Considerations for Use of Square-Paddle Resonators for Arrays of Micro- and Nanoscale Devices

Judge, John A.; Woods, Teresa J.; Vignola, Joseph F.

doi:10.1115/detc2009-87441

Cited by 4 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…then the problem becomes combinatoric in scale and challenging to manufacture, design, and tune for a desired application. As such, most studies have focused on coupling modalities that are practically achievable with modern fabrication techniques, resulting in 1-D or 2-D lattice-like structures (Judge et al 2006(Judge et al , 2010Ryan et al 2012), or more generally, structures that are coupled more strongly locally than remotely. Additional important questions in design consider the type of excitation (directly controlled, or parametric e.g.…”

Section: Introductionmentioning

confidence: 99%

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Borra

Bajaj

Rhoads

et al. 2022

Preprint

View full text Add to dashboard Cite

This work considers the response of a globally coupled array of oscillators, each with cubic nonlinear stiffness, in the presence of global reactive and dissipative coupling. Based on the continuum formulation for this system first presented in C. Borra et al (Journal of Sound and Vibration, 393:232–239, 2017), in the present work the individual resonators are excited to sufficient amplitude to allow for multiple coexisting equilibrium distributions. The method of multiple scales is then applied to the system to describe evolution equations for the amplitude and phase of each resonator. Because of the global nature of the coupling, this leads to an integro-differential equation for the stationary populations. Moreover, the characteristic equation used to determine the stability of these states is also an integral equation and admits both a discrete and continuous spectrum for its eigenvalues. The equilibrium structure of the system is studied as the reactive and dissipative coupling parameters are varied. For specific families of the equilibrium distributions two-parameter bifurcation sheets can be constructed. These sheets are connected as individual resonators transition between different branches for the corresponding individual resonators. The resulting one-parameter bifurcation curves are then understood in terms of the collections of these identified bifurcation sheets. The analysis is demonstrated for a system of N = 10 coupled resonators with mass detuning and extended results with N = 100 coupled resonators are illustrated.

show abstract

Section: Introductionmentioning

confidence: 99%

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Borra

Bajaj

Rhoads

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Mode localization has also been used in accelerometers [27] and light processing applications [28]. Previous reports highlight the influence of various system parameters such as the mass-ratio [24], measurement noise [23], non-ideal clamping [29], coupling stiffness [30], anisotropy of the Youngs modulus [31], and global and dissipative coupling [32] on the array dynamics. In these arrayed structures, vibrations are possible only within the allowed propagation band [33], defined as the interval of frequencies between the lower ( f L ) and the upper ( f U ) cut-off values.…”

Section: Introductionmentioning

confidence: 99%

Actuation of Higher Harmonics in Large Arrays of Micromechanical Cantilevers for Expanded Resonant Peak Separation

Dick

Grutzik

Wallin

et al. 2018

Journal of Vibration and Acoustics

View full text Add to dashboard Cite

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array’s dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.

show abstract

Time‐domain chemical vapour mass sensor using a functionalized subordinate array

Glean¹,

Sonne

Judge

et al. 2020

Med Devices & Sens

Self Cite

View full text Add to dashboard Cite

This work describes a chemical vapour detection scheme based on observing changes in the time‐domain impulse response of a single structure to which an array of smaller cantilevers is attached. The distribution of properties of the cantilevers in the array is chosen to transfer vibration energy to the array and confine it there for a specified duration τ. Accumulation of added mass on the cantilevers changes the array properties, altering the duration for which energy is confined. When every second cantilever is functionalized to adsorb mass, a portion of the vibration energy returns to the primary structure in half the original time. The amount of added mass can be estimated by comparing the vibration energy in the primary structure to the total energy in the array at the return time τ/2. Numerical analysis is used to investigate the performance of the proposed detection scheme. It is shown that increasing the number of sensing elements reduces errors in mass predictions due to mass adsorption variability and increases mass sensitivity. However, reducing the number of sensing elements improves the signal‐to‐noise ratio. These opposing effects require consideration for a specific sensing application. Experimental results using a centimetre scale prototype demonstrate feasibility of this interferometric approach for MEMS‐scale implementation.

show abstract

Considerations for Use of Square-Paddle Resonators for Arrays of Micro- and Nanoscale Devices

Cited by 4 publications

References 0 publications

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Actuation of Higher Harmonics in Large Arrays of Micromechanical Cantilevers for Expanded Resonant Peak Separation

Time‐domain chemical vapour mass sensor using a functionalized subordinate array

Contact Info

Product

Resources

About