Vibration is the repetitive oscillatory motion of an object or medium. It is usually unwanted in mechanical systems as it may lead to fatigue failure, instability issues, noise, wear and tear, and energy losses. However, vibration also has useful applications in different scientific fields. Broadly, vibrations can be classified into four main types based on the motion of the vibrating object.
Free Vibration
Free vibration refers to the vibration of an object or system when it is disturbed from its equilibrium position and allowed to vibrate freely. In free vibration, there are no external forces acting on the system once it has been displaced from its equilibrium position. The system will vibrate at one or more of its natural frequencies and the amplitude of oscillations depends on the initial conditions. Examples of free vibration include the oscillations of a simple pendulum, vibrating strings, vibrating beams, etc. Some key points regarding free vibrations:
- The frequency of free vibrations depends only on the properties of the system i.e., mass, stiffness, damping, etc.
- Free vibrations occur when the system oscillates under its own internal restoring forces once disturbed.
- Free vibrations are damped and decay over time if the system has damping or energy losses.
- Multiple modes of free vibrations are possible depending on the geometry and material of the system.
- The lowest natural frequency is called the fundamental or first mode of vibration. Higher frequencies are harmonics.
Free vibrations are studied to determine the natural frequencies and mode shapes of mechanical systems. This helps avoid resonance and design for appropriate dynamic characteristics. Examples where studying free vibration is useful include designing buildings and bridges for earthquake loads, analyzing acoustic properties, finding modal shapes in structural analysis, etc.
Forced Vibration
Forced vibration refers to the oscillation of a system due to an external force or excitation. The external force repeatedly disturbs or displaces the system from its equilibrium position. This perpetuates the oscillations as long as the external force is active. Some examples of forced vibrations include the shaking of a washing machine, vibrations induced by unbalanced rotors, vibrations from earthquake ground motion, etc. Key points regarding forced vibrations:
- Forced vibrations occur due to an external force acting on the system.
- The frequency of forced vibrations is equal to the frequency of the excitation force.
- The amplitude of vibrations depends on the frequency and magnitude of the excitation force.
- Resonance occurs when the forced vibration frequency matches the natural frequency of the system, resulting in large vibrations.
- Forced vibrations can be steady-state or transient depending on the nature of the excitation.
Forced vibrations analysis helps identify resonant frequencies to avoid during design and operations. Anti-vibration mounts, vibration isolators, and dampers help mitigate the harmful effects of forced vibrations.
Damped Vibration
Damped vibration refers to the oscillation of a system in which energy is dissipated over time due to damping. Damping reduces the amplitude of vibrations caused by either free or forced excitation. It occurs due to the conversion of mechanical energy into thermal energy. Various mechanisms account for damping in materials and structures:
- Material damping – Energy dissipation within the material due to thermal losses.
- Frictional damping – Frictional sliding and deformation between components and joints.
- Fluid damping – Fluid viscosity and turbulence effects.
- Acoustic radiation – Sound wave transmission into surrounding medium.
The degree of damping dictates the decay rate and duration of vibrations. Underdamped systems experience oscillatory decay. Critically damped systems return to equilibrium rapidly without oscillation. Overdamped systems slowly return to equilibrium without oscillation. Key aspects regarding damped vibrations:
- Damping reduces vibration amplitudes and allows the system to achieve steady-state faster.
- Damping modifies the dynamic behavior and stability characteristics of the system.
- Damping mechanisms dissipate unwanted vibration energy and heat.
- Mathematical modeling of damping is important for accurate analysis of real-world vibrations.
- Proper damping design is crucial for vibration isolation and noise reduction.
Examples where damped vibration analysis is important include vehicle suspension systems, vibration isolation tables, door closers, turbine blades, and earthquake proof buildings.
Self-Excited Vibration
Self-excited vibration refers to sustained oscillations occurring due to some positive feedback within the system rather than direct external excitation. These vibrations persist once triggered and sufficient energy is available in the system. Some common causes of self-excited vibration include:
- Friction or Stick-Slip – Frictional sliding leading to oscillation during stick and slip cycles.
- Flutter – Interaction between aerodynamic forces and system natural modes.
- Galloping – Wind forces inducing negative damping at some velocities.
- Aeroelastic instabilities – Coupling between inertial, elastic and aerodynamic forces.
- Flow instabilities – Fluid flow feedback causing oscillations.
Self-excited vibrations can be destructive as the amplitudes are often uncontrolled. These vibrations may limit operating speeds in rotors and other machinery. Some ways to avoid harmful self-excited vibrations:
- Changing system parameters to eliminate negative damping.
- Altering system geometry and stiffness characteristics.
- Adding damping using friction dampers or viscoelastic materials.
- Isolating the system from unwanted feedback forces.
- Active vibration control methods.
Self-excited vibrations form an interesting study area in non-linear dynamics. Their analysis helps troubleshoot problems like brake squeals, steam whistle, aircraft wing flutter, and machine tool chatter.
Conclusion
The four main types of mechanical vibration include:
- Free Vibration – Oscillations due to system’s internal restoring forces.
- Forced Vibration – Oscillations due to external excitation forces.
- Damped Vibration – Oscillations with energy dissipation due to damping.
- Self-Excited Vibration – Self-perpetuating oscillations sustained by system feedback.
Understanding the characteristics of each vibration type is important for dynamic analysis and troubleshooting problems like resonance, fatigue, noise, and instability in mechanical systems. Proper vibration control techniques like isolation, absorption, damping, and tuning operating speeds help mitigate harmful vibrational effects and failures in real-world applications across aerospace, automotive, construction, power, and process industries.