Some recently obtained results in classical vibration and acoustics: coexistence of traveling and standing waves in a one-dimensional non-dispersive continuum

Antoine Blanchard; Yongxiong Xiao; D. Michael McFarland; Alexander F. Vakakis; Lawrence A. Bergman

doi:10.1117/12.2264418

10 April 2017 Some recently obtained results in classical vibration and acoustics: coexistence of traveling and standing waves in a one-dimensional non-dispersive continuum

Antoine Blanchard, Yongxiong Xiao, D. Michael McFarland, Alexander F. Vakakis, Lawrence A. Bergman

Author Affiliations +

Proceedings Volume 10172, A Tribute Conference Honoring Daniel Inman; 1017203 (2017) https://doi.org/10.1117/12.2264418
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2017, Portland, Oregon, United States

Abstract

The problem of free vibration of a linear uniform axial bar, fixed at one end and connected to ground at the other end through a linear viscous damper has been carefully studied by several researchers. It’s known that, for a fixed set of bar parameters and the special case of the damping coefficient λ equal to EA / c (c being the speed of sound in the continuum), no eigenvalues exist. Thus, energy imparted to the bar via harmonic motion of the fixed support will propagate through the bar and be fully dissipated in the damper, in effect making the bar appear to be semi-infinite. I will show some recent results by the present authors in which this phenomenon has been exploited in several other nondispersive media, the taut string and the circular acoustic duct, incorporating viscoelastic supports or absorbers to produce responses to harmonic motion at one or both boundaries that exhibit complete separation of traveling and standing waves, in effect localizing the vibration over a portion of the domain.

Citation Download Citation

Antoine Blanchard, Yongxiong Xiao, D. Michael McFarland, Alexander F. Vakakis, and Lawrence A. Bergman "Some recently obtained results in classical vibration and acoustics: coexistence of traveling and standing waves in a one-dimensional non-dispersive continuum", Proc. SPIE 10172, A Tribute Conference Honoring Daniel Inman, 1017203 (10 April 2017); https://doi.org/10.1117/12.2264418

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