Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section

Herrera-May, Agustín L.; Aguilera-Cortés, Luz Antonio; Mora, Héctor Plascencia; Rodriguez-Morales, Angel Luis; Lu, Jian

doi:10.3390/s110908203

Cited by 14 publications

(7 citation statements)

References 47 publications

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“…Multilayer beam-based micro- and nanomechanical resonators often use sensitive coating or piezoelectric layers for mass and gas detections [ 74 ]. Most of them have a variable cross-section that complicates the prediction the resonant frequency using conventional beam models [ 75 , 76 , 77 , 78 , 79 ].…”

Section: General Resonance Behaviormentioning

confidence: 99%

Tunable Micro- and Nanomechanical Resonators

Zhang

Peng

et al. 2015

Sensors

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Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

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Section: General Resonance Behaviormentioning

confidence: 99%

Tunable Micro- and Nanomechanical Resonators

Zhang

Peng

et al. 2015

Sensors

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“…To determine the first bending resonant frequency of the microdevice structure, we employed the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Based on the Rayleigh method, the resonant frequency of a cantilever can be obtained through the maximum potential energy ( P m ) and kinetic energy ( K m ) [20,21]:Pm=12true∫0LEI(x)(∂2y(x)∂x2)2dx Km=false(2πffalse)22true∫0LρA(x)y2(x)dx where y ( x ) is the bending displacement at a given point along x -axis of the cantilever, f is the resonator frequency, L, A, E, I, and ρ are the length, cross-section area, Young’s modulus, moment of inertia, and density of the cantilever, respectively.…”

Section: Modeling Of the Pveh Microdevicementioning

confidence: 99%

Electromechanical Modeling of a Piezoelectric Vibration Energy Harvesting Microdevice Based on Multilayer Resonator for Air Conditioning Vents at Office Buildings

et al. 2019

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Piezoelectric vibration energy harvesting (pVEH) microdevices can convert the mechanical vibrations to electrical voltages. In the future, these microdevices can provide an alternative to replace the electrochemical batteries, which cause contamination due to their toxic materials. We present the electromechanical modeling of a pVEH microdevice with a novel resonant structure for air conditioning vents at office buildings. This electromechanical modeling includes different multilayers and cross-sections of the microdevice resonator as well as the air damping. This microdevice uses a flexible substrate and it does not include toxics materials. The microdevice has a resonant structure formed by multilayer beams and U-shape proof mass of UV-resin (730 μm thickness). The multilayer beams contain flexible substrates (160 μm thickness) of polyethylene terephthalate (PET), two aluminum electrodes (100 nm thickness), and a ZnO layer (2 μm thickness). An analytical model is developed to predict the first bending resonant frequency and deflections of the microdevice. This model considers the Rayleigh and Macaulay methods, and the Euler-Bernoulli beam theory. In addition, the electromechanical behavior of the microdevice is determined through the finite element method (FEM) models. In these FEM models, the output power of the microdevice is obtained using different sinusoidal accelerations. The microdevice has a resonant frequency of 60.3 Hz, a maximum deflection of 2.485 mm considering an acceleration of 1.5 m/s2, an output voltage of 2.854 V and generated power of 37.45 μW with a load resistance of 217.5 kΩ. An array of pVEH microdevices connected in series could be used to convert the displacements of air conditioning vents at office buildings into voltages for electronic devices and sensors.

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“…There are four variable parameters in the width function (16). Different parameters have different effects on the microbeam shape, and the changes in the shape will further affect the dynamic behavior of the microbeam.…”

Section: Numerical Analysismentioning

confidence: 99%

“…The goal of their research is to enhance the static and dynamic pull-in ranges of electrostatically actuated microbeams, but they did not discuss the impact of the resulting optimized shape on the dynamic response of the microbeam. Herrera-May et al [14][15][16] not only studied the resonant characteristic of the single layer variable cross-section microbeam but also researched the bending resonant frequency of multilayered microresonators with variable cross-section. So far, the research on the dynamic characteristic of the optimized microbeam is fewer.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam

Zhang

Peng

et al. 2015

Shock and Vibration

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We mainly analyze the dynamic characteristics of electrostatically actuated shape optimized variable geometry microbeam. A nonlinear dynamic model considering midplane stretching, electrostatic force, and electrical field fringing effects is developed. Firstly, we study the static responses of the optimized microbeams under DC polarization voltage. The generalized differential quadrature method (GDQM) is used. Secondly, the dynamic responses of the shape optimized microbeams driven by DC and AC voltages are investigated using GDQM in conjunction with Levenberg-Marquardt optimization method. The results show that the more gradual change in width, the larger the resonant frequency and the maximum amplitude at resonance. Then we further discuss in detail how do the maximum width, midsection width, and curvature of the width function affect the frequency response of the microbeams. We find that the amplitude and resonant frequency of the dynamic response are not monotonically increasing as the curvature of the width function increases and there exists a critical curvature. This analysis will be helpful in the optimal design of MEMS actuators. Finally, for more consideration, different residual stress, squeeze-film damping, and fringing effect models are introduced into the governing equation of motion and we compare the corresponding dynamic response.

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Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section

Cited by 14 publications

References 47 publications

Tunable Micro- and Nanomechanical Resonators

Tunable Micro- and Nanomechanical Resonators

Electromechanical Modeling of a Piezoelectric Vibration Energy Harvesting Microdevice Based on Multilayer Resonator for Air Conditioning Vents at Office Buildings

Dynamic Characteristics of Electrostatically Actuated Shape Optimized Variable Geometry Microbeam

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