Hambric Vibroacoustic Demonstrators

Straight beam modes of vibration oscillate with standing wave patterns, where bending waves travel back and forth along the beam, reflecting from the ends to form the seemingly 'standing' wave pattern. In reality, however, there are indeed waves traveling back and forth underneath that pattern. The mode shapes and their frequencies and resonance depend on the (a) length, (b) cross-sectional geometry (in this simple example a rectangle), (c) material properties (Young's Modulus and mass density), and (d) the end boundary conditions (combinations of free, simply supported, and fixed).

In this interactive demo you can adjust all these parameters and visualize the mode shapes and mobilities for several common boundary condition types up to their tenth harmonic. Of course, higher harmonics exist, but they just aren't shown here. You can also animate the mode shapes over a few cycles.

Drive point mobilities are shown in the right plot, along with the mean mobility and approximate upper bound mobility at resonances. Watch the levels and resonance frequencies change as you adjust beam length, thickness, and material properties. You can also change where the drive location is - see the black dot on the mode shape plot and the slider on the lower right. Either move the slider, or just click somewhere on the beam mode shape to move the drive. Try moving the drive location to where the mode shapes peak (the 'antinodes'), and where they go to zero (the 'nodes') and observe the effects on mobility.