scholarly journals Experimental and Theoretical Study of Two-to-One Internal Resonance of MEMS Resonators

2018 ◽  
Author(s):  
Amal Z. Hajjaj ◽  
Feras K. Alfosail ◽  
Mohammad I. Younis
Keyword(s):  
Internal Resonance ◽  
Nonlinear Response ◽  
Perturbation Technique ◽  
Vibrational Modes ◽  
Reduced Order ◽  
Simultaneous Excitation ◽  
Direct Excitation ◽  
Mems Resonators ◽  
Resonance Frequencies ◽  
Good Agreement

In this paper, we investigate experimentally and theoretically the two-to-one (2:1) internal resonance between the first two symmetric vibrational modes of microelectromechanical (MEMS) arch resonator electrothermally tuned and electrostatically driven. Applying electrothermal voltage across the beam anchors controls its stiffness and then its resonance frequencies. Hence the ratio between the two frequencies can be tuned to a ratio of two. Then, we study the dynamic response of the arch beam during internal resonance. In the studied case, the presence of high AC bias excitation leads to the direct simultaneous excitation of the 1st and 3rd frequencies in addition to the activation of the internal resonance. A reduced order model and perturbation techniques are presented to analyze the nonlinear response of the structure. In the perturbation technique, the direct excitation of the 3rd resonance frequency is taken into consideration. Results show the presence of Hopf bifurcations, which can lead to chaotic motion at higher excitation. A good agreement among the theoretical and experimental results is shown.

scholarly journals Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Feras K. Alfosail ◽  
Amal Z. Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Internal Resonance ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Hopf Bifurcations ◽  
Chaotic Motions ◽  
Different Types ◽  
Quadratic Nonlinearities ◽  
Multiple Scales Perturbation Method ◽  
Good Agreement ◽  
Perturbation Solutions

We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

scholarly journals Experimental Study on Nonlinear Vibrations of Fixed-Fixed Curved Beams

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Ajay Kumar ◽  
B. P. Patel
Keyword(s):  
Experimental Study ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Excitation Amplitude ◽  
Curved Beam ◽  
Symmetric Mode ◽  
Curved Beams ◽  
Direct Excitation ◽  
First Time ◽  
Good Agreement

AbstractNonlinear dynamic behavior of fixed-fixed shallow and deep curved beams is studied experimentally using non-contact type of electromagnetic shaker and acceleration measurements. The frequency response obtained from acceleration measurements is found to be in fairly good agreement with the computational response. The travellingwave phenomenon along with participation of higher harmonics and softening nonlinearity are observed. The experimental results on the internal resonance of curved beams due to direct excitation of anti-symmetric mode are reported for the first time. The deep curved beam depicts chaotic response at higher excitation amplitude.

scholarly journals A Time-Shifting Algorithm for Alleviating Convergence Difficulties at Interior Acoustic Resonance Frequencies

2021 ◽  
Vol 11 (6) ◽  
pp. 2701
Author(s):  
Jui Hsiang Kao
Keyword(s):  
Point Source ◽  
Time Domain ◽  
Internal Resonance ◽  
Acoustic Resonance ◽  
Time Step ◽  
Resonance Frequencies ◽  
True Frequency ◽  
The Time Domain ◽  
Acoustic Domain ◽  
Good Agreement

This paper proposes a time-shifting boundary element method in the time domain to calculate the radiating pressures of an arbitrary object pulsating at eigenfrequencies of the interior (i.e., interior resonance frequencies). In this paper, the frequency shifting is time-step-dependent and could be viewed as an iterative, or relaxation, technique for the solution of the problem. The proposed method avoids numerical problems due to the internal resonance frequency by initializing the iteration with each scaled frequency. The scaled frequency is approximately equal to the true frequency at the last iterating time step. A sphere pulsating at the eigenfrequency in an infinite acoustic domain was calculated first; the result was compared with the analytical solution, and they were in good agreement. Moreover, two arbitrary-shaped radiators were taken as study cases to predict the radiating pressures at the interior resonance frequencies, and robustly convergent results were obtained. Finally, the accuracy of the proposed method was tested using a problem with a known solution. A point source was placed inside the object to compute the surface velocities; the computed surface pressures were identical to the pressures computed using the point source.

