An Expose on Internal Resonance, External Resonance, and Characteristic Modes

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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Hybrid Technique of Fast RCS Computation With Characteristic Modes and AWE

IEEE Antennas and Wireless Propagation Letters ◽

10.1109/lawp.2007.906293 ◽

2007 ◽

Vol 6 ◽

pp. 464-467 ◽

Cited By ~ 3

Author(s):

You-Bao Wang ◽

Y. M. Bo ◽

G. Q. Ji ◽

D. Ben ◽

G. X. Jiang ◽

...

Keyword(s):

Hybrid Technique ◽

Characteristic Modes

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Internal resonance characteristics of hyperelastic thin-walled cylindrical shells composed of Mooney–Rivlin materials

Thin-Walled Structures ◽

10.1016/j.tws.2021.107754 ◽

2021 ◽

Vol 163 ◽

pp. 107754

Author(s):

Wei Zhao ◽

Jing Zhang ◽

Wenzheng Zhang ◽

Xuegang Yuan

Keyword(s):

Internal Resonance ◽

Cylindrical Shells ◽

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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Optimized MIMO Antenna Port Placement using Characteristic Modes

2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting ◽

10.1109/ieeeconf35879.2020.9329674 ◽

2020 ◽

Author(s):

Kyle Thackston ◽

Jori Platt ◽

Daniel F. Sievenpiper

Keyword(s):

Port Placement ◽

Mimo Antenna ◽

Characteristic Modes

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Vibration Characteristics of Hot Rolling Mill Rolls Based on Elastoplastic Hysteretic Deformation

Metals ◽

10.3390/met11060869 ◽

2021 ◽

Vol 11 (6) ◽

pp. 869

Author(s):

Rongrong Peng ◽

Xingzhong Zhang ◽

Peiming Shi

Keyword(s):

Hot Rolling ◽

Internal Resonance ◽

Rolling Mill ◽

Rolling Force ◽

Subharmonic Resonance ◽

Force Model ◽

Maximum Lyapunov Exponent ◽

Vibration System ◽

Hot Rolling Mill ◽

Rolling Mill Vibration

Based on the analysis of the influence of roll vibration on the elastoplastic deformation state of a workpiece in a rolling process, a dynamic rolling force model with the hysteresis effect is established. Taking the rolling parameters of a 1780 mm hot rolling mill as an example, we analyzed the hysteresis between the dynamic rolling force and the roll vibration displacement by varying the rolling speed, roll radius, entry thickness, front tension, back tension, and strip width. Under the effect of the dynamic rolling force and considering the nonlinear effect between the backup and work rolls as well as the structural constraints on the rolling mill, a hysteretic nonlinear vertical vibration model of a four-high hot rolling mill was established. The amplitude-frequency equations corresponding to 1/2 subharmonic resonance and 1:1 internal resonance of the rolling mill rolls were obtained using a multi-scale approximation method. The amplitude-frequency characteristics of the rolling mill vibration system with different parameters were studied through a numerical simulation. The parametric stiffness and nonlinear stiffness corresponding to the dynamic rolling force were found to have a significant influence on the amplitude of the subharmonic resonance system, the bending degree of the vibration curve, and the size of the resonance region. Moreover, with the change in the parametric stiffness, the internal resonance exhibited an evident jump phenomenon. Finally, the chaotic characteristics of the rolling mill vibration system were studied, and the dynamic behavior of the vibration system was analyzed and verified using a bifurcation diagram, maximum Lyapunov exponent, phase trajectory, and Poincare section. Our research provides a theoretical reference for eliminating and suppressing the chatter in rolling mills subjected to an elastoplastic hysteresis deformation.

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