An Electrically Actuated Microbeam-Based MEMS Device: Experimental and Theoretical Investigation

2017 ◽  
Author(s):  
Laura Ruzziconi ◽  
Nizar Jaber ◽  
Lakshmoji Kosuru ◽  
Mohammed L. Bellaredj ◽  
Stefano Lenci ◽  
...  
Keyword(s):  
Microelectromechanical Systems ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Parametric Identification ◽  
Unknown Parameters ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Electrically Actuated ◽  
Nonlinear Features ◽  
Frequency Sweeps

The present paper deals with the dynamic behavior of a microelectromechanical systems (MEMS). The device consists of a clamped-clamped microbeam electrostatically and electrodynamically actuated. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. In the first part of the paper an extensive experimental investigation is conducted. The microbeam is perfectly straight. The first three experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted. The experimental data show the coexistence of the nonresonant and the resonant branch, which perform a bending toward higher frequencies values before undergoing jump or pull-in dynamics. This kind of bending is not particularly common in MEMS. In the second part of the paper, a theoretical single degree-of-freedom model is derived. The unknown parameters are extracted and settled via parametric identification. A single mode reduced-order model is considered, which is obtained via the Galerkin technique. To enhance the computational efficiency, the contribution of the electric force term is computed in advance and stored in a table. Extensive numerical simulations are performed at increasing values of electrodynamic excitation. They are observed to properly predict all the main nonlinear features arising in the device response. This occurs not only at low values of electrodynamic excitation, but also at higher ones.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

Nonlinear Dynamic Response of an Electrically Actuated Imperfect Microbeam Resonator

2013 ◽  
Author(s):  
Laura Ruzziconi ◽  
Ahmad M. Bataineh ◽  
Mohammad I. Younis ◽  
Weili Cui ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Theoretical Analysis ◽  
Ritz Method ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Reduced Order Models ◽  
Nonlinear Dynamic Response ◽  
Reduced Order ◽  
Combined Use ◽  
Experimental Complex

We present a study of the dynamic behavior of a MEMS device constituted of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is capable also to capture the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach.

scholarly journals Software Sensor to Enhance Online Parametric Identification for Nonlinear Closed-Loop Systems for Robotic Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3653
Author(s):  
Lilia Sidhom ◽  
Ines Chihi ◽  
Ernest Nlandu Kamavuako
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Parametric Identification ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Closed Loop Identification ◽  
Input Variables ◽  
Robotic Applications

This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differentiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algorithm’s effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.

Nonlinear Coupled Transverse and Axial Vibration of Variable Cross-Section Beam Flexures Interconnecting Rigid Body

2016 ◽  
Author(s):  
Hasan Malaeke ◽  
Hamid Moeenfard ◽  
Amir H. Ghasemi
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Cross Section ◽  
Multiple Scales ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Closed Form Solutions ◽  
Dynamic Performances

The objective of this paper is to analytically study the nonlinear behavior of variable cross-section beam flexures interconnecting an eccentric rigid body. Hamilton’s principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. Using a single mode approximation, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. The method of multiple scales are employed to obtain parametric closed-form solutions. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. These analytical expressions provide design insights for modeling and optimization of more complex flexure mechanisms for improved dynamic performances.

Optical bistable switching in pyran dye-doped polymers

2014 ◽  
Vol 23 (02) ◽  
pp. 1450018 ◽  
Author(s):  
Purnima ◽  
Devendra Mohan
Keyword(s):  
Solid State ◽  
Communication Systems ◽  
Optical Bistability ◽  
Nonlinear Refraction ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Third Order ◽  
Bistable Switching ◽  
Fabry Perot ◽  
Doped Polymers

In the present frame of work, optical bistability using a Fabry–Perot (FP) cavity containing 4-dicyanomethylene-2-methyl-6-p-dimethylaminostyryl-4H-pyran (DCM) dye entrapped in poly-methylmethacrylate (PMMA) matrix is experimentally investigated. Optical nonlinear behavior of solid-state samples is studied using a single-mode Q-switched nanosecond Nd:YAG laser operating at 532 nm. Various optical nonlinear parameters such as nonlinear refractive index (n2) and third-order susceptibility (χ3) of the material are numerically estimated from bistability loops. The origin of optically bistable behavior is attributed to photoisomerization-assisted nonlinear refraction phenomenon. It is observed that nonlinear refraction dominates over nonlinear absorption in giving rise to the optical bistability. The study shows that DCM dye entrapped in solid-state matrices are promising candidate for polymer-based optical switches, data processing, and communication systems.

