by Floriane Dian

(Cranfield, UK)

**Original Text: **

ANALYSIS OF VIBRATIONS

It is interesting to know the characteristics of the vibration source (frequencies, acceleration, amplitude) and also how much power is contained in it.

If we assume that the vibrations of the engine are constant over time and occur at only one frequency (harmonic motion), the energy of the system would be conservative i.e. the sum of potential and kinetic energy is constant. The kinetic energy is maximal when the velocity is at maximum (at zero displacement) and the potential energy is maximal when the displacement is maximal (at zero velocity). There is an exchange between kinetic and potential energy, the total energy remaining constant and equal to the maximum kinetic energy during all the period of vibration

As previously mentioned, the engine vibrations are not harmonic.

The successful repeatability test reveals that the vibrations are periodic (so there is no dissipation of energy, energy is probably constant). They have several frequencies and occur in the three directions. Moreover, as said previously, the engine is not a rigid block, the parts move relative to one another and it is impossible to know the mass of each part moving.

The calculation of the energy content in the vibrations is therefore very complex.

Nevertheless, a global data of the energy contained in the vibration is not the more relevant data because it does not reveal the distribution of levels according to frequency, nevertheless very important for system.

From the theory concerning the harmonic vibration we know that the power contained in vibrations is proportional to the square of the acceleration and inversely proportional to the frequency. It indicates that more power is contained in low frequency and high acceleration.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~**Revised Text: **

It is interesting to know the characteristics of the vibration source (frequencies, acceleration, amplitude) and also how much power is contained in it.

If we assume that the vibrations of the engine are constant over time, and occur at only one frequency (harmonic motion), the energy of the system would be conservative, i.e. the sum of potential and kinetic energy is constant.

The kinetic energy is maximal when the velocity is at maximum (at zero displacement) and the potential energy is maximal when the displacement is maximal (at zero velocity). There is an exchange between kinetic and potential energy, the total energy remains constant and equal to the maximum kinetic energy during the entire period of vibration.

As previously mentioned, the engine vibrations are not harmonic.

The successful repeatability test reveals that the vibrations are periodic (there is no dissipation of energy, which is probably constant). They have several frequencies and occur in the three directions. Moreover, as previously, the engine is not a rigid block. The parts move relative to one another and it is impossible to know the mass of each part moving. The calculation of the energy content in the vibrations is therefore very complex.

The global data of the energy contained in the vibration is not the most relevant data because it does not reveal the distribution of levels according to frequency, nevertheless it is very important for the system.

From the theory concerning the harmonic vibration, we know that the power contained in vibrations is proportional to the square of the acceleration and inversely proportional to the frequency. This indicates that more power is contained in low frequency and high acceleration. **Editor:**

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