Vibration phenomena that might be modeled well using linear vibration theory include small amplitude vibrations of long slender objects like long bridges,aeroplane wings,helicopter blades etc.In this article,I am going to explain about what is the theory of Non linear and Random Vibrations in detailed manner.

## Applications of Non linear and Random Vibrations:

- Small rocking motions of ships in calm waters
- The simplest whirling motions of flexible shafts
- Interactions between bridges and foundations
- Interactions between wings/blades and air
- Interactions between ships and waves
- Interactions between shafts and bearings and so on are all nonlinear.

### Nonlinear systems can display behaviors that linear systems cannot. These include:

- Multiple steady state solutions in which some are stable and some are unstable in response to the same inputs.
- Jump phenomena, involving discontinuous and significant changes in the response of the system as some forcing parameter is slowly varied.
- Response at frequencies other than the forcing frequency.
- Internal resonances, involving different parts of the system vibrating at different frequencies, all with steady amplitudes (the frequencies are usually in rational ratios, such as 1:2, 1:3, 3:5, etc.),
- Self sustained oscillations in the absence of explicit external periodic forcing.
- Complex, irregular motions that are extremely sensitive to initial conditions.

#### Random Vibrations:

- In Mechanical Engineering
**random vibration**is a motion which is non-deterministic,meaning that future behavior cannot be precisely predicted. - The randomness is a characteristic of the excitation or input, not the modeshapes or natural frequencies.
- Some common examples include an automobile riding on a rough road, wave height on the water or the load induced on an airplane wing during flight.
- Structural response to random vibration is usually treated using statistical or probabilistic approaches.
- In mathematical terms, random vibration is characterized as a stationary process.

** You can also read about:**

- What is Damped Free Vibrations?
- What is the theory of vibration Isolation and transimissibility?
- What is the theory of vibrations due to unbalance?

The detailed information about Theory of Non -Linear and Random Vibrations is presented briefly in the PPT shown below.