Generalized topology for resonators having N commensurate harmonics

Danzi, Francesco; Gibert, James M.; Frulla, Giacomo; Cestino, Enrico

doi:10.1016/j.jsv.2017.10.001

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…More recently, applications have been explored in micro-and nanosystems, such as improving the sensitivity of resonator-based mass sensors [1,2], signal filtering applications [3], and improving the frequency stability of resonators [4,5]. Also, mode coupling is utilized to maximize the generated power by increasing the bandwidth of the energy harvester [6][7][8][9][10][11][12]. Another application of mode coupling is enhancing the higher harmonic signal of the atomic force microscopy cantilever, which improves the compositional measurements [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Different methods have been proposed to tune the resonant frequencies and achieve the commensurate ratio, such as tuning axial stress using thermal energy [21], controlling the relative orientation between coupled beams [12], using DC voltage in electrostatically actuated micro-mirrors [22], and by optimizing a structure's geometry [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Development and Parameter Estimation of a Low Order Model for a Hyperelastic Cantilever Plate Exhibiting 2:1 Resonant Response

Jaber

Bilal

Bajaj

2022

Preprint

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This work presents the results of an experimental investigation and a low-order model development for complex resonant dynamics of a cantilever macro-plate. The plate is fabricated from a material using 3D additive manufacturing technology and the material is assumed to be ‘hyperelastic’. The geometry of the plate with cut-outs is analytically optimized assuming a linear elastic material such that the second bending mode frequency 𝜔02 is approximately twice the first twisting mode frequency 𝜔11. Based on the observed ‘near’ 2:1 resonant response under harmonic excitation near 𝜔02, a low-order 2 DOF nonlinear dynamic model is developed to simulate the plate response. A unique and novel stepwise iterative approach is developed for the modal parameter extraction. The unknown modal parameters are extracted using Harmonic Balance solutions, constructing frequency response curves, and curve-fitting techniques. The results are then validated using long-time integration for the developed model. A good agreement is observed between the analytical and experimental results for the different excitation levels considered.

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