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<p>The present work investigates the vibrations of the traditional singing bowl (SB), analyzing its damped and undamped beat sounds through spectral, nonlinear time series, recurrence, and complex network analyses. When the spectral analyses reveal the generation of 855 and 856&#xa0;Hz as the reason for the beat sound in damped vibrations in the SB, 854&#xa0;Hz and 857&#xa0;Hz account for the beat sound in undamped oscillations. Phase space reconstruction, Lyapunov exponent and sample entropy, recurrence plot, and recurrence network analyses reveal intricate dynamics of SB. The 3D phase portrait of damped vibrations demonstrates initial chaos and energy dissipation, whereas forced vibrations display an elliptical trajectory, indicative of beats and minimal phase trajectory divergence. As revealed in the recurrence plot and network analyses, lower entropy and Lyapunov exponent values of undamped oscillations from the time series analysis&#xa0;also&#xa0;denote a more regular system. The comprehensive analysis of SB vibrations paves the way to explore its applications as digital drugs.</p>

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Comprehensive analysis of singing bowl vibrations: nonlinear time series, network, and spectral approaches

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • M. S. Swapna,
  • S. Sankararaman

摘要

The present work investigates the vibrations of the traditional singing bowl (SB), analyzing its damped and undamped beat sounds through spectral, nonlinear time series, recurrence, and complex network analyses. When the spectral analyses reveal the generation of 855 and 856 Hz as the reason for the beat sound in damped vibrations in the SB, 854 Hz and 857 Hz account for the beat sound in undamped oscillations. Phase space reconstruction, Lyapunov exponent and sample entropy, recurrence plot, and recurrence network analyses reveal intricate dynamics of SB. The 3D phase portrait of damped vibrations demonstrates initial chaos and energy dissipation, whereas forced vibrations display an elliptical trajectory, indicative of beats and minimal phase trajectory divergence. As revealed in the recurrence plot and network analyses, lower entropy and Lyapunov exponent values of undamped oscillations from the time series analysis also denote a more regular system. The comprehensive analysis of SB vibrations paves the way to explore its applications as digital drugs.