The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

Thermoelastic Damping in Micro- and Nano-Mechanical Systems.

Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

/pdf/linear-and-nonlinear-dynamics-of-micro-and-nano-resonators-1pznaruyjr.pdf

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

https://hal.archives-ouvertes.fr/hal-01084700/document

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

A multiphysics model of a hybrid piezoelectric–electromagnetic vibration energy harvester (VEH), including the main sources of nonlinearities, is developed. The continuum problem is derived on the basis of the extended Hamilton principle, and the modal Galerkin decomposition method is used in order to obtain a reduced-order model consisting of a nonlinear Duffing equation of motion coupled with two transduction equations. The resulting system is solved analytically using the method of multiple time scales and numerically by means of the harmonic balance method coupled with the asymptotic numerical continuation technique. Closed-form expressions for the moving magnet critical amplitude and the critical load resistance are provided in order to allow evaluation of the linear dynamic range of the proposed device. Several numerical simulations have been performed to highlight the performance of the hybrid VEH. In particular, the power density and the frequency bandwidth can be boosted, by up to 60% and 29% respectively, compared to those for a VEH with pure magnetic levitation thanks to the nonlinear elastic guidance. Moreover, the hybrid transduction permits enhancement of the power density by up to 84%.

https://iopscience.iop.org/article/10.1088/0964-1726/23/7/075024/pdf

Enhancement of the performance of a hybrid nonlinear vibration energy harvester based on piezoelectric and electromagnetic transductions

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

/pdf/tunable-micro-and-nanomechanical-resonators-4p2t0pybs2.pdf

Tunable Micro- and Nanomechanical Resonators

In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler–Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

/pdf/nonlinear-dynamics-of-nanomechanical-beam-resonators-f4vmpjjunf.pdf

Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors

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Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors