Global dynamics and integrity of a micro-plate pressure sensor

Belardinelli, Pierpaolo; Sajadi, Banafsheh; Lenci, Stefano; Alijani, Farbod

doi:10.1016/j.cnsns.2018.09.027

Cited by 11 publications

(4 citation statements)

References 39 publications

(42 reference statements)

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“…These include the investigations of the static and dynamic behaviors of slightly curved and imperfect microplates by studies [34,35], which were formulated in the framework of couple-stress theory and studies where electrostatic actuation was taken into account [28,36,37]. Initially flat plates pre-loaded by a uniform constant pressure and then loaded by the nonlinear electrostatic force were shown to be bistable in studies [38,39]. The bistability of the pressurized graphene membrane was investigated in studies [39,40].…”

Section: Introductionmentioning

confidence: 99%

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

2022

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Configuration-dependent spectral behavior of initially curved circular microplates loaded by a distributed nonlinear electrostatic force is investigated. The structures under consideration are distinguished by two interesting features. The first is that the plates are initially bell-shaped, rather than flat or spherical, and therefore have regions of both positive and negative curvature. Second, the plates are sufficiently curved to exhibit snap-through buckling and bistability. The structure is described in the framework of the nonlinear Föppl von Kármán shallow plate theory. The influence of the initial curvature and loading on the free vibrations around unloaded and deformed equilibria is investigated. The results of the Galerkin model backed by the finite elements analysis show that the modes of even slightly curved bell-shaped unloaded plates differ significantly from those of the initially flat plates. As a result, when the natural modes of a curved plate are used as the base functions, a significantly better convergence of the RO model is achieved. In the vicinity of the critical snap-through and snap-back configurations, the sensitivity of the natural frequencies to the plate deflection is much higher than in the unloaded state. This high tunability opens new opportunities for the design of better resonant sensors with enhanced performance.

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Section: Introductionmentioning

confidence: 99%

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

2022

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“…The design of bi-stable microplate/beambased devices are compatible with conventional N/MEMS fabrication processes. These bi-stable N/MEMS devices are widely used as sensors [1][2][3], switches [4], energy harvesters [5,6], and micromechanical memories [7].…”

Section: Introductionmentioning

confidence: 99%

Interaction of transverse pressure and in-plane internal stresses on bi-stability of electrostatically rectangular microplates

Kumar

Bhushan

2022

Eng. Res. Express

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Bi-stability behavior is commonly observed in an electrostatically actuated pressurised or initially curved microplates. Additionally, presence of in-plane internal stresses considerably changes the mechanical behaviour of the electrostatically actuated microplate. In this paper, the effects of in-plane internal stresses on bi-stability criteria of pressurised rectangular microplates are investigated. For this, the governing di erential equation of motion of a rectangular plate is derived using Kirchhoff's plate theory including von Karman's nonlinearity, transverse pressure, axial in-plane internal stresses, and non-linear electrostatic actuation force. Further, Galerkin's based reduced-order modelling technique is applied to solve the equation. The problem has been solved for two different sets of plate boundary conditions: simply supported and clamped. The analysis reveals that the presence of tensile or compressive in-plane internal stresses signi cantly changes the transverse pressure range for the occurrence of bi-stability on the voltage-defection equilibrium path. Further, we have investigated the variation of required threshold gap between microplate and substrate for bi-stability in presence of in-plane internal stresses. Results of this investigation can be used to design more e cient microplate based bi-stable N/MEMS devices.

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“…The efficiency of the basin stability method in comparison to the basins of attractions is especially visible when the dimension of phase space is larger than two. In such a case, the classical approach requires much larger computational effort and interpretation of results is very complex (necessity of projections of results on two dimensional cross-sections of multi-dimensional phase space) [33][34][35] . The basin stability method gives statistical information on existing solutions (the volume of basins of attractions in relation to the total volume of considered phase space) and their location in the phase space.…”

Section: Introductionmentioning

confidence: 99%

Dynamical response of a rocking rigid block

Liu

Chávez

Brzeski

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates the complex dynamical behavior of a rigid block structure under harmonic ground excitation, thereby mimicking, for instance, the oscillation of the system under seismic excitation or containers placed on a ship under periodic acting of sea waves. The equations of motion are derived assuming a large frictional coefficient at the interface between the block and the ground, in such a way that sliding cannot occur. In addition, the mathematical model assumes a loss of kinetic energy when an impact with the ground takes place. The resulting mathematical model is then formulated and studied in the framework of impulsive dynamical systems. Its complex dynamical response is studied in detail using two different approaches, based on direct numerical integration and path-following techniques, the latter implemented via the continuation platform COCO (Dankowicz & Schilder). Our study reveals the presence of various dynamical phenomena, such as branching points, fold and period-doubling bifurcation of limit cycles, symmetric and asymmetric periodic responses, as well as chaotic motion. By using basin stability method we also investigate the properties of solutions and their ranges of existence in phase and parameters spaces. Moreover, the study considers ground excitation conditions leading to the overturning of the block structure and shows parameters regions wherein such behavior can be avoided.

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Global dynamics and integrity of a micro-plate pressure sensor

Cited by 11 publications

References 39 publications

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

Interaction of transverse pressure and in-plane internal stresses on bi-stability of electrostatically rectangular microplates

Dynamical response of a rocking rigid block

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