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Research Papers

Complex Modal Analysis of the Swimming Motion of a Whiting

[+] Author and Article Information
B. F. Feeny

Dynamics and Vibrations Research Laboratory,
Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: feeny@egr.msu.edu

A. K. Feeny

Department of Biomedical Engineering,
Johns Hopkins University,
Baltimore, MD 21218
e-mail: afeeny1@jhu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics Manuscript received October 24, 2011; final manuscript received September 8, 2012; published online February 25, 2013. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 135(2), 021004 (Feb 25, 2013) (8 pages) Paper No: VIB-11-1252; doi: 10.1115/1.4023056 History: Received October 24, 2011; Revised September 08, 2012

The kinematics of the transverse motion of a swimming fish are analyzed using a complex modal decomposition. Cinematographic images of a swimming whiting (Gadus merlangus) were obtained from the work of Sir James Gray (1933, “Studies in Animal Locomotion III. The Propulsive Mechanism of the Whiting (Gadus merlangus),” J. Exp. Biol., 10, pp. 391–402). The position of the midline for each image was determined and used to produce planar positions of virtual markers distributed along the midline of the fish. Transverse deflections of each virtual marker were then used for the complex orthogonal decomposition of modes. This method was applied to images of a whiting before and after amputation in a Newtonian frame of reference and an “anterior-body-fixed” frame as well. The fish motions were well represented by a single complex mode, which was then used as a modal filter. The extracted mode and modal coordinate were used to estimate the frequency, wavelength, and wave speed. The amputated fish was compared to the nonamputated fish, and the amount of traveling in the respective waveforms was quantified. The dominant complex mode shape and the estimated modal frequency were employed to reanimate the fish motion.

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Figures

Grahic Jump Location
Fig. 1

An illustration of the whiting

Grahic Jump Location
Fig. 2

A sample of midlines superposed onto fish images obtained from Gray [2]. (a) Prior to tail amputation. (b) After amputation.

Grahic Jump Location
Fig. 3

Intact fish transverse displacements. The top shows snapshots of all the midlines of the intact whiting through one full cycle (from two half cycles). The bottom shows time traces of the odd virtual markers. Column (a), after image processing, and (b) using only the dominant mode acquired after COD.

Grahic Jump Location
Fig. 4

(a) Snapshots of all the midlines of the amputated whiting through one full cycle (from two half cycles) after image processing. (b) Representations of the midlines using only the dominant mode acquired after COD.

Grahic Jump Location
Fig. 5

(a) Represents the dominant COM of the intact whiting in the complex plane. The endpoint close to the origin represents the head. (b) The real (solid line) and imaginary (dashed line) parts of the dominant COM, plotted against the fish midline.

Grahic Jump Location
Fig. 6

(a) The modal coordinate of the intact fish in the complex plane. (b) The real part of the modal coordinate versus time.

Grahic Jump Location
Fig. 7

(a) The dominant COM of the amputated whiting in the complex plane. The lower endpoint represents the head. (b) The real and imaginary parts of the dominant COM plotted against the fish midline.

Grahic Jump Location
Fig. 8

(a) The modal coordinate of the amputated fish in the complex plane. (b) The real part of the modal coordinate versus time.

Grahic Jump Location
Fig. 9

The separated traveling and standing parts of the fish motion. The superposed snapshots of (a) the traveling part of the primary modal motion of the intact whiting, and (b) the standing part of the primary modal motion.

Grahic Jump Location
Fig. 10

The local wavelength of the traveling part of the primary mode at each point along the midline of (a) the intact fish, (b) the amputated fish

Grahic Jump Location
Fig. 11

The separated traveling and standing parts of the amputated fish motion. (a) The reanimated traveling part of the primary modal motion, and (b) the reanimated standing part of the primary modal motion.

Grahic Jump Location
Fig. 12

The real and imaginary parts of the primary mode of the deflections transverse to the anterior-body-fixed axis. (a) Intact fish, (b) amputated fish.

Grahic Jump Location
Fig. 13

The single mode transverse deflections in a anterior-body-fixed frame. The top figures are superposed snapshots, and the bottom figures are odd marker histories, for columns (a) the intact fish, (b) the amputated fish.

Grahic Jump Location
Fig. 14

The single mode reanimated motion, based on a complex exponential modulation of the extracted dominant mode at the frequency defined by the mean whirl rate of the complex modal coordinate. (a) Intact fish, (b) amputated fish.

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