Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

Vyas, Ashwin; Peroulis, Dimitrios; Bajaj, Anil K.

doi:10.1007/s11071-007-9326-y

Cited by 46 publications

(26 citation statements)

References 28 publications

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“…For verification of the mode shapes, the lowest two natural frequencies and the corresponding mode shapes of the structure shown in Fig. 4(b) were obtained using Hamilton's Principle [5] and compared with the results obtained from FEM and curve fitting. For a more exact description of the application of Hamilton's Principle to the structure shown in Fig.…”

Section: Linear Structure Synthesismentioning

confidence: 99%

“…In the past decade, there has been an increased emphasis on using nonlinear dynamics in the design of MEMS devices [1][2][3]. In particular, the phenomenon of internal resonance has recently attracted attention due to the several advantages it can provide for MEMS based sensing [4,5]. These advantages include extreme sensitivity to perturbations in the measured quantity such as mass and ease of measurement [5].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the phenomenon of internal resonance has recently attracted attention due to the several advantages it can provide for MEMS based sensing [4,5]. These advantages include extreme sensitivity to perturbations in the measured quantity such as mass and ease of measurement [5]. Internal resonance is a nonlinear phenomenon in which transfer of energy can take place between modes depending on the type of nonlinearity present; for example if a system has quadratic nonlinearities and has two of its modal frequencies in ratio of 1:2, then it can exhibit 1:2 internal resonance if the excitation amplitude is above some threshold [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

Tripathi¹,

Bajaj

2013

Journal of Vibration and Acoustics

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Nonlinear phenomena such as internal resonances have significant potential applications in micro electro mechanical systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoreti-cal systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance and that are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer’s prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computation-ally. In this work, a preliminary work on computer based synthesis of structures consist-ing of beams for desired internal resonance is presented. The linear structural design is accomplished by a Finite Element Method (FEM) formulation implemented in MATLAB to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared. [DOI: 10.1115/1.4024845

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Section: Linear Structure Synthesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

Tripathi¹,

Bajaj

2013

Journal of Vibration and Acoustics

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“…The force created by the attraction of opposite charges is well known but infrequently felt at the macro-scale, yet its length-scale dependence is such that it can be very effective at the micro-scale. The RF MEMS community has been very creative with the huge range of device designs [1][2][3], yet the simple geometries of a fixed-fixed beam and a cantilever beam have remained popular, again due to their relative simplicity in implementation. As such, the electrostatically actuated micro beam has become a topic frequented by researchers and covered by many works [4,5] including this one.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Reduced-Order Models of Electrostatically Actuated MEMS Switches and Their Dynamics Including Impact and Bounce

Snow

Bajaj

2010

Volume 4: 12th International Conference on Advanced Vehicle and Tire Technologies; 4th International Conference on Micro- And N

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As MEMS technology develops it is becoming better understood that MEMS designers must account for the large uncertainties characteristic of the relevant manufacturing processes. Uncertainty quantification tasks the designer with evaluating many different possible outcomes from the manufacturing process which creates a demand for models that are accurate and comprehensive, yet fast to evaluate. This work presents a comprehensive reduced-order model of electrostatically actuated switches incorporating a range of effects that are typically included only in FE modeling codes. Specifically, the model accounts for variable electrode geometry, stretching of centerline or large displacement effects, fringing field, squeeze film and rarefied gas damping, and allows for elastic contact with the dielectric substrate. Individual compact models for each of these effects are taken from literature and included in the model for the system. The dielectric substrate is modeled as an elastic foundation. The resulting partial differential equation for the switch modeled as a beam is discritized via a Galerkin method into ordinary differential equations for modal amplitudes. The Galerkin method uses the linear un-damped mode shapes of the beam to approximate the solution. Both cantilever and fixed-fixed type switches are analyzed. Static equilibrium solutions as a function of the applied voltage are developed along with their stability. Static pull-in voltages, first time of switch closure, and voltage for lift-off are studied with the model.

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“…They [22] presented a lumped-parameter model, including the mechanical nonlinearities, and closed-form expressions describing the SIR due to both types of intermodulation. To date, there has been few attempts to develop rigorous models encompassing the mechanical and electric nonlinearities as well as the spatial variation of the constituent structures of MEMS filters [20].…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of electrostatic MEMS filters

2009

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We present an analytical model and closedform expressions describing the response of a tunable MEMS filter made of two electrostatic resonators coupled by a weak microbeam. The model accounts for the filter geometric and electric nonlinearities as well as the coupling between them. It is obtained by discretizing the distributed-parameter system to produce a reduced-order model. We predict the filter deflection and static pull-in voltage by solving a boundary-value problem (BVP). We also solve an eigenvalue problem (EVP) to determine the filter poles (the natural frequencies delineating the filter bandwidth). We found a good agreement between the results obtained using our model and published experimental results. We found that, when the input and output resonators are mismatched, the first mode is localized in the softer resonator whereas the second mode is localized in the stiffer resonator. We demonstrated that mismatch between the resonators can be countermanded by applying different DC voltages to the resonators. As the effective nonlinearities of the filter grow, multi-valued responses appear and distort the filter performance.Once again, we found that the filter can be tuned to operate linearly by choosing a DC voltage that makes the effective nonlinearities vanish.

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Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

Cited by 46 publications

References 28 publications

Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

Comprehensive Reduced-Order Models of Electrostatically Actuated MEMS Switches and Their Dynamics Including Impact and Bounce

Modeling and analysis of electrostatic MEMS filters

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