Modeling of plates with multiple anisotropic layers and residual stress

Engholm, Mathias; Pedersen, Thomas; Thomsen, Erik Vilain

doi:10.1016/j.sna.2016.01.054

Cited by 17 publications

(13 citation statements)

References 36 publications

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“…The value of the tensile stress of the Si 3 N 4 is found by measuring the curvature of a double side polished wafer with a layer of Si 3 N 4 of known thickness on one side and then applying Stoney's equation. The tensile stress increases both the resonance frequency and pull-in voltage compared with a similar plate with no stress [11].…”

Section: Devicesmentioning

confidence: 94%

Combined colorimetric and gravimetric CMUT sensor for detection of phenylacetone

Molgaard¹,

Laustsen²,

Thygesen³

et al. 2017

2017 IEEE International Ultrasonics Symposium (IUS)

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The detection of phenylacetone is of interest as it is a common precursor for the synthesis of (meth)amphetamine. Resonant gravimetric sensors can be used to detect the mass and hereby the concentration of a gas while colorimetric arrays typically have an exceptional selectivity to the target analyte if the right colorimetric dyes are chosen. We present a sensor system consisting of a Capacitive Micromachined Ultrasonic Transducer (CMUT) and a colorimetric array for detection of phenylacetone. The CMUT is used as a resonant gravimetric gas sensor where the resonance frequency shift due to mass loading of the plate. A single Local Oxidation of Silicon (LOCOS) step was used to define the cavities which were sealed with a Si3N4 plate with a thickness of 100 nm, resulting in a resonance frequency of 38.8 MHz and a theoretical mass sensitivity of 28.3 zg Hz•µm 2. The CMUTs were functionalized with the same dyes used to fabricate colorimetric arrays. While both the CMUTs and the colorimetric arrays showed selectivity to phenylacetone, the best selectivity was achieved by the colorimetric array. Furthermore, the mass of the phenylacetone was found as a function of time. Thus, the combination of the colorimetric array and the CMUT results in a good selectivity and a quantitative value for the mass.

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Section: Devicesmentioning

confidence: 94%

Combined colorimetric and gravimetric CMUT sensor for detection of phenylacetone

Molgaard¹,

Laustsen²,

Thygesen³

et al. 2017

2017 IEEE International Ultrasonics Symposium (IUS)

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show abstract

“…(15) and approximates the first mode-shape of the circular plate. Moreover, it has been employed in electrostatic analysis of circular microplate, previously [4,24].…”

Section: Differential Equation For the One-sided Cmutmentioning

confidence: 99%

“…For all of these studies mentioned above, methodology of analysis comprise either lumped element models (LEM) [3,17] or continuum models, such as plate [2,12] or membrane models [22,23]. Membrane models have a low accuracy because the flexural rigidity of the microplate is negligible [24]. LEM is a simple method that has been frequently utilized for modeling of both one-sided and two-sided CMUTs, but it lacks sufficient level of accuracy for describing the static pull-in voltage and dynamics of the system, particularly in higher frequencies [5,17].…”

Section: Introductionmentioning

confidence: 99%

Differences between plate theory and lumped element model in electrostatic analysis of one-sided and two-sided CMUTs with circular microplates

Saadatmand¹,

Kook

2020

J Braz. Soc. Mech. Sci. Eng.

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An analytical study of capacitive micromachined ultrasonic transducers (CMUTs) with circular microplates has been carried out. The study comprises one-sided (single electrode back-plate) and two-sided (double electrode back-plate) systems, and derives universal correction factors for pull-in voltage and critical displacement to be used in lumped element model (LEM) analysis. We employ von Karman plate theory and the single-mode Galerkin decomposition method to solve the equations. Consequently, voltage-deflection relations have been derived. By comparing results from plate theory with LEM, it is concluded: (1) for the one-sided CMUT by neglecting geometrical nonlinearity, we find

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“…Because the integration is performed over the entire region, the modal contours of the DFUT for CMUT operation can be plotted. At the fundamental thickness-bending vibration mode, the relative deflection of the laminated plates is given to be [ 24 , 33 , 34 ]:

where W 0 is the center deflection, α is the plate shape factor, related to the geometric parameters of the DFUT and the orientation of the anisotropic materials.…”

Section: Theoretical Analysis and Modellingmentioning

confidence: 99%

Numerical Study and Optimisation of a Novel Single-Element Dual-Frequency Ultrasound Transducer

Sun

Jiang

Liu

2018

Sensors

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A dual-frequency ultrasound transducer (DFUT) is usually preferred for its numerous advantageous applications, especially in biomedical imaging and sensing. However, most of DFUTs are based on the combination of fundamental and harmonic operations, or integration of multiple different single-frequency ultrasound transducers, hindering perfect beam alignment and acoustic impedance matching. A novel single-element DFUT has been proposed in this paper. A small piezoelectric membrane is used as the high-frequency ultrasound transducer, which is stacked on a large non-piezoelectric elastic membrane with a groove used as the low-frequency capacitive ultrasound transducer. Such a capacitive-piezoelectric hybrid structure is theoretically analysed in details, based on the electrostatic attraction force and converse piezoelectric effect. Both the low and high resonance frequencies are independently derived, with a maximum deviation of less than 4% from the finite element simulations. Besides, a lumped-parameter equivalent circuit model of combining both the capacitive and piezoelectric ultrasound transducers was also described. Based on our dual-frequency structure design, a high-to-low frequency ratio of about 2 to more than 20 could be achieved, with easy and independent controllability of two frequencies, and the high-frequency operation shows at least an order-of-magnitude displacement sensitivity improvement compared with the conventional harmonic operations.

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Modeling of plates with multiple anisotropic layers and residual stress

Cited by 17 publications

References 36 publications

Combined colorimetric and gravimetric CMUT sensor for detection of phenylacetone

Combined colorimetric and gravimetric CMUT sensor for detection of phenylacetone

Differences between plate theory and lumped element model in electrostatic analysis of one-sided and two-sided CMUTs with circular microplates

Numerical Study and Optimisation of a Novel Single-Element Dual-Frequency Ultrasound Transducer

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