Mass detection based on pure parametric excitation of a micro beam actuated by piezoelectric layers

Azizi, Saber; Kivi, Araz Rezaei; Marzbanrad, Javad

doi:10.1007/s00542-016-2813-7

Cited by 10 publications

(5 citation statements)

References 32 publications

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“…Moreover, two stationary electrodes with the length of 𝐿 𝑒 and the same width and thickness as of the microbeam are symmetrically placed on both sides of the microbeam for the fringing-field electrostatic actuation. The horizontal distance between the actuation electrodes and the edges of the microbeam on the 𝑥𝑦 plane is g. Upon applying DC voltage 𝑉 𝑝 to each of the piezoelectric patches, the resulting axial force is applied along the length to the microbeam as follows [29,30]:…”

Section: Mathematical Modelingmentioning

confidence: 99%

Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

Rashidi,

Azizi,

Rahmani

2023

Preprint

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This paper explores the nonlinear dynamics of a piezoelectrically laminated microbeam resonator with an initial curvature, which is subjected to electrostatic actuation caused by fringing fields. The resonator is fully clamped at both of its ends and is coated with two piezoelectric layers, encompassing both the top and bottom surfaces. The fringing field electrostatic force is assessed through finite element modeling, and the resulting data is accurately fitted to a suitable hyperbolic function. The nonlinear motion equation accounts for the geometric nonlinearity and the nonlinear electrostatic force. The motion equation is discretized using Galerkin method and the reduced order system is numerically integrated over the time for the time response. The variation of the first three natural frequencies with respect to the applied electrostatic voltage is determined and the frequency response curve is determined. The bifurcation points have been examined and their types have been clarified based on the loci of the Floquet exponents on the complex plane. The period -doubled branches of the frequency response curves originating from the period doubling (PD) bifurcation points are stablished. It's demonstrated that the succession PD cascades leads to chaotic behavior. The chaotic behavior is identified qualitatively by constructing the corresponding Poincaré section and analyzing the response's associated frequency components. The chaotic response is regularized by applying an appropriate piezoelectric voltage which shifts the frequency response curve along the frequency axis.

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Section: Mathematical Modelingmentioning

confidence: 99%

Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

Rashidi,

Azizi,

Rahmani

2023

Preprint

Self Cite

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“…Various sensing mechanisms have been proposed for small mass sensing purposes; these methods include frequency shift in the resonance zone due to the added mass (Park et al 2012 ; Chauhan and Ansari 2021 ; Chellasivalingam et al 2020 ; Joshi et al 2019 ) symmetry-breaking of the vibration (Baguet et al 2019 ; Chellasivalingam et al 2020 ) and nonlinear bifurcations (Meesala et al 2020 ). From the sensing type point of view, various sensing mechanisms have been applied so far which include piezoelectric (Chellasivalingam et al 2020 ; Joshi et al 2019 ; Azizi et al 2017 ; Kumar et al 2011 ), piezoresistive (Chu et al 2018 ), electrostatic (Baguet et al 2019 ), magnetic (Jafari et al 2017 ) and nanocrystalline ZnO thin films (Bhattacharyya et al 2008 ). The dynamic range enhancement of MEMS mass sensors has also been studied.…”

Section: Introductionmentioning

confidence: 99%

On the nonlinear dynamics of a piezoresistive based mass switch based on catastrophic bifurcation

Azizi

Madinei

Khodaparast

et al. 2023

Int J Mech Mater Des

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This research investigates the feasibility of mass sensing in piezoresistive MEMS devices based on catastrophic bifurcation and sensitivity enhancement due to the orientation adjustment of the device with respect to the crystallographic orientation of the silicon wafer. The model studied is a cantilever microbeam at the end of which an electrostatically actuated tip mass is attached. The piezoresistive layers are bonded to the vicinity of the clamped end of the cantilever and the device is set to operate in the resonance regime by means of harmonic electrostatic excitation. The nonlinearities due to curvature, shortening and electrostatic excitation have been considered in the modelling process. It is shown that once the mass is deposited on the tip mass, the system undergoes a cyclic fold bifurcation in the frequency domain, which yields a sudden jump in the output voltage of the piezoresistive layers; this bifurcation is attributed to the nonlinearities governing the dynamics of the response. The partial differential equations of the motion are derived and discretized to give a finite degree of freedom model based on the Galerkin method, and the limit cycles are captured in the frequency domain by using the shooting method. The effect of the orientation of the device with respect to the crystallographic coordinates of the silicon and the effect of the orientation of the piezoresistive layers with respect to the microbeam length on the sensitivity of the device is also investigated. Thanks to the nonlinearity and the orientation adjustment of the device and piezoresistive layers, a twofold sensitivity enhancement due to the added mass was achieved. This achievement is due to the combined amplification of the sensitivity in the vicinity of the bifurcation point, which is attributed to the nonlinearity and maximizing the sensitivity by orientation adjustment of the anisotropic piezoresistive coefficients.

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“…Numerous studies have been carried out to explore new mass detection strategies exploiting nonlinear effects. A parametrically excited clamped-clamped beam with cubic stiffness nonlinearity is explored as micromass sensor in [30]. The principle is based on the passage from the stable region to the unstable region across the transition curves of the Strutt diagrams.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Response of Nanocomposite Microbeams Array for Multiple Mass Sensing

2023

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A nonlinear MEMS multimass sensor is numerically investigated, designed as a single input-single output (SISO) system consisting of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is constrained by a linear spring and a dashpot. The microcantilevers are made of a nanostructured material, a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT). The linear as well as the nonlinear detection capabilities of the device are explored by computing the shifts of the frequency response peaks caused by the mass deposition onto one or more microcantilever tips. The frequency response curves of the device are obtained by a pathfollowing algorithm applied to the reduced-order model of the system. The microcantilevers are described by a nonlinear Euler-Bernoulli inextensible beam theory, which is enriched by a meso-scale constitutive law of the nanocomposite. In particular, the microcantilever constitutive law depends on the CNT volume fraction suitably used for each cantilever to tune the frequency bandwidth of the whole device. Through an extensive numerical campaign, the mass sensor sensitivity estimated in the linear and nonlinear dynamic range shows that, for relatively large displacements, the accuracy of the added mass detectability can be improved due to the larger nonlinear frequency shifts at resonance (up to 12%).

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Mass detection based on pure parametric excitation of a micro beam actuated by piezoelectric layers

Cited by 10 publications

References 32 publications

Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

On the nonlinear dynamics of a piezoresistive based mass switch based on catastrophic bifurcation

Nonlinear Dynamic Response of Nanocomposite Microbeams Array for Multiple Mass Sensing

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