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Vibrations

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A vibration is a mechanical oscillation motion around a stable equilibrium position or an average trajectory. The vibration of a system can be free or forced.

According to the type and nature of vibration, and according to the measuring means, it can be measured in amplitude (linear or angular distance), power or rms value with respect to a reference (decibel), frequency (hertz), etc.

Perception of vibrations by living organisms

Many living organisms are sensitive to vibrations through specialized organs or sensors that allow them to communicate, detect congeners, prey or potential predators, especially in water (fish, marine mammals, crustaceans, burrowing molluscs, and other bivalves …) or in the nocturnal environment. Hearing is one of the organs of perception of the vibratory environment, but often the skin and the whole body also contributes to this perception. Their instinct for example causes worms (earthworms) to rise to the surface in the event of repeated ground vibrations, perhaps in response to earthquakes or when approaching one of their burrowing predators such as the mole or badger.

Excitation of a mechanical structure

In industry, we are interested in vibration analysis for two reasons:

  • excessive vibration excitation can lead to damage, such as vibratory fatigue failure, or noise pollution;
  • vibration analysis of a machine can be used to diagnose balancing or shaft alignment problems, as well as bearing or orbit defects.
Modal analysis of a car door
Source https://commons.wikimedia.org/wiki/File:Modal_testing.tif

(Modal analysis of a car door. )

Excessive vibration excitation can be caused by excitation of normal modes (resonant frequencies) of the structure. One or more sources generate vibrations on a specific mode of vibration of the structure, the amplitude of the vibration of the structure is then much greater than the amplitude of the excitation and can thus cause fatigue ruin. The expertise here consists in identifying the vibration modes of the structure.

There are two methods for determining the normal frequencies of a system:

  • use of a vibratory pot for vibratory characterization of the part (determination of resonant frequencies), vibratory fatigue tests, etc.

Vibratory pot characterization is mainly used for sizing or qualifying equipment in the laboratory before use;

  • use of a shock hammer impact for modal analysis of structure, the part being excited successively at several points and the vibration reaction measured using an acceleration sensor (accelerometer, laser vibrometer).

Impact hammer analysis is used for in situ characterization of the structure.

Experimental modal analysis allows to determine the deformations of the structure as a function of frequency.

Measurement of operational deformity in operation (Operational Deflection Shape) makes it possible to determine the actual deformation of the structure in operation.

Modeling calculations of the finite element structure make it possible to evaluate the normal modes of the structure.

The hammer impact excites the structure on all frequencies (up to about 10 kHz) with the same energy. Different tips are available depending on the frequencies to be excited (soft endpiece: low frequencies, hard endpiece: medium frequencies).

Once the normal modes of the structure identified, it is either:

  • to shift the excitation frequency, by modifying the source of vibration;
  • to shift the normal modes of the structure by adding mass or stiffness (the resonance frequency of a simple system being given by the formula f = 1/2π·√(K/M), where f is the resonant frequency of the system, K its stiffness and M its mass.

Modeling then makes it possible to precisely dimension the addition of mass or stiffness on the structure;

  • use a dynamic vibration absorber or stress limiting device;
  • isolate the structure of the source of vibration using a properly dimensioned anti-vibratile elastomer.

Calculations by finite element can be used to calculate the maximum permissible vibration on the structure to avoid the risk of vibratory fatigue failure.

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