1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Recent advances in nonlinear passive vibration isolators

Synchronization:a universal concept in nonlinear science

MEMS-based oscillators are an emerging class of highly miniaturized, batch manufacturable timing devices that can rival the electrical performance of well-established quartz-based oscillators. In this review, a description is given of the key properties of a MEMS resonator that determine the overall performance of a MEMS oscillator. Piezoelectric, capacitive and active resonator transduction methods are compared and their impact on oscillator noise and power dissipation is explained. An overview is given of the performance of MEMS resonators and MEMS-based oscillators that have been demonstrated to date. Mechanisms that affect the frequency stability of the resonator, such as temperature-induced frequency drift, are explained and an overview is given of methods that have been demonstrated to improve the frequency stability. The aforementioned performance indicators of MEMS-based oscillators are benchmarked against established quartz and CMOS technologies.

https://iopscience.iop.org/article/10.1088/0960-1317/22/1/013001/pdf

A review of MEMS oscillators for frequency reference and timing applications

formulas for natural frequency and mode shape is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the formulas for natural frequency and mode shape is universally compatible with any devices to read.

Formulas For Natural Frequency And Mode Shape

Nonlinearities in MEMS silicon resonators are caused by different effects. Depending on the resonator layout, different nonlinearities may be dominant in the resonator response. Based on experimental results, a modelling approach is proposed to arrive at a nonlinear dynamic model that potentially captures the observed behaviour. Apart from the model, consisting of a mechanical and an electrical (measurement) part, the effect of thermal noise is also estimated. With the proposed model, a quantitative match between the simulation and experimental results is established such that a good starting point is achieved for a more thorough modelling procedure.

http://www.mate.tue.nl/mate/pdfs/7868.pdf

Modelling the dynamics of a MEMS resonator : simulations and experiments

This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to identify the character of the long term behavior of a nonlinear dynamic system, which may be periodic, quasi-periodic or chaotic. Periodic solutions are calculated efficiently by solving a two-point boundary value problem using finite differences. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. The methods presented are applied to a beam system supported by a one-sided linear spring, which reveals very rich, complex dynamic behavior.

/pdf/long-term-structural-dynamics-of-mechanical-systems-with-36di8wff03.pdf

Long term structural dynamics of mechanical systems with local nonlinearities

By means of a combined analytical-numerical and experimental approach, the nonlinear dynamic behavior of a clamped–clamped beam MEMS resonator has been investigated. A good qualitative correspondence between simulations and experiments has been obtained. First-principles based multiphysics modeling is applied to derive a reduced-order model of the resonator. The model includes nonlinear geometric and electrostatic effects as well as thermoelastic damping. Both simulations and experiments show hardening and softening nonlinear dynamic behavior depending on the excitation parameters. The model captures the observed nonlinear behavior qualitatively and allows for design optimization with respect to nonlinear effects.

http://www.mate.tue.nl/mate/pdfs/11664.pdf

Simulations and experiments of hardening and softening resonances in a clamped-clamped beam MEMS resonator

This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.

/pdf/application-of-a-dynamic-vibration-absorber-to-a-piecewise-4o8bbbir2p.pdf

Application of a dynamic vibration absorber to a piecewise linear beam system

Steady-state behaviour of reduced dynamic systems with local nonlinearities , Steady-state behaviour of reduced dynamic systems with local nonlinearities , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

/pdf/steady-state-behaviour-of-reduced-dynamic-systems-with-local-2kgmm6evz2.pdf

Rhb Rob Fey

Papers

Modelling the dynamics of a MEMS resonator : simulations and experiments

Long term structural dynamics of mechanical systems with local nonlinearities

Simulations and experiments of hardening and softening resonances in a clamped-clamped beam MEMS resonator

Application of a dynamic vibration absorber to a piecewise linear beam system

Steady-state behaviour of reduced dynamic systems with local nonlinearities