On the study of nonlocal effect on the internal resonances of axial oscillation of nanorods

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

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Multiple internal resonances in nonlinear vibrations of rotating thin-walled cylindrical shells

Journal of Sound and Vibration ◽

10.1016/j.jsv.2021.116313 ◽

2021 ◽

pp. 116313

Author(s):

Shupeng Sun ◽

Lun Liu

Keyword(s):

Nonlinear Vibrations ◽

Cylindrical Shells ◽

Internal Resonances ◽

Thin Walled

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Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

Nature Communications ◽

10.1038/s41467-021-21334-w ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 1

Author(s):

Ata Keşkekler ◽

Oriel Shoshani ◽

Martin Lee ◽

Herre S. J. van der Zant ◽

Peter G. Steeneken ◽

...

Keyword(s):

Parametric Resonance ◽

Internal Resonance ◽

Microscopic Theory ◽

Fold Increase ◽

Nonlinear Damping ◽

Supporting Evidence ◽

Nonlinear Dissipation ◽

Modal Interactions ◽

Solid State Physics ◽

Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

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