scholarly journals Utilization of 2:1 Internal Resonance in Microsystems

Micromachines ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 448 ◽  
Author(s):  
Navid Noori ◽  
Atabak Sarrafan ◽  
Farid Golnaraghi ◽  
Behraad Bahreyni
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Beam Structure ◽  
Nonlinear Mode Coupling ◽  
T Beam ◽  
Low Frequency Mode

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange’s energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

Transfer of Energy From High- to Low-Frequency Modes in the Bending-Torsion Oscillation of Cantilever Beams

1999 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Virtual Work ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Nonlinear Bending ◽  
Torsional Mode ◽  
Bending Mode ◽  
Plane Bending

Abstract We investigate the nonlinear bending-torsion response of a cantilever beam to a transverse harmonic excitation, where the forcing frequency is near the natural frequency of the first torsional mode. We analyze the case where the first in-plane bending mode is activated by a nonresonant mechanism. We use the method of time-averaged Lagrangian and virtual work to determine the equations governing the modulations of the phases and amplitudes of the interacting modes. These equations are then used to investigate the nonlinear behavior of limit-cycle oscillations of the beam as the excitation amplitude is slowly varied. As an example, we consider the response of an aluminum beam for which the natural frequency of the first in-plane bending mode is fv1 ≈ 5.7 Hz and the natural frequency of the first torsional mode is fϕ1 ≈ 138.9 Hz.

Low-frequency measurements and predictions of the structural-acoustic properties of the INCE standard T-beam structure

2002 ◽  
Vol 50 (3) ◽  
pp. 90 ◽  
Author(s):  
Stephen A. Hambric ◽  
Joseph M. Cuschieri ◽  
C. Roger Halkyard ◽  
Brian R. Mace ◽  
Richard P. Szwerc
Keyword(s):  
Low Frequency ◽  
Acoustic Properties ◽  
Beam Structure ◽  
Frequency Measurements ◽  
T Beam

scholarly journals Nonlinear mode coupling and internal resonance observed in a dusty plasma

2019 ◽  
Vol 21 (10) ◽  
pp. 103051 ◽  
Author(s):  
Zhiyue Ding ◽  
Ke Qiao ◽  
Nicholas Ernst ◽  
Jie Kong ◽  
Mudi Chen ◽  
...  
Keyword(s):  
Dusty Plasma ◽  
Internal Resonance ◽  
Mode Coupling ◽  
Nonlinear Mode ◽  
Nonlinear Mode Coupling

An Experimental Investigation of Multimode Responses in a Cantilever Beam

1997 ◽  
Vol 119 (4) ◽  
pp. 532-538 ◽  
Author(s):  
M. Tabaddor ◽  
A. H. Nayfeh
Keyword(s):  
Experimental Investigation ◽  
Cantilever Beam ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Frequency Mode ◽  
Response Curves ◽  
Additive Type ◽  
Low Frequency Mode

An experimental investigation into the planar, multimode response of a cantilever metallic beam to a transverse harmonic excitation is presented. The cantilever beam was tested in both the horizontal and vertical directions. In the vertical configuration, the beam was excited near its fourth natural frequency and energy was transferred from the directly excited fourth mode to a low-frequency mode through both resonant and nonresonant modal interactions. In the latter case, the response contained contributions from the first and fourth modes, whereas in the former case, the response contained contributions from the fourth, second, and fifth modes. The mechanism responsible for the resonant interaction involving the three modes is a subcombination internal resonance of the additive type; that is, Ω ≈ ω4 ≈ 1/2(ω2 + ω5), where the ωi are the natural frequencies of the beam. This type of resonance occurs in systems with a dominant cubic nonlinearity. In the horizontal configuration, the beam was excited near its fourth and sixth natural frequencies. Again, energy was transferred to a low-frequency mode, but in this case only through a resonant interaction due to a subcombination internal resonance of the additive type. Power spectra, time series, and frequency- and amplitude-response curves were obtained for characterization of the dynamic multimode responses.

scholarly journals Mode coupling internal resonance characteristics of submerged floating tunnel tether

2021 ◽  
Vol 3 (12) ◽  
Author(s):  
Sheng-nan Sun ◽  
Yu-long Pan ◽  
Zhi-bin Su
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Damping Ratio ◽  
Excitation Amplitude ◽  
Analysis Method ◽  
External Excitation ◽  
Modal Coupling ◽  
Out Of Plane ◽  
Submerged Floating Tunnel ◽  
The One

Abstract This study presents the mode coupling internal resonance characteristics of submerged floating tunnel tether. In which, in-plane and out-of-plane coupling of tether is taken into account. And the coupled vibration equations of tether for the in-plane first mode and out-of-plane first mode are obtained. The one-to-one mode coupling internal resonance characteristics of submerged floating tunnel tether are studied by numerical analysis method. It is shown that, when the conditions of modal coupling internal resonance are met, with the increase of the external excitation amplitude of the tether, the mid-span displacement of the tether increases gradually. When the amplitude of external excitation is less than a certain value, the internal resonance of tether will not occur. With the increase of damping ratio, the mid-span displacement of the tether decreases gradually. When the damping ratio increases to a certain value, the internal resonance will not occur. The study is helpful to restrain the vibration of submerged floating tunnel tether.

