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

## Other Details of Non linear and Random Vibrations:

## 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.

- In Mechanical Engineering

- 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.