Nonlinear hardening and softening resonances in micromechanical cantilever-nanotube systems originated from nanoscale geometric nonlinearities

Cho, Han Na; Jeong, Bongwon; Yu, Min; Vakakis, Alexander F.; McFarland, D. Michael; Bergman, Lawrence A.

doi:10.1016/j.ijsolstr.2012.04.016

Cited by 59 publications

(40 citation statements)

References 20 publications

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“…In most previous studies, devices have been designed that demonstrate the behaviour of interest, but more recently researchers have started to explore the possibility of tailoring systems for targeted responses. For single-mode resonators, tuning the nonlinear resonances with hardening and softening behaviour is considered by Cho et al [8], where the orientation of a nano-tube connecting two cantilever structures was changed to obtain hardening or softening behaviour, and Dai et al [9], where the impact of topology variation on the hardening behaviour was investigated in dynamic tests of an energy harvesting device. For coupled-mode resonators with internal resonances, Tripathi & Bajaj [10] presented a procedure to synthesize families of structures with two commensurable natural frequencies (such as 1:2 or 1:3 relations).…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Structural optimization for nonlinear dynamic response

Dou

Strachan

Shaw

et al. 2015

Phil. Trans. R. Soc. A.

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“…Finally, a backside deep reactive ion etching (ICP-DRIE) was performed to release the free-standing microcantilever-polymer system. In contrast to the previous works in [31][32][33], where the nonlinear attachments (i.e., BN nanotube) were manually integrated in a one-by-one and strenuous fashion, the proposed device was manufactured by a massively parallel, scalable process, suitable for the practical MEMS applications.…”

Section: System Description and Fabricationmentioning

confidence: 99%

“…For example, authors' previous works have successfully introduced strong geometric nonlinearity by coupling a nanoscale structure such as a boron nitride (BN) nanotube [31,33] or a silicon nano-membrane [32] into a silicon micro-cantilever. However, these systems require the manual integration of nanotube and nanomembrane and, thereby, they are not practical to be integrated into the batchfabricated MEMS devices.…”

Section: Introductionmentioning

confidence: 99%

Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

Asadi

Peshin

et al. 2017

Phys. Rev. B

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Implementation of geometric nonlinearity in micro-electro-mechanical system (MEMS) resonators offers a flexible and efficient design to overcome the limitations of linear MEMS by utilizing beneficial nonlinear characteristics not attainable in a linear setting. Integration of nonlinear coupling elements into an otherwise purely linear microcantilever is one promising way to intentionally realize geometric nonlinearity. Here, we demonstrate that a nonlinear, heterogeneous micro-resonator system, consisting of a silicon micro-cantilever with a polymer attachment exhibits strong nonlinear hardening behavior not only in the first flexural mode but also in the higher modes (i.e., second and third flexural modes). In this design, we deliberately implement a drastic and reversed change in the axial vs. bending stiffness between the Si and polymer components by varying the geometric and material properties. By doing so, the resonant oscillations induce the large axial stretching within the polymer component, which effectively introduces the geometric stiffness and damping nonlinearity. The efficacy of the design and the mechanism of geometric nonlinearity are corroborated through a comprehensive experimental, analytical, and numerical (Finite Element) analysis on the nonlinear dynamics of the proposed system. 2

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“…3 reflects the two different regimes that occur in the dynamics of the flexible connection, namely nonlinear stretching (hardening) above the breaking point x b , and buckling (softening) below the breaking point. Similar hardening/softening behavior of beams, shells and membranes have been studied extensively in the literature in nonlinear vibration problems [20][21][22][23][24].…”

Section: System Descriptionmentioning

confidence: 99%