Linearity of vibratory phenomena

Even intense vibrations only involve small displacements, and the higher the frequency, the smaller the displacement: a vibration of 1 "g" (g being the acceleration of gravity), i.e. 10 m · s ^–2 RMS (root mean square RMS : root mean square), which is already very significant, corresponds at 10 Hz to a peak amplitude of 4 mm, but at 100 Hz the peak amplitude is only 40 μm, and 0.4 μm at 1 kHz: this is well below the elasticity limits of common materials.

So, in most cases, it's legitimate to postulate that deformation is proportional to stress at all points, or, more simply, that the vibratory response of the structure is exactly proportional to the alternating forces exerted. This allows us to postulate the linearity of the vibro-acoustic response of structures in almost all practical situations.

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