Experimental Investigation of 2:1 and 3:1 Internal Resonances in Nonlinear MEMS Arch Resonators

2016 ◽  
Author(s):  
Abdallah Ramini ◽  
Amal Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Experimental Investigation ◽  
Frequency Response ◽  
Electrical Current ◽  
Vibrational Modes ◽  
Response Curves ◽  
Internal Resonances ◽  
Mems Resonators ◽  
Resonance Frequencies ◽  
Doped Silicon

We demonstrate experimentally internal resonances in MEMS resonators. The investigation is conducted on in-plane MEMS arch resonators fabricated with a highly doped silicon. The resonators are actuated electrostatically and their stiffness are tuned by electrothermal loading by passing an electrical current though the microstructures. We show that through this tuning, the ratio of the various resonance frequencies can be varied and set at certain ratios. Particularly, we adjust the resonance frequencies of two different vibrational modes to 2:1 and 3:1. Finally, we validate the internal resonances at these ratios through frequency-response curves and FFTs.

Ground Flutter Simulation Test Based on Reduced Order Modeling of Aerodynamics by CFD/CSD Coupling Method

2019 ◽  
Vol 11 (01) ◽  
pp. 1950008
Author(s):  
Binwen Wang ◽  
Xueling Fan
Keyword(s):  
Aerodynamic Force ◽  
Test System ◽  
Simulation Test ◽  
Robust Controller ◽  
Test Technique ◽  
Reduced Order ◽  
Aerodynamic Model ◽  
Flutter Boundary ◽  
Computational Fluid Dynamics Cfd ◽  
Good Agreement

Flutter is an aeroelastic phenomenon that may cause severe damage to aircraft. Traditional flutter evaluation methods have many disadvantages (e.g., complex, costly and time-consuming) which could be overcome by ground flutter test technique. In this study, an unsteady aerodynamic model is obtained using computational fluid dynamics (CFD) code according to the procedure of frequency domain aerodynamic calculation. Then, the genetic algorithm (GA) method is adopted to optimize interpolation points for both excitation and response. Furthermore, the minimum-state method is utilized for rational fitting so as to establish an aerodynamic model in time domain. The aerodynamic force is simulated through exciters and the precision of simulation is guaranteed by multi-input and multi-output robust controller. Finally, ground flutter simulation test system is employed to acquire the flutter boundary through response under a range of air speeds. A good agreement is observed for both velocity and frequency of flutter between the test and modeling results.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

Analysis of Collective Resonances in Clusters: Metals and Carbon

1992 ◽  
Vol 272 ◽  
Author(s):  
Vitaly V. Kresin
Keyword(s):  
Random Phase Approximation ◽  
Sum Rules ◽  
Random Phase ◽  
Closed Shell ◽  
Dynamical Response ◽  
Many Body ◽  
Resonance Frequencies ◽  
Unified View ◽  
Small Clusters ◽  
Good Agreement

ABSTRACTDipole photoabsorption spectra of small clusters are analyzed. Two types of systems are considered: metal clusters and the carbon fullerenes. Both have been found to exhibit strong collective photoabsorption modes associated with the motion of delocalized electrons. We describe analytical results for the resonance frequencies in both spherical (closed-shell metallic, C60 ) and spheroidal (openshell metallic, C70) particles. The calculation is based on the techniques of many-body physics (random-phase approximation, sum rules), affords a unified view of the dynamical response of microscopic clusters, and leads to good agreement with experimental data.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2019 ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness Evaluation Procedure (STEP) and then corrected by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The Linear Normal Modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parametrised with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearised ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

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