Hambric Vibroacoustic Demonstrators

This demonstrator shows the bending/flexural wave speed in a flat panel along with the waves radiated by the panel into an adjacent fluid medium.

Bending in a beam or plate is a mix of extensional and shear behavior. The 'fibers' on the top and bottom of a panel cross section bear most of the extensional strain caused by flexure. The center or core of the panel bear most of the transverse shear strain. The net effect is a flexural wave whose wavespeed varies with frequency. This phenomenon is called dispersion. At low frequencies and for thin panels, the shear strain effect is negligible, as is the rotary inertia, and a simple bending wave speed may be calculated based solely on flexural rigidity and panel mass/area. At higher frequencies and for thick panels the shear and rotary inertia effectively slow flexural waves, leading to a much more complicated bending wave speed calculation. At very high frequencies, flexural waves become pure shear waves, and non-dispersive.

Since bending wave speeds are dispersive (increase with frequency) there is a specific frequency where they coincide with acoustic wave speeds, called the coincidence, or critical frequency. Below coincidence, bending waves in infinite panels radiate no far-field sound. The only pressure waves in the adjacent acoustic medium are evanescent, and decay quickly with distance. At and above coincidence, however, the bending and acoustic waves align at a specific trace angle, and sound radiates perfectly to the far-field.

Adjust the panel material and/or panel thickness to change the flexural wavespeeds, and therefore the critical frequencies (watch the title to view the critical frequencies calculated using thin and thick plate theory). Also watch the acoustic waves change in orientation as the panel wavespeed changes. You can also adjust the frequency for the acoustic wave plot, as well as animate the waves. Adjust the frequency close to the critical frequency to watch the acoustic waves shift from evanescent to propagating. At coincidence, the acoustic and structural wave speeds (and wavelengths) are identical, and the radiating waves are aligned perfectly with those of the structure. Above coincidence, the trace matching of the different wavelengths leads to increasing radiation angles (check the title above the plots for the radiation angle). Finally, critical frequencies are much higher for panels in water - change the acoustic medium between air and water to see the effect.