Investigation of 3:1 Internal Resonance of Electrostatically Actuated Microbeams With Flexible Supports

2021 ◽  
Author(s):  
Praveen Kumar ◽  
Dnyanesh N. Pawaskar ◽  
Mandar M. Inamdar
Keyword(s):  
Internal Resonance ◽  
Electrostatically Actuated ◽  
Flexible Supports

Investigation of 3:1 Internal Resonance of Electrostatically Actuated Microbeams With Flexible Supports

2020 ◽  
Author(s):  
Praveen Kumar ◽  
Mandar M. Inamdar ◽  
Dnyanesh N. Pawaskar
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time Integration ◽  
External Source ◽  
Mems Devices ◽  
Electrode Gap ◽  
Dynamical Equations ◽  
Electrostatically Actuated ◽  
Second Mode ◽  
Flexible Supports

Abstract Interaction between modes due to internal resonance has many applications in MEMS devices. In this paper, we investigate the modal interaction through 3 : 1 internal resonance of an electrostatically actuated microbeam with flexible supports in the form of rotational and transversal springs. The static displacement and the first three modal frequencies are obtained at the applied DC voltage by a reduced order model for a specified ratio of electrode gap and thickness. We then obtain the value of applied voltage for which 3 : 1 internal resonance exists for four different combinations of unequal end support stiffnesses. We calculate the coefficients of the coupled dynamical equations of first two modes for all the four cases and solve them by using numerical time integration and the method of multiple scales. We observe the interaction between the first and the second mode when each of the modes is independently excited by an external source. When the second mode is externally excited, interestingly, we also find that the undriven mode response amplitude is twice that of the driven mode.

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.

Comments on Energy Harvesting on a 2:1 Internal Resonance Portal Frame Support Structure, Using a Nonlinear-Energy Sink as a Passive Controller

2016 ◽  
Vol 10 (3) ◽  
pp. 147 ◽  
Author(s):  
Rodrigo Tumolin Rocha ◽  
Jose Manoel Balthazar ◽  
Angelo Marcelo Tusset ◽  
Vinicius Piccirillo ◽  
Jorge Luis Palacios Felix
Keyword(s):  
Energy Harvesting ◽  
Internal Resonance ◽  
Nonlinear Energy Sink ◽  
Support Structure ◽  
Portal Frame ◽  
Energy Sink ◽  
Nonlinear Energy

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

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.

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

2021 ◽  
Vol 12 (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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