Abstract
The principal anatomical structures in the cicada that radiate sound are two platelets referred to as tymbals, which vibrate after being struck by ribs that have undergone buckling. This research effort investigates the sound of these ribbed finite plates connected to a parallel surface by a nonlinear spring. When individual ribs are placed under compression, the linearized version of the model predicts eventual exponential growth of the transverse displacement when the compressional load exceeds the buckling load. The nonlinear spring, however, stops this growth and a subsequent oscillation ensues. The actual anatomy of the cicada is more complicated than this basic model. However, this simplified mathematical explanation is given as a means to describe sound emitted in a sequence of closely spaced tone bursts. The energy from these sound impulses are stored in tensed muscles and released via buckling into the kinetic energy of ribs, which is similar to striking a drum. The tymbals “ring” at a frequency controlled by the mass of the tymbals and the air cavity “spring” within the abdomen. This ringing vibration affects the amplitude, cycles within each pulse, and the damping of the tymbal function to generate the efficiency of the cicada sound radiation.
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