers to the temporary or short-duration vibrations that occur in a system due to a sudden or momentary disturbance. It happens when a force acts for a short time and then disappears, such as a hammer blow, sudden load change, or impact. After the force is removed, the system continues to vibrate freely for a short period until it settles back to its equilibrium position.

Transient vibrations are very common in machines and structures, especially during operations such as starting, stopping, or sudden contact with another body. The characteristics of these vibrations depend on system parameters like mass, stiffness, damping, and natural frequency.

1. Principle of Transient Vibration

Transient vibration occurs when a mechanical system is disturbed suddenly and then left to vibrate freely.
To understand this, consider a mass-spring-damper system:

When the system is at rest and a sudden force is applied (such as an impulse), it displaces the mass. After the force is removed, the mass starts vibrating about its mean position due to the restoring action of the spring. The amplitude of vibration decreases with time because of damping, and eventually, the motion stops.

The equation of motion for a damped single degree of freedom (SDOF) system under transient vibration is:

Where,

•  = mass of the system
•  = damping coefficient
•  = stiffness of the spring
•  = external force applied

In transient vibration,  is a short-duration force, meaning it acts for a very small time. Once it stops, the remaining motion is the transient response, which decays with time due to damping.

2. Characteristics of Transient Vibration

1. Short Duration:
   It occurs only for a limited time after the system is disturbed.
2. Damped Response:
   The amplitude of vibration decreases gradually with time because of the damping effect.
3. Depends on Initial Conditions:
   The amplitude and frequency depend on the initial displacement or velocity of the system.
4. Temporary Nature:
   Once the system’s energy is dissipated through damping, vibration stops completely.
5. No Continuous Excitation:
   The external force causing the vibration acts for a very short duration and then ceases.
6. System Property Dependence:
   The frequency of transient vibration equals the system’s natural frequency, since it is a free vibration after the initial disturbance.

3. Mathematical Representation

If an impulse force is applied to a damped system, the equation of motion becomes:

The solution for displacement  in a damped system is:

Where,

•  = initial amplitude
•  = damping ratio
•  = natural frequency
•  = damped natural frequency
•  = phase angle

This equation shows that the motion is oscillatory and decays exponentially with time because of the damping term .

4. Types of Transient Vibration

Transient vibrations can be categorized based on the type of disturbance:

1. Impulse Type:
   Caused by a short, high-magnitude force such as a hammer blow or collision.
   Example: Striking a metal plate with a hammer.
2. Step Type:
   Caused by a sudden application or removal of a constant load.
   Example: Sudden engagement or disengagement of a machine part.
3. Periodic Transient:
   Caused by repeated impacts or disturbances occurring at intervals.
   Example: Gear tooth impact or piston slap in an engine.

Each type of transient vibration produces a temporary oscillation that decays over time.

5. Examples of Transient Vibration

1. Machine Startup or Shutdown:
   When a rotating machine starts or stops suddenly, its parts experience short-term vibrations.
2. Hammering on a Structure:
   A hammer impact produces an impulse that causes the structure to vibrate briefly.
3. Vehicle Passing Over a Bump:
   The wheels experience transient vibrations as they encounter uneven road surfaces.
4. Earthquake Impact on Buildings:
   A sudden ground movement causes the building to vibrate for a few seconds before returning to rest.
5. Switching Electrical Machines:
   Electric motors or transformers experience transient vibrations due to magnetic forces when switched on or off.

6. Difference Between Transient and Steady-State Vibration

Parameter	Transient Vibration	Steady-State Vibration
Duration	Short-lived	Continuous as long as excitation exists
Cause	Sudden force or impact	Continuous periodic force
Nature	Temporary	Permanent
Amplitude	Decreases with time	Remains constant
Example	Hammer blow, startup vibration	Unbalanced rotor vibration

7. Importance of Studying Transient Vibration

• Helps in designing machines to withstand sudden shocks and loads.
• Useful in analyzing startup and shutdown conditions of rotating machinery.
• Helps in predicting failure or resonance due to short-term disturbances.
• Provides insight into the damping characteristics of materials and systems.
• Aids in developing vibration control techniques such as isolators and absorbers.

By studying transient vibrations, engineers can ensure safety and improve the life and performance of mechanical systems.

8. Control of Transient Vibration

1. Adding Damping:
   Increasing damping reduces the duration and amplitude of transient vibration.
2. Shock Absorbers:
   Used in vehicles and machines to absorb sudden energy and minimize vibrations.
3. Vibration Isolators:
   Rubber mounts or springs are used to reduce transmission of transient forces.
4. Gradual Start and Stop Mechanisms:
   Soft starters or speed controllers minimize transient vibrations in machines.
5. Proper Maintenance:
   Ensures that loose or worn components do not amplify transient effects.

Conclusion:

Transient vibration is a temporary vibration that occurs when a mechanical system is suddenly disturbed and then allowed to return to its equilibrium. It is short-lived, decays with time, and depends on system properties such as damping, stiffness, and natural frequency. Understanding transient vibrations helps engineers design machines and structures that can resist sudden shocks and impacts, ensuring smooth operation, safety, and longer life of equipment.