Insects have evolved a great diversity of sound-producing mechanisms largely attributable to their hardened exoskeleton, which can be rubbed, vibrated or tapped against different substrates to produce acoustic signals. However, sound production by forced air, while common in vertebrates, is poorly understood in insects. We report on a caterpillar that 'vocalizes' by forcing air into and out of its gut. When disturbed, larvae of the Nessus sphinx hawkmoth (Sphingidae: ) produce sound trains comprising a stereotyped pattern of long (370 ms) followed by multiple short-duration (23 ms) units. Sounds are emitted from the oral cavity, as confirmed by close-up videos and comparing sound amplitudes at different body regions. Numerical models using measurements of the caterpillar foregut were constructed to test hypotheses explaining sound production. We propose that sound is generated by ring vortices created as air flows through the orifice between two foregut chambers (crop and oesophagus), a mechanism analogous to a whistling kettle. As air flows past the orifice, certain sound frequencies are amplified by a Helmholtz resonator effect of the oesophagus chamber. Long sound units occur during inflation, while short sound units occur during deflation. Several other insects have been reported to produce sounds by forced air, but the aeroacoustic mechanisms of such sounds remain elusive. Our results provide evidence for this mechanism by showing that caterpillars employ mechanisms similar to rocket engines to produce sounds.
This study focuses on using a dynamic mechanical analyzer (DMA) for obtaining frequency domain data suitable for constructing an accurate Prony series for a viscoelastic material. Polymethyl methacrylate (PMMA) specimens were used in each experiment, following the ASTM D4000 and ASTM D5023 standards. The experiments were completed using a frequency range of 1 to 100 Hz at multiple temperatures to capture the long‐term behavior via time–temperature superposition. Prony series were fit to the data from these experiments, and used to establish the time domain viscoelastic modulus of PMMA. The effect of the fitting function, material soak time, noise, and reference temperature selection were each investigated for their effect on the Prony series. The raw data may be processed via four paths, which are then compared for statistical error. The most accurate path resulted in a cumulative error of 2.1% for the storage modulus and 26% for the loss modulus. The impact of these errors on the tip displacement of a reference cantilever beam subject to axial loading for 15 years is a variation of over 25%.
Divergence and flutter of lifting surfaces obeying fractional derivative (FD) viscoelastic material constitutive relations under separate fractional derivative servo-controls are analytically investigated. The analytical and computational complexities of FD formulations are examined and compared to Prony series formulations, which are the equivalent of integer derivative viscoelastic characterizations. An approximate formulation is offered that facilitates the Fourier transform but not the evaluation of the convolution integrals. Stability in the form flutter and torsional divergence of a two DOF system is investigated in the Laplace transform space by modified Nyquist plots. Illustrative examples demonstrate that the use of Prony series modulus/compliance characterizations offers a much simpler path to stability determinations in real time than the quest for intersections of curves of flight speeds and frequencies associated with fractional derivative representations.
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