For a thick steel plate

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Vibrating bodies, musical and architectural acoustics · Vibrating bodies, musical and architectural acoustics

Bending, Ringing, Breaking and Flowing, Ch Vibrations of rods, beams and plates

Problem

For a

2\,\mathrm{mm}

thick steel plate, thin-plate bending theory is already about

6\,\%

high at a wavelength of ten thicknesses, near

46\,\mathrm{kHz}

, and becomes impossible (predicting a bending-wave speed faster than the Rayleigh wave) at a wavelength of about

3.3h

, near

440\,\mathrm{kHz}

. Estimate the corresponding two frequencies: the onset of a noticeable (

\sim6\,\%

) error, and the point of outright failure, for a steel sheet only

1\,\mathrm{mm}

thick.

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