Stress and Strain Limits on the Attainable Velocity in Mechanical Vibration

Abstract

The maximum peak velocity which can be developed at the free end of a slender rod driven at resonance in a normal mode of longitudinal vibration is given by v0 = c0 Sxx, where c0 is the Young's modulus speed of sound (E/ρ)12 and Sxx is the limiting value of extensional strain for the rod material. In a similar way, the ratio of allowable stress to the maximum peak velocity is given by Txx/v0 = ρc0, where the characteristic specific acoustic impedance plays in this case the role of a transfer impedance relating the stress at a node to the velocity at an antinode. Similar expressions, modified only by numerical factors which range from 12 to 2, describe the relations between the maximum allowable stress or strain and the normal component of velocity at the antinodes of displacement for thin bars or plates vibrating in flexure.