scholarly journals Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190532 ◽  
Author(s):  
Igor V. Andrianov ◽  
Vladyslav V. Danishevskyy ◽  
Graham Rogerson
Keyword(s):  
High Frequency ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Finite Size ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Energy Transfers ◽  
Fourth Order Method ◽  
Nonlinear Elastic

We aim to study how the interplay between the effects of nonlinearity and heterogeneity can influence on the distribution and localization of energy in discrete lattice-type structures. As the classical example, vibrations of a cubically nonlinear elastic lattice are considered. In contrast with many other authors, who dealt with infinite and periodic lattices, we examine a finite-size model. Supposing the length of the lattice to be much larger than the distance between the particles, continuous macroscopic equations suitable to describe both low- and high-frequency motions are derived. Acoustic and optical vibrations are studied asymptotically by the method of multiple time scales. For numerical simulations, the Runge–Kutta fourth-order method is employed. Internal resonances and energy exchange between the vibrating modes are predicted and analysed. It is shown that the decrease in the number of particles restricts energy transfers to higher-order modes and prevents the equipartition of energy between all degrees of freedom. The conditions for a possible reduction in the original nonlinear system are also discussed.

Nycthemeral Rhythm of the Frequency and Biomechanical Energy of High Frequency Intraocular Pressure Fluctuations

2013 ◽  
Author(s):  
Vincent Libertiaux ◽  
William P. Seigfreid ◽  
Massimo A. Fazio ◽  
Juan F. Reynaud ◽  
Claude F. Burgoyne ◽  
...  
Keyword(s):  
Intraocular Pressure ◽  
High Frequency ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Pulse Amplitude ◽  
Mean Value ◽  
Multiple Time Scales ◽  
Dynamic Contour Tonometry ◽  
Multiple Time ◽  
Ocular Pulse

The optic nerve head (ONH) is the site of insult in glaucoma, the second leading cause of blindness worldwide. Intraocular pressure (IOP) is commonly regarded as a major factor in the onset and progression of the disease1 and lowering IOP is the only clinical treatment that has been shown to retard the onset and progression of glaucoma2. However, many patients continue to progress even at an epidemiologically-determined normal level of IOP3. This suggests that in addition to the mean value of IOP, IOP fluctuations could be a factor in glaucomatous pathophysiology. The importance of low frequency fluctuations of clinically-measured mean IOP remains controversial. These studies all rely on snapshot measurements of mean IOP at each time point, and those measurements are taken at relatively infrequent intervals (hourly at the most frequent, but usually monthly or longer). Recently however, there has been some interest in ocular pulse amplitude, or the fluctuation in IOP associated with the cardiac cycle, which can be measured by Dynamic Contour Tonometry (DCT). DCT provides continuous measurement of IOP, but only for a period of tens of seconds in which a patient can tolerate corneal contact without blinking or eye movement, which ironically are two of the most common sources of large high frequency IOP fluctuations according to our telemetric data collected from monkeys4 and previous human studies. In a recent report, continuous IOP telemetry was used in three nonhuman primates to characterize IOP dynamics at multiple time scales for multiple 24-hour periods5.

Nonlinear Dynamic Response of a Thin Plate in a Fractional Viscoelastic Medium under Internal Resonance 1:1:2

2014 ◽  
Vol 518 ◽  
pp. 60-65 ◽  
Author(s):  
Yury Rossikhin ◽  
Marina Shitikova
Keyword(s):  
Nonlinear Equations ◽  
Time Scales ◽  
Viscoelastic Medium ◽  
Equations Of Motion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Nonlinear Dynamic Response ◽  
New Approach ◽  
New Type

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the internal resonances two-to-one has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find a new type of the internal resonanse, i.e., one-to-one-to-two, as well as to solve the problems of vibrations of thin bodies more efficiently.

scholarly journals Quantifying the Multiscale Predictability of Financial Time Series by an Information-Theoretic Approach

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 684 ◽  
Author(s):  
Xiaojun Zhao ◽  
Chenxu Liang ◽  
Na Zhang ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
High Frequency ◽  
Stock Price ◽  
Financial Time Series ◽  
High Frequency Data ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Information Theoretic ◽  
Daily Data ◽  
Wide Range

Making predictions on the dynamics of time series of a system is a very interesting topic. A fundamental prerequisite of this work is to evaluate the predictability of the system over a wide range of time. In this paper, we propose an information-theoretic tool, multiscale entropy difference (MED), to evaluate the predictability of nonlinear financial time series on multiple time scales. We discuss the predictability of the isolated system and open systems, respectively. Evidence from the analysis of the logistic map, Hénon map, and the Lorenz system manifests that the MED method is accurate, robust, and has a wide range of applications. We apply the new method to five-minute high-frequency data and the daily data of Chinese stock markets. Results show that the logarithmic change of stock price (logarithmic return) has a lower possibility of being predicted than the volatility. The logarithmic change of trading volume contributes significantly to the prediction of the logarithmic change of stock price on multiple time scales. The daily data are found to have a larger possibility of being predicted than the five-minute high-frequency data. This indicates that the arbitrage opportunity exists in the Chinese stock markets, which thus cannot be approximated by the effective market hypothesis (EMH).

scholarly journals New Approach for the Analysis of Damped Vibrations of Fractional Oscillators

