Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Zhang, Wenhua; Baskaran, Rajashree; Turner, Kimberly L.

doi:10.1016/s0924-4247(02)00299-6

Cited by 261 publications

(195 citation statements)

References 26 publications

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“…where the linear modal coupling coefficients α (2) ij and the nonlinear modal coupling coefficients, α (3) ijk and α (4) ijkl , are explicitly expressed as…”

Section: Analysis and Optimization (A) Characterization Theorymentioning

confidence: 99%

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Structural optimization for nonlinear dynamic response

Dou

Strachan

Shaw

et al. 2015

Phil. Trans. R. Soc. A.

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One contribution of 11 to a theme issue 'A field guide to nonlinearity in structural dynamics' . Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

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“…where the linear modal coupling coefficients α (2) ij and the nonlinear modal coupling coefficients, α (3) ijk and α (4) ijkl , are explicitly expressed as…”

Section: Analysis and Optimization (A) Characterization Theorymentioning

confidence: 99%

“…It is noted that the two quantities ∂α (3) ijk /∂Φ p and ∂α (4) ijkl /∂Φ p are assembled from the corresponding element-wise quantities ∂α (3) ijk /∂φ e p and ∂α (4) ijk /∂φ e p . For convenience of computational implementation, the adjoint equations are expressed in matrix form as…”

Section: (B) Optimization and Sensitivity Analysismentioning

confidence: 99%

Structural optimization for nonlinear dynamic response

Dou

Strachan

Shaw

et al. 2015

Phil. Trans. R. Soc. A.

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show abstract

“…The simplest and probably most commonly used on the micron scale is to use an external electrode that can induce an external potential. If the external potential is modulated in time it can change the effective spring constant of the resonator [24,51,52,66,71,72]. Based on our treatment of this situation in Section 8.1.3, this method is likely to modulate all the coefficients in the potential felt by the resonator, thus also modulating, for example, the Duffing parameter α.…”

Section: Parametric Excitation Of a Damped Duffing Resonatormentioning

confidence: 99%

Nonlinear Dynamics of Nanomechanical Resonators

Lifshitz

Cross

2010

Nonlinear Dynamics of Nanosystems

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“…The relevance of nanotechnology is well recognized, so new developments and applications based on nonlinear dynamics, chaos, fractals, and nonlinear control, are nowadays reached in an interdisciplinary framework [1,2]. Resonant MEMS devices are widely used to measure strain, force or displacement [3][4][5]. Electrostatically actuated resonators have the advantages of simple structures that allow easy batch fabrications and they form a major component in many MEMS devices, such as capacitive switch [3], filter [4], and mass sensor [5].…”

Section: Introductionmentioning

confidence: 99%

“…Resonant MEMS devices are widely used to measure strain, force or displacement [3][4][5]. Electrostatically actuated resonators have the advantages of simple structures that allow easy batch fabrications and they form a major component in many MEMS devices, such as capacitive switch [3], filter [4], and mass sensor [5].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

Zhang

Meng

Wei

2010

Shock and Vibration

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Abstract. In this paper, nonlinear dynamics and chaos of electrostatically actuated MEMS resonators under two-frequency parametric and external excitations are investigated analytically and numerically. A nonlinear mass-spring-damping model is used to accounting for squeeze film damping and the parallel plate electrostatic force. The micro-structure is excited by a dc bias electrostatic force and a harmonic force with a frequency tuned closely to their fundamental natural frequencies (combination oscillation). The quality factor is calculated for the microcantilever beam of the resonator considering squeeze film damping. The effect of nonlinear squeeze film damping on the frequency response, quality factor, resonant frequency and nonlinear dynamic characteristics of the dynamic system are provided with numerical simulations using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait. The results show that the dynamic system goes through a complex nonlinear vibration as the system parameters change. It is indicated that the effect of nonlinear squeeze film damping should be considered due to its decreasing the quality factor and changing the nonlinear phenomena of the MEMS resonators.

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Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Cited by 261 publications

References 26 publications

Structural optimization for nonlinear dynamic response

Structural optimization for nonlinear dynamic response

Nonlinear Dynamics of Nanomechanical Resonators

Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

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