Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

Asadi, Keivan; Li, Junfeng; Peshin, Snehan; Yeom, Junghoon; Cho, Han Na

doi:10.1103/physrevb.96.115306

Cited by 11 publications

(5 citation statements)

References 34 publications

(45 reference statements)

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“…Previous studies [13,14,33] have reported a tuning effect of the electrical nonlinearity and mechanical nonlinearity in silicon-based MEMS by applying dc bias. The electrical nonlinearity is typically produced by electrostatic force [34,35] in plate capacitor, and the mechanical nonlinearity is produced by the intrinsic material and geometric nonlinearity [36,37]. These previous works have reported that the current handling in quartz or silicon MEMS resonators can be explained by the nonlinear A-f dependence effect.…”

Section: Resultsmentioning

confidence: 99%

Tuning the nonlinearity of graphene mechanical resonators by Joule heating

Suo¹,

Li²,

Cheng³

et al. 2022

J. Phys.: Condens. Matter

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As an inherent property of the device itself, nonlinearity in micro-/nano- electromechanical resonators is difficult to eliminate, and it has shown a wide range of applications in basic research, sensing and other fields. While many application scenarios require tunability of the nonlinearity, inherent nonlinearity of a mechanical resonator is difficult to be changed. Here, we report the experimental observation of a Joule heating induced tuning effect on the nonlinearity of graphene mechanical resonators. We fabricated multiple graphene mechanical resonators and detected their resonant properties by an optical interference method. The mechanical vibration of the resonators will enter from the linear to the nonlinear intervals if we enhance the external driving power to a certain value. We found that at a fixed drive power, the nonlinearity of a mechanical resonator can be tuned by applying a dc bias on the resonator itself. The tuning mechanism could be explained by the nonlinear amplitude-frequency dependence theory. Our results may provide a research platform for the study of mechanical nonlinearity by using atomic-thin layer materials.

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Section: Resultsmentioning

confidence: 99%

Tuning the nonlinearity of graphene mechanical resonators by Joule heating

Suo¹,

Li²,

Cheng³

et al. 2022

J. Phys.: Condens. Matter

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“…Finally, changes in the stiffness of the MEMS structure will lead to nonlinearity, and these changes of stiffness can be attained by using certain materials, particularly piezoelectric ones [ 28 ]. These changes in stiffness can also be induced by the use of geometrical nonlinearity, as MEMS devices generally undergo relatively large deformation [ 32 ]. This geometrical nonlinearity can be caused by a wide range of factors, such as large deflections or rotations, initial stresses, or load stiffening.…”

Section: Methodsmentioning

confidence: 99%

Control of Spring Softening and Hardening in the Squared Daisy

et al. 2021

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Nonlinear, mechanical microelectromechanical system (MEMS) resonating structures exhibit large displacement and a relatively broad operating bandwidth. These unique features make them particularly of interest for the development of MEMS actuators and sensors. In this work, a mechanical MEMS structure allowing the designer to determine the type of nonlinearity, that is, softening or hardening, based on its anchor scheme is presented. Effects of the excitation signal on the behavior of the proposed MEMS in the frequency domain are investigated. In this regard, a comprehensive experimental comparison among the nonlinear behaviors of softening and hardening has been conducted. To reduce the hysteresis effect to a minimum, an excitation approach, which is a pulsed sweep in frequency with a discrete resolution, is presented. The maximal velocity, quality factor, bandwidth, and resonant frequency of these two types of nonlinear MEMS resonators are compared under three different types of excitation. Finally, it is shown that the performance and characteristics extracted from nonlinear mechanical MEMS resonating structures are highly dependent on the excitation method. Hence, in the present case, the apparent performances of the MEMS resonator can increase by up to 150% or decrease by up to 21%, depending on the excitation approaches. This implies the necessity of a standardized testing methodology for nonlinear MEMS resonators for given end applications.

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“…In this design, the axial stiffness of the attached polymer component is~40 times lower than that of the Si microbeam. Hence, when the system oscillates, the freestanding polymer component is axially stretched, resulting in geometric nonlinearity 52 . The dimensions of the structural components were deliberately chosen to produce the desired 1:2 ratio between the second and third mode frequencies: the length (L), width (b), and thickness (h) of the silicon microbeam (subscript 1) and polymer coupling (subscript 2) are…”

Section: Experimental Characterization Of Internal Resonancementioning

confidence: 99%

“…The thermomechanical response measured by a laser Doppler vibrometer (LDV) showed that the first three linearized mode frequencies were f 1 ffi 42 kHz; f 2 ffi 107 kHz, and f 3 ffi 214 kHz and that the second and third mode frequency values satisfied the 1:2 relation of commensurability. The strong geometric nonlinearity in the heterogeneous nonprismatic design 52 , combined with the 1:2 ratio between the mode frequencies, triggers the IR in the dynamic response. This outcome implies that the second and third modal responses can be internally coupled if the system is driven hard enough into the nonlinear regime.…”

Section: Experimental Characterization Of Internal Resonancementioning

confidence: 99%

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

2021

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Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefits of IR in micro/nanosystems.

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Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

Cited by 11 publications

References 34 publications

Tuning the nonlinearity of graphene mechanical resonators by Joule heating

Tuning the nonlinearity of graphene mechanical resonators by Joule heating

Control of Spring Softening and Hardening in the Squared Daisy

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

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