Internal Resonance and Localization in Micro-Resonator Arrays

2007 ◽  
Author(s):  
Andrew J. Dick ◽  
Balakumar Balachandran ◽  
C. Daniel Mote
Keyword(s):  
Internal Resonance ◽  
Filter Design ◽  
Nonlinear Behavior ◽  
Vibration Modes ◽  
Intrinsic Localized Modes ◽  
Micro Scale ◽  
Localization Phenomenon ◽  
Resonator Arrays ◽  
Forced Nonlinear Vibration ◽  
The Individual

Intrinsic Localized Modes (ILMs) are localization caused by intrinsic nonlinearities within an array of perfectly periodic oscillators. This localization phenomenon is studied in the context of arrays of coupled micro-scale cantilevers and of coupled piezoelectric micro-scale resonators. Recent studies have identified the individual devices to be capable of producing nonlinear behavior and efforts are currently underway to develop resonator arrays to improve performance capabilities. It is important to determine whether an ILM would limit the performance of such an array and/or if one could take advantage of this type of localization in filter design. Previous studies have shown that it is possible to realize ILMs as forced nonlinear vibration modes. The effects of internal resonance conditions on the behavior of these localization events are explored here using analytical and numerical methods.

Intrinsic Localized Modes and Nonlinear Normal Modes in Micro-Resonator Arrays

2005 ◽  
Author(s):  
A. J. Dick ◽  
B. Balachandran ◽  
C. D. Mote
Keyword(s):  
Normal Modes ◽  
Nonlinear Phenomena ◽  
Strong Nonlinearity ◽  
Nonlinear Phenomenon ◽  
Solid State Physics ◽  
Localized Modes ◽  
Intrinsic Localized Modes ◽  
Micro Scale ◽  
Resonator Arrays ◽  
Nonlinear Normal

In the solid-state physics literature, nonlinear phenomena such as localizations have been studied for a number of decades in lattice structures. These localizations, which occur in periodic and strongly nonlinear discrete systems, have been found to result from a combination of the discreteness and the strong nonlinearity rather than the defects or impurities in the system. Intrinsic Localized Modes (ILMs), which are defined as spatial localization due to strong nonlinearity within arrays of oscillators, have been studied recently in the context of coupled micro-scale cantilevers. Within this paper, the hypothesis that an intrinsic localized mode may be realized as a nonlinear normal mode is explored in order to gain a better understanding of this nonlinear phenomenon. It is believed that an understanding of this phenomenon would be valuable for the design of piezoelectric micro-scale resonator arrays that are being developed for signal processing, communication, and sensor applications.

scholarly journals Understanding permaculturist motivations among residents of the “PermaKulturRaum” in Goettingen, Germany: a qualitative analysis

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Heinrich Petri ◽  
Heiko Faust
Keyword(s):  
Global Scale ◽  
Qualitative Approach ◽  
Childhood Experiences ◽  
Behavioral Determinants ◽  
Individual Level ◽  
Micro Scale ◽  
The Core ◽  
Behavioral Studies ◽  
The Individual

AbstractBy using an inductive qualitative approach, investigating the micro scale, that is, the individual level, we conducted a case study on the PermaKulturRaum in Goettingen, Germany—an experimental space for students to explore alternative lifedesigns. On the supposition that only a radical transition can achieve sustainability on a global scale, we identified permaculture as an appropriate method to achieve this. However, permaculture is not widely spread and largely ignored by scientific research. We started a first attempt to understand the underlying motivations of permaculturists. Using behavioral studies as our theoretical framework, we found out that behavioral determinants, like biospheric values, green-identity, and the intention to act green were extraordinarily high and that the core of their pro-environmental behavior is most likely their strong intrinsic motivation. Regarding the PermaKulturRaum, we could formulate following theses: (1) a comprehensive implementation of permacultural aspects requires an urge for an alternative lifedesign, (2) a radical lifedesign attracts primarily like-minded people, which creates isolated spaces, (3) early childhood experiences or single key moments are important to trigger a pro-environmental interest.