On the Nonlinear Mode-Coupling in Ultra Precision Manufacturing Machines: Experimental and Analytical Analyses

2020 ◽  
Author(s):  
Sunit K. Gupta ◽  
Mohammad A. Bukhari ◽  
Oumar R. Barry ◽  
Chinedum E. Okwudire
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Vibration Isolation ◽  
Mathematical Formulation ◽  
Resonance Case ◽  
Precision Manufacturing ◽  
Resonant Case ◽  
Nonlinear Mode ◽  
Ultra Precision ◽  
Nonlinear Mode Coupling

Abstract Recent studies in passively-isolated systems have shown that mode coupling is desirable for best vibration suppression, thus refuting the long-standing rule of mode decoupling. However, these studies have ignored the non-linearities in the isolators. In this work, we consider stiffness nonlinearity from pneumatic isolators and study the nonlinear free undamped vibrations of a passively-isolated ultra-precision manufacturing (UPM) machine. Experimental analysis is conducted to guide the mathematical formulation. The system comprises linearly and nonlinearly coupled in-plane horizontal and rotational motion of the UPM machine with quadratic nonlinear stiffness from the isolators. We present closed-form expressions using the method of multiple scales for two cases viz. the non-resonant case and the bounded internal resonance case. We validate our theoretical findings through direct numerical simulations. For the non-resonant case, we show that the system behaves similar to a linear system. However, for the nearly internal resonance case, we demonstrate strong energy exchange between the modes stemming from nonlinear mode coupling. We further study the effect of nonlinear mode coupling on the vibration isolation performance and demonstrate that mode coupling is not always desirable.

Numerical Investigation of Modal Amplitude Saturation in Micromechanical Cantilever Beam Resonators

2017 ◽  
Author(s):  
Tianyi Zhang ◽  
Zhuangde Jiang ◽  
Xueyong Wei
Keyword(s):  
Cantilever Beam ◽  
Mode Coupling ◽  
Nonlinear Behavior ◽  
Softening Effect ◽  
Flexural Mode ◽  
Micromechanical Resonators ◽  
Beam Resonator ◽  
Modal Amplitude ◽  
Nonlinear Mode Coupling ◽  
External Driving

Micromechanical resonators have extensive applications but unavoidably exhibit nonlinearities that may degrade the devices’ performances. A good understanding of their nonlinear dynamics is essential to the design of resonant devices. In this paper, we numerically investigated the dynamics of a cantilever beam resonator working at a coupled extensional and flexural vibrational modes with a 2:1 internal resonance. An amplitude saturation behavior is observed in the cantilever beam resonator by controlling the external driving force. The flexural mode shows a complex nonlinear behavior changing from a softening effect to a hardening effect and the extensional mode shows nonlinear behavior due to the nonlinear mode coupling.

Microresonators Based on 1:2 Internal Resonance

2005 ◽  
Author(s):  
Ashwin Vyas ◽  
Anil K. Bajaj
Keyword(s):  
Internal Resonance ◽  
Unique Feature ◽  
Rf Mems ◽  
Primary Resonance ◽  
Mems Devices ◽  
Beam Structure ◽  
Electrostatically Actuated ◽  
Autoparametric Resonance ◽  
Second Mode ◽  
T Beam

A nonlinear autoparametric resonance based microresonator concept is explored in this study. The concept is illustrated by modelling an electrostatically actuated T-beam structure, with the first two modes of the structure in 1:2 internal resonance. The response of the system to primary resonance of the first and second mode is presented. When the second mode is resonantly actuated, the second mode in turn excites the first mode due to 1:2 internal resonance and the nonlinear coupling between the two modes. The structure therefore oscillates in first mode with half the frequency of excitation voltage. This is a unique feature of this microresonator, and as a result of this feature, the resonator can serve as a filter as well as a mixer in RF MEMS devices. When the first mode is excited, the structure oscillates in both the first and the second mode and thus has an output signal with frequency twice the input signal. The response also showed Hopf-bifurcations for higher actuation voltages.

Theoretical Stability Analysis of Self-Excited Vibration in a Thin Film Wrapped Around an Air-Turn Bar

2010 ◽  
Author(s):  
Masahiro Watanabe ◽  
Kensuke Hara
Keyword(s):  
Stability Analysis ◽  
Theoretical Model ◽  
Flow Instability ◽  
Equations Of Motion ◽  
Air Flow ◽  
Low Frequency ◽  
The Self ◽  
Excited Vibration ◽  
Basic Equations ◽  
Low Frequency Mode

This paper deals with a theoretical stability analysis of a self-excited vibration generated in a film wrapped around an air-turn bar. In this paper, firstly, vibration characteristics of the self-excited vibration are examined experimentally, and it is shown that two different types of self-excited vibration, which are low-frequency and high-frequency modes, occur in the film. Secondly, stability of the low-frequency mode is examined theoretically. A theoretical model of the film wrapped around the air-turn bar is developed. Basic equations of the air flow in the gap between the film and air-turn bar, and pressurized air flow inside the air-turn bar are derived. The characteristics equation of the system is derived from the basic equations of motion of the film coupled with the air flow. Instability condition in which the self-excited vibration occurs is shown as a function of air flow rate and tension applied to the film. Moreover, instability mechanism of the self-excited vibration is discussed based on the theoretical model.

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