Optimization of nonlinear structural resonance using the incremental harmonic balance method

Dou, Suguang; Jensen, Jakob Søndergaard

doi:10.1016/j.jsv.2014.08.023

Cited by 40 publications

(34 citation statements)

References 49 publications

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“…In these optimizations, the objective function is increased by a factor of 13 and reduced by a factor of 4, respectively. The optimized designs are in accordance with the results in [18], obtained using the incremental harmonic balance method, where we found the nonlinear strain energy due to mid-plane stretching reaches its local maximum around x = 1 4 L and x = 3 4 L, which is precisely where the optimized structures are altered most significantly relative to their general thickness. Furthermore, the eigenfrequency of the first flexural mode decreases during optimization of maximizing the cubic nonlinearity, and increases during optimization of minimizing the cubic nonlinearity.…”

Section: Examplessupporting

confidence: 86%

“…The initial design has a uniform in-plane thickness of 4 µm and is discretized with 400 beam elements as described in [18]. During shape optimization, the in-plane thickness h is varied to tailor the cubic nonlinearity in the reduced-order model.…”

Section: Examplesmentioning

confidence: 99%

“…The linear and nonlinear formulation of the beam element used here can be found in article [18]. Its nonlinear modal coupling coefficients in the Hamiltonian H can be written as α (3) ijk =…”

Section: Appendix Amentioning

confidence: 99%

“…In previous research, it has been applied in nonlinear structural dynamics to optimize the amplitude of transient responses [13,14], periodic responses [15,16] and also eigenfrequencies of deformed structures with geometrical nonlinearities [17]. For a clamped-clamped beam, optimal shape design associated with nonlinear frequency responses, including primary resonances and superharmonic resonances, was studied by Dou & Jensen [18] using the incremental harmonic balance method. Another related work is the optimal shape design of comb fingers for electrostatic forces as investigated by Ye et al [19], which produced combinations of linear, quadratic and cubic driving-force profiles.…”

Section: Introductionmentioning

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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Section: Examplessupporting

confidence: 86%

Section: Examplesmentioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

Section: Introductionmentioning

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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“…In the recent years, substantial efforts have been put forth to tailor the strength of structural nonlinearity [18,28,29]. Saghafi et al [28] provided an analytical scheme based on a continuous system model to predict the onset of nonlinearity in a bilayer clamped-clamped micro-beam to enhance the working dynamic range.…”

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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An Improved Formulation for Structural Optimization of Nonlinear Dynamic Response

Dou

2021

NODYCON Conference Proceedings Series

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Nonlinear dynamics is widely exploited in micro-mechanical resonators with a number of applications. One of the crucial issues in these applications is to intentionally tailor the intrinsic nonlinearity in these structures. In this study, a structural optimization methodology is improved for tailoring the intrinsic nonlinearity in these resonators by manipulating their structural geometry. In the optimization, the objective function is defined based on the nonlinear modal coupling coefficients as well as eigenfrequencies and modal shapes of the vibration modes. A preliminary study shows that the improved formulation of the optimization problem enables better designs.

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Optimization of nonlinear structural resonance using the incremental harmonic balance method

Cited by 40 publications

References 49 publications

Structural optimization for nonlinear dynamic response

Structural optimization for nonlinear dynamic response

Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

An Improved Formulation for Structural Optimization of Nonlinear Dynamic Response

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