Short Answer:

Self-excited vibration is a type of vibration that occurs when the energy required to sustain the motion is supplied by the system itself rather than by an external periodic force. In this vibration, the system draws energy from a constant source and converts it into vibratory motion through internal feedback.

In simple words, self-excited vibration continues automatically once it starts because the system generates and maintains its own energy to keep vibrating. Examples include vibrations in machine tools during cutting (chatter), vibrations in aircraft wings, and the singing of telephone wires in the wind.

Detailed Explanation :

Self-Excited Vibration

Self-excited vibration is a type of vibration in which the amplitude of motion increases due to an internal source of energy within the system. Unlike forced vibration, where an external periodic force drives the motion, or free vibration, where motion is caused by an initial disturbance, self-excited vibration sustains itself because the system feeds energy into its own motion through feedback mechanisms.

This type of vibration often occurs in mechanical, fluid, or thermal systems where a steady energy input is present. The system itself modifies or converts this steady input into oscillating energy due to internal feedback effects. The energy supply may be constant, but because of the feedback process, the output vibration becomes variable or oscillatory.

In many practical applications, self-excited vibration is undesirable because it can lead to instability, excessive noise, or even failure of the system. However, in some special devices like oscillators and musical instruments, self-excited vibrations are useful and intentionally produced.

Nature of Self-Excited Vibration

In self-excited vibration, once the motion starts (usually due to a small disturbance), the system extracts energy from an external steady source (like electric, thermal, or fluid energy). The system then supplies part of this energy back into the vibration in such a way that it reinforces the motion rather than damping it.

If the energy supplied per cycle equals the energy lost due to damping, the vibration continues at a constant amplitude. If the supplied energy exceeds the losses, the vibration amplitude increases, leading to instability.

Thus, the essential characteristic of self-excited vibration is feedback — the process by which the system amplifies its own oscillation using part of the energy already present.

Mathematical Representation

The general differential equation of self-excited vibration can be written as:

where,

• m = mass of the vibrating system (kg)
• c(x, dx/dt) = damping coefficient, which depends on displacement and velocity
• k = stiffness (N/m)
• x = displacement (m)

In normal damped vibrations, the damping term (c) is positive, which means it opposes motion. However, in self-excited vibration, the damping term becomes negative due to feedback effects. This means the system supplies energy instead of absorbing it, which causes the vibration amplitude to increase.

A well-known example is Van der Pol’s equation, which represents self-excited oscillations in electrical and mechanical systems:

where μ is a constant representing the amount of nonlinearity or self-excitation in the system.

Examples of Self-Excited Vibrations

1. Machine Tool Chatter:
   During metal cutting, the interaction between the cutting tool and the workpiece can cause self-excited vibrations known as chatter. The friction between tool and material causes feedback, leading to vibration growth.
2. Aeroelastic Flutter:
   Aircraft wings or turbine blades can experience self-excited vibrations when airflow interacts with their motion, causing energy feedback that sustains oscillation.
3. Singing Telephone or Power Lines:
   Wind flowing past wires or cables can induce self-excited vibrations due to aerodynamic feedback, producing humming or whistling sounds.
4. Hydraulic Systems:
   Valves and fluid lines can exhibit oscillations when fluid flow interacts with moving components, creating feedback that excites vibrations.
5. Musical Instruments:
   Instruments like violins or clarinets produce self-excited vibrations where steady airflow or motion generates continuous oscillation through controlled feedback.

Characteristics of Self-Excited Vibrations

1. Energy Source:
   The energy comes from a constant input (mechanical, electrical, or thermal) and is modified into oscillations by the system itself.
2. Non-Periodic Excitation:
   Unlike forced vibrations, the excitation is not externally periodic but generated internally.
3. Feedback Mechanism:
   The feedback between system elements transforms steady input energy into oscillatory motion.
4. Amplitude Growth:
   The vibration amplitude increases when the supplied energy exceeds damping losses, leading to instability.
5. Nonlinear Behavior:
   Self-excited vibrations often involve nonlinear equations and complex motion patterns.

Types of Self-Excited Vibrations

1. Stable Self-Excited Vibration:
   In this case, the system reaches a steady amplitude when energy input equals energy dissipation. The vibration continues with constant amplitude.
   Example: Musical instrument vibrations or oscillators.
2. Unstable Self-Excited Vibration:
   Here, the energy input exceeds the damping losses, leading to a continuous increase in vibration amplitude. Eventually, the system becomes unstable and may fail.
   Example: Flutter in aircraft wings or chatter in machining operations.

Causes of Self-Excited Vibrations

• Frictional forces: Uneven friction causes feedback leading to vibrations (e.g., tool chatter).
• Aerodynamic forces: Interaction of air with structures like wings or wires.
• Fluid flow feedback: Hydraulic systems and pipes may experience vibrations due to pressure fluctuations.
• Thermal feedback: Expansion and contraction due to temperature variation can cause oscillations.
• Electromechanical interaction: Electric currents interacting with mechanical motion in devices like motors or generators.

Advantages and Disadvantages

Advantages:

• Useful in devices where continuous oscillation is needed (oscillators, musical instruments).
• Helps in studying system stability and energy feedback behavior.

Disadvantages:

• Can cause severe damage due to excessive vibration amplitude.
• Reduces accuracy and surface finish in machining.
• May lead to fatigue or structural failure in rotating and aerodynamic systems.

Methods to Control Self-Excited Vibrations

1. Increasing Damping:
   Adding damping elements (like shock absorbers) helps absorb extra energy and reduce vibration amplitude.
2. Reducing Feedback:
   Design modifications that limit feedback loops can prevent the conversion of steady energy into oscillations.
3. Stiffening Components:
   Increasing stiffness reduces deflection and vibration energy storage in flexible systems.
4. Proper System Design:
   Avoiding critical speeds and improving dynamic balance minimize the possibility of self-excitation.
5. Active Control Systems:
   Modern systems use sensors and actuators to detect and suppress unwanted vibrations automatically.

Conclusion

Self-excited vibration is a type of vibration where the system itself provides the energy to sustain oscillations through internal feedback mechanisms. Unlike forced vibration, there is no external periodic force; instead, the energy from a constant source is converted into vibratory motion. Such vibrations are common in mechanical, aerodynamic, and fluid systems. While they are useful in some applications like oscillators, they are mostly undesirable because they can cause instability and damage. Proper damping, design improvement, and control systems are essential to prevent harmful self-excited vibrations.