Nonlinear Dynamics of an Electrically Actuated MEMS Device: Experimental and Theoretical Investigation

2013 ◽  
Author(s):  
Laura Ruzziconi ◽  
Abdallah H. Ramini ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Theoretical Investigation ◽  
Initial Conditions ◽  
Micro Electro Mechanical System ◽  
Mass Model ◽  
Design Guideline ◽  
Electrically Actuated ◽  
Theoretical Predictions ◽  
Frequency Sweeps ◽  
Safe Condition

This study deals with an experimental and theoretical investigation of an electrically actuated micro-electro-mechanical system (MEMS). The experimental nonlinear dynamics are explored via frequency sweeps in a neighborhood of the first symmetric natural frequency, at increasing values of electrodynamic excitation. Both the non-resonant branch, the resonant one, the jump between them, and the presence of a range of inevitable escape (dynamic pull-in) are observed. To simulate the experimental behavior, a single degree-of-freedom spring mass model is derived, which is based on the information coming from the experimentation. Despite the apparent simplicity, the model is able to catch all the most relevant aspects of the device response. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Nevertheless, the theoretical predictions are not completely fulfilled in some aspects. In particular, the range of existence of each attractor is smaller in practice than in the simulations. This is because, under realistic conditions, disturbances are inevitably encountered (e.g. discontinuous steps when performing the sweeping, approximations in the modeling, etc.) and give uncertainties to the operating initial conditions. A reliable prediction of the actual (and not only theoretical) response is essential in applications. To take disturbances into account, we develop a dynamical integrity analysis. Integrity profiles and integrity charts are performed. They are able to detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable. Moreover, depending on the magnitude of the expected disturbances, the integrity charts can serve as a design guideline, in order to effectively operate the device in safe condition, according to the desired outcome.

scholarly journals Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

2014 ◽  
Author(s):  
Mohammad I. Younis
Keyword(s):  
Analytical Solutions ◽  
Galerkin Approximation ◽  
Single Mode ◽  
Beam Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Analytical Formulas ◽  
Euler Bernoulli Beam ◽  
Analytical Expressions ◽  
Multi Mode

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

Reduced-Order Modeling and Experimental Studies of Two-Way Coupled Fluid-Structure Interaction in Flapping Wings

2019 ◽  
Author(s):  
Ryan K. Schwab ◽  
Heidi E. Reid ◽  
Mark A. Jankauski
Keyword(s):  
Fluid Structure Interaction ◽  
Experimental Studies ◽  
Flapping Wing ◽  
Flexible Wings ◽  
Single Degree Of Freedom ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Rotation Stage ◽  
Computational Resources

Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.

Maximum Amplification of Blade Response in Mistuned Multi Stage Assemblies

2010 ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet
Keyword(s):  
Mass Matrix ◽  
Optimization Strategy ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Multi Stage ◽  
Maximum Amplification ◽  
Blade Model ◽  
Computational Validation ◽  
Theoretical Developments

This paper focuses on the determination of the maximum amplification of blade response due to mistuning in multi stage assemblies. The modal optimization strategy developed earlier in connection with single stage models is extended here to multi stage configurations. Theoretical developments are carried out first and lead to the new upper limit of (1+N1+N2(g2/g1)+…)/2, where Ni are the number of blades on the stages and gi = FiTMi−1Fi with Fi the force vector applied on a sector of stage i and Mi its mass matrix. For identical stages, this maximum equals the Whitehead limit observed with single stages but with the number of blades equal to sum of the numbers of blades of the coupled stages. A computational validation of the theoretical results is achieved next on both a single degree of freedom per blade model and a reduced order model of a blisk. These numerical optimization efforts confirm the theoretical developments and demonstrate that such high amplification factors can indeed be achieved with small levels of mistuning. The effects of the number of blades on the different stages, damping in the system, stage coupling strength, etc are discussed in details.

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