Multistable Cosine-Curved Dome System for Elastic Energy Dissipation

2019 ◽  
Vol 86 (9) ◽  
Author(s):  
Mansour Alturki ◽  
Rigoberto Burgueño
Keyword(s):  
Energy Dissipation ◽  
Analytical Model ◽  
Nonlinear Behavior ◽  
Experimental Tests ◽  
High Energy ◽  
Bistable System ◽  
Dissipated Energy ◽  
Element Analysis ◽  
The Individual ◽  
Hysteretic Response

This paper presents a new energy dissipation system composed of multistable cosine-curved domes (CCD) connected in series. The system exhibits multiple consecutive snap-through and snap-back buckling behavior with a hysteretic response. The response of the CCDs is within the elastic regime and hence the system's original configuration is fully recoverable. Numerical studies and experimental tests were conducted on the geometric properties of the individual CCD units and their number in the system to examine the force–displacement and energy dissipation characteristics. Finite element analysis (FEA) was performed to simulate the response of the system to develop a multilinear analytical model for the hysteretic response that considers the nonlinear behavior of the system. The model was used to study the energy dissipation characteristics of the system. Experimental tests on 3D printed specimens were conducted to analyze the system and validate numerical results. Results show that the energy dissipation mainly depends on the number and the apex height-to-thickness ratio of the CCD units. The developed multilinear analytical model yields conservative yet accurate values for the dissipated energy of the system. The proposed system offered reliable high energy dissipation with a maximum loss factor value of 0.14 for a monostable (self-recoverable) system and higher for a bistable system.

scholarly journals Utilization of 2:1 Internal Resonance in Microsystems

Micromachines ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 448 ◽  
Author(s):  
Navid Noori ◽  
Atabak Sarrafan ◽  
Farid Golnaraghi ◽  
Behraad Bahreyni
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Beam Structure ◽  
Nonlinear Mode Coupling ◽  
T Beam ◽  
Low Frequency Mode

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange’s energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

Micro-Scale Cantilever Testing of Linear Elastic and Elastic-Plastic Materials

2012 ◽  
Vol 525-526 ◽  
pp. 57-60 ◽  
Author(s):  
J.E. Darnbrough ◽  
S. Mahalingam ◽  
Peter E.J. Flewitt
Keyword(s):  
Mechanical Properties ◽  
Single Crystal Silicon ◽  
Ion Milling ◽  
Crystal Silicon ◽  
Micro Scale ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Dual Beam ◽  
The Individual ◽  
Elastic Plastic Materials

t is increasingly a requirement to be able to determine the mechanical properties of materials: (i) at the micro-scale, (ii) that are in the form of surface coatings and (iii) that have nanoscale microstructures. As a consequence micro-scale testing is an important tool that has been developed to aid the evaluation of the mechanical properties of such materials. In this work cantilever beam specimens (typically 2μm by 2μm by 10μm in size) have been prepared by gallium ion milling and then deformed in-situ within a FEI Helios Dual Beam workstation. The latter is achieved using a force probe with a geometry suitable for loading the micro-scale test specimens. Thus force and displacement can be measured together with observing the deformation and fracture of the individual specimens. This paper considers the evaluation of the mechanical properties in particular elastic modulus, yield strength and fracture strength of materials that result in relatively large deflections to the micro-scale cantilever beams. Two materials are considered the first is linear elastic single crystal silicon and the other elastic-plastic nanocrystalline (nc) nickel. The results are discussed with respect to the reproducibility of this method of mechanical testing and the evaluated properties are compared with those derived by alternative procedures.

scholarly journals Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

2021 ◽  
Author(s):  
Gilbert-Rainer Gillich ◽  
Nuno M. M. Maia ◽  
Magd Abdel Wahab ◽  
Cristian Tufisi ◽  
Zoltan-Iosif Korka ◽  
...  
Keyword(s):  
Relative Frequency ◽  
Superposition Principle ◽  
Detection Methods ◽  
Multiple Cracks ◽  
Superposition Method ◽  
Vibration Modes ◽  
Engineering Structures ◽  
Frequency Shifts ◽  
Frequency Drop ◽  
The Individual

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we have found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity trough experiments and thus prove the reliability of the proposed method.

scholarly journals Numerical Modeling of Historic Masonry Structures

2016 ◽  
pp. 27-68
Author(s):  
Panagiotis G. Asteris ◽  
Vasilis Sarhosis ◽  
Amin Mohebkhah ◽  
Vagelis Plevris ◽  
L. Papaloizou ◽  
...  
Keyword(s):  
Structural Component ◽  
Applied Load ◽  
Nonlinear Behavior ◽  
Masonry Walls ◽  
Filling Material ◽  
Masonry Structures ◽  
Historic Masonry ◽  
The Individual ◽  
Masonry Units ◽  
Joint Material

The majority of historical and heritage structures around the world consist of unreinforced masonry walls. A masonry structure is composed of masonry units, such as brick or marble blocks, with or without a joint filling material, such as mortar. A masonry with a joint material is usually made of two different materials (i.e. masonry units and mortar), representing a non-homogeneous and anisotropic structural component. In other words, masonry is a discontinuous structural component whose deformations and failure mechanism are governed by its blocky behavior. Some ancient masonry structures, such as ancient columns and colonnades, are constructed without any form of joint material between the individual blocks. Therefore, the isotropic elastic continuum-based models are not suitable for the simulation of the real nonlinear behavior of masonry walls under applied load.

