Classification of vibration

We can classify vibrations in several ways.

First classification: Free and Forced Vibrations

Free vibrations. If we have a system that is left to vibrate or oscillate around equilibrium position after the initial disturbance these vibrations are called free vibrations. That means that no external force acts on the system. The oscillation of a simple pendulum or system with mass m and spring with stiffness k (if we neglect the friction force) are good examples of free vibration.

Forced vibrations – are vibrations of the system that is subjected to an external force, the resulting vibration is known as forced vibration. The oscillation that arises in machines such as diesel engines is an example of forced vibrations.

If the frequency of the external force is equal with the natural frequency of the system, a condition known as resonance occurs, and the system undergoes dangerously large oscillations.

Second Classification: Undamped and Damped Vibration

Undamped vibration – occurs in a system where no energy is lost or dissipated in friction or other resistance during oscillation.

Damped vibration- occurs in a system where energy due to the friction or damper is lost.

In some physical systems, the amount of damping is so small that it can be disregarded for most engineering purposes.

Third Classification: Linear and Nonlinear Vibrations

If all components of the system (spring, damper and mass) behave linearly then we can say that the systems resulting vibrations are linear. On the other hand if some of the components of the system behave nonlinearly than the resulting vibrations are nonlinear.

Many mechanical systems are nonlinear but we simplify them to get approximated linear system. The reason for that is because nonlinear analysis of vibration demands understanding and knowing complicated methods which are used to determine the nonlinear vibrations. Approximated results that we get from linear analysis are in some cases acceptable and can be used to get general idea of system behavior.

As I mentioned in the previous post even the simple pendulum system has a some nonlinear components. Now if we include these nonlinear components into analysis like aerodynamic drag than the system would become nonlinear. That means that we need to apply one of many nonlinear methods to solve this nonlinear system. To analyze the pendulum linearly we simply neglect the nonlinear components and by doing so we can derive the linear differential equation which describes the vibrations of pendulum.

Fourth Classification: Deterministic and Random Vibration

Deterministic vibrations – If the value or magnitude of the excitation acting on a vibratory system is known at any given time, the excitation is called deterministic.

Nondeterministic or random vibration occurs when we cannot predict excitation at a given time. It is possible in these cases to estimate the averages such as the mean and mean square values of excitations. Example of random excitations are wind velocity, road roughness etc.