Conceptual design of bond graphs as the transfer of energy between two elements.
Schematic and bond graph representations of (A) a simple mass-spring-damper system in the mechanical domain and (B) flow into a fluid capacitance and through a narrow pipe in the pneumatic domain.
Examples of two anuran calls. Oscillogram (A) and spectrogram (B) of the pulsed call of the American toad (Bufo americanus). Only the first 500 ms of the call is shown. Oscillogram (C) and spectrogram (D) of the amplitude and frequency modulated “whine-chuck” call of the túngara frog (Physalaemus pustulosus). Note the subharmonics present near the end of the whine. The chuck is not present in all calls.
Vocal system of a generalized anuran. Lu = lungs, BP = bronchial passages, LxP = posterior laryngeal chamber, Cr = cricoid cartilage, VF =vocal folds with fibrous masses, LxA = anterior laryngeal chamber, AC=arytenoid cartilages, BC = buccal cavity, VSA = vocal sac apertures, VS = vocal sac.
Bond graph model of the anuran vocal system. All system components that are common among anuran taxa are included. Lu =lungs, BP = bronchial passages, LxP = posterior laryngeal chamber, VF = vocal folds, LxA = anterior laryngeal chamber, AC = arytenoid cartilages, BC = buccal cavity, VSA = vocal sac apertures, VS = vocal sac. Bilateral symmetry is indicated in gray.
Bond graph model of the anuran sound source. Only the top half of the bond graph is modeled, assuming bilateral symmetry as shown in gray. Indicated efforts (P = pressure, F = force) and flows (Q = volume flow rate, v = velocity) are discussed in the text.
Output for the first 4 ms of vocal fold model simulation. Pressure in the posterior laryngeal chamber (A), displacement of the vocal folds from the median of the larynx (B), and rate of flow through the vocal fold aperture (C).
(Color online) Rate of flow through the vocal folds (solid line) as a function of pressure in the posterior laryngeal chamber (dotted line) and vocal fold displacement (dashed line). Superimposed from model output presented in Fig. 7 .
Frequency of sustained oscillations in the vocal fold model simulation. FFT of vocal fold vibration (A) and volume flow through the larynx (B).
Sensitivity of model output to changes in flow from the lungs, posterior laryngeal chamber volume, vocal fold mass, and vocal fold compliance. Maximum pressure in the posterior laryngeal chamber (A), maximum vocal fold displacement (B), and fundamental frequency of vocal fold oscillation (C). Reference lines indicate model output at parameter values listed in Table III .
Energy and power variables for bond graph modeling in the mechanical and pneumatic domains. Symbols and units indicated follow Karnopp et al. (2006) and are those used in the remainder of the paper.
Summary of bond graph elements.
Model parameters and constants for simulation of the anuran vocal folds.
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