Effects of Pulsatility on the Laminar Mixing Surface in Converging Microchannel Flows

2002 ◽  
Author(s):  
D. L. Hitt ◽  
M. McGarry ◽  
R. D. Prabhu
Keyword(s):  
Nonlinear Behavior ◽  
Numerical Data ◽  
Interfacial Area ◽  
Interfacial Structure ◽  
Micro Scale ◽  
Flow Mixing ◽  
Laminar Mixing ◽  
Microchannel Flows ◽  
Mixing Techniques ◽  
The Impact

With the growing interest and development of microfluidic systems, the need for micro-scale laminar flow mixing techniques is evident. Traditional mixing methods often rely upon turbulent flow for mixing which is generally not present on the micro-scale and so alternative approaches must be sought. In this work, we report on the impact of flow pulsatility on the laminar mixing surface/interface formed between two converging microchannel flows. The motivation behind the study is to assess the potential for pulsatility as a possible MEMS-mixing strategy. A 3-D computational model of the converging flow at a 90° junction is developed using the Fluent6® CFD software and the volume-of-fluid algorithm is used to track time-dependent behavior of the interface downstream of the junction. Results thus far have shown that for certain parametric regimes a complex, evolving interfacial distortion can form which propagates and persists downstream of the junction. Time-series for the total interfacial area and the interfacial motion have been extracted from numerical data and spectral analyses have been performed; some interesting nonlinear behavior has been observed. Of particular importance, the results also show that the complexity of the interfacial structure is only significant at higher frequencies (order of kHz) which is appropriate for MEMS-based pumping devices.

Speed- and Range-based Filter Design for Dual-Stage Actuator Control

2021 ◽  
pp. 1-9
Author(s):  
James Peyton-Jones ◽  
Aleksandra Mitrovic ◽  
G. M. Clayton
Keyword(s):  
Filter Design ◽  
Low Frequency ◽  
Response Characteristics ◽  
Speed Range ◽  
Dual Stage ◽  
The Individual ◽  
Actuator Control ◽  
Different Characteristics ◽  
Dual Stage Actuator ◽  
First Time

Abstract Dual-stage actuators, which combine two actuators with different characteristics, have gained interest due to their large-range, high-resolution positioning capabilities. Control of such systems is challenging because it requires balancing the relative contributions of the individual actuators in terms of speed, range and precision. The most common approach is to allocate effort to the actuators based on frequency but this can lead to misallocation in the case of low-frequency short-range trajectories. In this paper, the problem of trajectory allocation in dual-stage actuator systems is addressed using a recently developed range-based filter. The theoretical basis of the range-based filter is rigorously derived for the first time and insights regarding its use, specifically its reinterpretation as a speed-based filter, and its range-frequency response characteristics are presented. The new analysis not only explains the behavior of the filter clearly, but it provides a more robust strategy for incorporating range constraints in filter design for different desired trajectories.

One-to-One Internal Resonance of Symmetric Crossply Laminated Shallow Shells

2000 ◽  
Vol 68 (4) ◽  
pp. 640-649 ◽  
Author(s):  
A. Abe ◽  
Y. Kobayashi ◽  
G. Yamada
Keyword(s):  
Internal Resonance ◽  
Shear Deformation Theory ◽  
Primary Resonance ◽  
Vibration Modes ◽  
Driving Frequency ◽  
Shallow Shells ◽  
State Response ◽  
Quadratic Nonlinearities ◽  
Galerkin's Procedure ◽  
Asymmetric Vibration

This paper presents the response of symmetric crossply laminated shallow shells with an internal resonance ω2≈ω3, where ω2 and ω3 are the linear natural frequencies of the asymmetric vibration modes (2,1) and (1,2), respectively. Galerkin’s procedure is applied to the nonlinear governing equations for the shells based on the von Ka´rma´n-type geometric nonlinear theory and the first-order shear deformation theory, and the shooting method is used to obtain the steady-state response when a driving frequency Ω is near ω2. In order to take into account the influence of quadratic nonlinearities, the displacement functions of the shells are approximated by the eigenfunctions for the linear vibration mode (1,1) in addition to the ones for the modes (2,1) and (1,2). This approximation overcomes the shortcomings in Galerkin’s procedure. In the numerical examples, the effect of the (1,1) mode on the primary resonance of the (2,1) mode is examined in detail, which allows us to conclude that the consideration of the (1,1) mode is indispensable for analyzing nonlinear vibrations of asymmetric vibration modes of shells.

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