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Research Papers

Dynamics of Cricket Sound Production

[+] Author and Article Information
Vamsy Godthi

Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: godthivamsy@gmail.com

Rudra Pratap

Professor
Department of Mechanical Engineering,
Indian Institute of Science
Centre for Nano Science and Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: pratap.mems@gmail.com

Although a FE model of the resonant structure in tree crickets is used by Mhatre et al. [1] to explain how the insects vary their carrier frequency, their analysis was to extract the ratio of the frequency and amplitude of the first two natural frequencies relative to the wing shape.

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 5, 2014; final manuscript received March 13, 2015; published online April 24, 2015. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 137(4), 041019 (Aug 01, 2015) (8 pages) Paper No: VIB-14-1284; doi: 10.1115/1.4030090 History: Received August 05, 2014; Revised March 13, 2015; Online April 24, 2015

The clever designs of natural transducers are a great source of inspiration for man-made systems. At small length scales, there are many transducers in nature that we are now beginning to understand and learn from. Here, we present an example of such a transducer that is used by field crickets to produce their characteristic song. This transducer uses two distinct components—a file of discrete teeth and a plectrum that engages intermittently to produce a series of impulses forming the loading, and an approximately triangular membrane, called the harp, that acts as a resonator and vibrates in response to the impulse-train loading. The file-and-plectrum act as a frequency multiplier taking the low wing beat frequency as the input and converting it into an impulse-train of sufficiently high frequency close to the resonant frequency of the harp. The forced vibration response results in beats producing the characteristic sound of the cricket song. With careful measurements of the harp geometry and experimental measurements of its mechanical properties (Young's modulus determined from nanoindentation tests), we construct a finite element (FE) model of the harp and carry out modal analysis to determine its natural frequency. We fine tune the model with appropriate elastic boundary conditions to match the natural frequency of the harp of a particular species—Gryllus bimaculatus. We model impulsive loading based on a loading scheme reported in literature and predict the transient response of the harp. We show that the harp indeed produces beats and its frequency content matches closely that of the recorded song. Subsequently, we use our FE model to show that the natural design is quite robust to perturbations in the file. The characteristic song frequency produced is unaffected by variations in the spacing of file-teeth and even by larger gaps. Based on the understanding of how this natural transducer works, one can design and fabricate efficient microscale acoustic devices such as microelectromechanical systems (MEMS) loudspeakers.

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References

Figures

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Fig. 1

Image of the right wing of a field cricket—G. bimaculatus

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Fig. 2

System diagram of the cricket sound production mechanism. The frequency multiplier converts the low frequency wing closure to a high frequency impulse train which causes the harp (a membrane) to vibrate at resonance and produce the characteristic cricket song.

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Fig. 3

The response of the equivalent SDOF system when subjected to a series of impulse loads

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Fig. 4

The two-dimensional (2D) FE model of G. bimaculatus harp: (a) boundary coordinates obtained from image processed data of an actual wing and (b) FE model meshed using SHELL281 elements with the inset showing a close-up of the mesh

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Fig. 5

The first mode shape and natural frequency of G. bimaculatus harp model

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Fig. 6

Variation in the fundamental frequency with the change in the out-of-plane stiffness of the boundary: (a) harp model with springs, (b) sides with equal springs and no constraint on the file edge, (c) sides with different springs and no constraint on the file edge, and (d) sides with different springs and 1000 N/m spring on the file edge

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Fig. 7

Data from one of the nanoindentations performed on the harp: (a) load versus time and (b) load versus displacement

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Fig. 8

The relative movement between the plectrum and a file tooth during one excitation period Tf

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Fig. 9

The transverse displacement of the node at the centroid of the 2D harp model of G. bimaculatus: (a) time response, (b) recreated chirps, and (c) fast Fourier transform (FFT) of the response (truncated since there is no significant amplitude beyond 6000 Hz)

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Fig. 10

Analysis of the recorded song of G. bimaculatus: (a) a pulse of the song, (b) recorded chirps, and (c) FFT of the song (truncated since there is no significant amplitude beyond 6000 Hz)

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Fig. 11

The vibrational shape of the harp as: (a) plectrum catches z = −A, (b) z = −A/2, (c) z = A/2, and (d) plectrum releases z = A

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Fig. 12

The response of the harp with modified actuation mechanism: (a) some teeth missing and (b) random tooth spacing

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Fig. 13

FFT of the response of the harp with modified actuation mechanism: (a) some teeth missing and (b) random tooth spacing

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Fig. 14

Cross section image of the harp taken using SEM

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Fig. 15

Improved FE model of the harp: (a) 3D FE model and (b) the first mode shape

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Fig. 16

Out-of-plane deflection of the 2D and 3D harp models subjected to the same pressure load: (a) 2D model and (b) 3D model

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