What is the theory of Non linear and Random Vibrations?

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.

What is the theory of Non linear and Random Vibrations

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.
    • 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:

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


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