Resonance? The original Tacoma Narrow Bridge, at all stages of its short life, was very active in the wind. Its nickname of Galloping Gertie was earned from its vertical motions in even very modest winds. Its collapse on November 7, 1940 is said to be related to an aerodynamically induced condition of self-excitation or “negative damping.” This paperemphasizes the fact that physically as well as mathematically, forced resonance and self-excitation are fundamentally different phenomena.
 
(Click image for 1.8Mb movie.)
An example of a wave with both longitudinal and transverse motion may be found in solids as a Rayleigh surface wave. The particles in a solid, through which a Rayleigh surface wave passes, move in elliptical paths, with the major axis of the ellipse perpendicular to the surface of the solid. As the depth into the solid increases the “width” of the elliptical path decreases. Rayleigh waves are different from water waves in one important way. In a water wave all particles travel in clockwise circles. However, in a Rayleigh surface wave, particles at the surface trace out a counter-clockwise ellipse, while particles at a depth of more than 1/5th of a wavelength trace out clockwise ellispes. This movie shows a Rayleigh wave travelling from left to right along the surface of a solid. Two particles are identified in yellow to illustrate
the counterclockwise-clockwise motion as a function of depth.

Text & movie taken from Professor Dan Russell’s Vibration & Waves Animation webpage. Visit this page for many excellent visualization tools for acoustics and vibration.

  
The (0,3) mode of a circular membrane, shown at right, has three circular nodes, but no diameter nodes. The frequency of the (0,3) mode is 3.598 times
the frequency of the (0,1) mode. Like the (0,1) and (0,2) modes, the (0,3) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,3) mode are rather complicated. This mode is excited when the membrane is struck at the center, and it dies away fairly quickly. As a result, it contributes to the “thump” sound when a drum is hit at the center, but does not contribute much to the musical
pitch of a drum when hit off center.

Text & movie taken from Professor Dan Russell’s Vibration & Waves Animation webpage. Visit this page for many excellent visualization tools for acoustics and vibration.

  
 More to come…