2009 ◽  
Vol 16 (4) ◽  
pp. 365-387 ◽  
Author(s):  
Yuriy A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Time Derivative ◽  
Fractional Power ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Derivative Term ◽  
Mechanical Oscillators ◽  
Definition Of ◽  
Nonlinear Elastic

The dynamic behavior of linear and nonlinear mechanical oscillators with constitutive equations involving fractional derivatives defined as a fractional power of the operator of conventional time-derivative is considered. Such a definition of the fractional derivative enables one to analyse approximately vibratory regimes of the oscillator without considering the drift of its position of equilibrium. The assumption of small fractional derivative terms allows one to use the method of multiple time scales whereby a comparative analysis of the solutions obtained for different orders of low-level fractional derivatives and nonlinear elastic terms is possible to be carried out. The interrelationship of the fractional parameter (order of the fractional operator) and nonlinearity manifests itself in full measure when orders of the small fractional derivative term and of the cubic nonlinearity entering in the oscillator's constitutive equation coincide.

An Alternative Perturbation Procedure of Multiple Scales for Nonlinear Dynamics Systems

1989 ◽  
Vol 56 (3) ◽  
pp. 667-675 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
Shuhui Chen
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Steady State Solution ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Almost Periodic ◽  
Perturbation Procedure ◽  
Incremental Harmonic Balance

An alternative perturbation procedure of multiple scales is presented in this paper which is capable of treating various periodic and almost periodic steady-state vibrations including combination resonance of nonlinear systems with multiple degrees-of-freedom. This procedure is a generalization of the Lindstedt-Poincare´ method. To show its essential features a typical example of cubic nonlinear systems, the clamped-hinged beam, is analyzed. The numerical results for the almost periodic-free vibration are surprisingly close to that obtained by the incremental harmonic balance (IHB) method, and the analytical formulae for steady-state solution are, in fact, identical with that of conventional method of multiple time scales. Moreover, detail calculations of this example revealed some interesting behavior of nonlinear responses, which is of significance for general cubic systems.

scholarly journals INTEREST GROUP SESSION—MEASUREMENT, STATISTICS, AND RESEARCH DESIGN: ANALYSIS OF DEVELOPMENTAL AND COMPLEX SYSTEMS: UNDERSTANDING THE DYNAMICS OF AGING

2019 ◽  
Vol 3 (Supplement_1) ◽  
pp. S376-S376
Author(s):  
Xiao Yang ◽  
Nilam Ram ◽  
Nilam Ram
Keyword(s):  
Complex Systems ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Developmental Trajectories ◽  
Dynamic Change ◽  
System Thinking ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Regulation Model

Abstract Aging is the product of numerous dynamic processes that span multiple domains of functioning (e.g., biological, psychological, social), multiple levels of analysis, and multiple time-scales. Scientific inquiry in many fields has benefited from articulation and analysis of complex systems. This symposium brings together a collection of papers that illustrate how dynamical systems modeling is contributing to both theory and understanding of aging. Yang and colleagues apply Boolean network approach to intensive longitudinal data to identify sequences of emotion and behavior that lead to a stable equilibrium, and suggest how that information can be used to design interventions that push individuals toward a healthier equilibrium. Rector and colleagues illustrate use of dynamic indicators and multiscale entropy measures as indicators of resilience and explain how those measures may be used in prediction of physical recovery. Brick highlights how sequence mining methods can be used to identify commonalities and differences in dynamic change, and how those patterns characterize and distinguish groups with respect to aging trajectories. Moulder and colleagues demonstrate how latent maximum Lyapunov exponents can be used to study sensitivity of individuals’ developmental trajectories to initial conditions. Boker and colleagues provide a general overview of how dynamic models, including an adaptive equilibrium regulation model, distinguish resilience to acute versus chronic stressors and patterns of regulation. Together these papers highlight the value complex system thinking can add to our understanding and optimization of aging.

Nonlinear Dynamic Response of a Thin Plate Embedded in a Fractional Viscoelastic Medium under Combinational Internal Resonances

2014 ◽  
Vol 595 ◽  
pp. 105-110 ◽  
Author(s):  
Yury Rossikhin ◽  
Marina Shitikova
Keyword(s):  
Nonlinear Equations ◽  
Time Scales ◽  
Viscoelastic Medium ◽  
Equations Of Motion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Nonlinear Dynamic Response ◽  
New Approach ◽  
Difference Type

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the combinational internal resonances of the additive and difference types has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in [2] allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find an additional combinational resonance of the additive-difference type, as well as to solve the problems of vibrations of thin bodies more efficiently.

A beam–ring circular truss antenna restrained by means of the negative speed feedback procedure

2021 ◽  
pp. 107754632110036
Author(s):  
Ashraf T EL-Sayed Taha ◽  
Hany S Bauomy
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Nonlinear Partial Differential Equations ◽  
Time Frame ◽  
Ring Structure ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Averaged Equations ◽  
Fractional Differential

The present article contemplates the nonlinear powerful exhibitions of affecting dynamic vibration controller over a beam–ring structure for demonstrating the circular truss antenna exposed to mixed excitations. The dynamic controller comprises the included negative speed input added to the framework’s idea. By using the statue, Hamilton, the nonlinear fractional differential administering conditions of movement and the limit conditions have inferred for the shaft ring structure. Through Galerkin’s method, the nonlinear partial differential equations referred to overseeing the movement of the shaft ring structure have diminished to a coupled normal differential equations extending the nonlinearities square terms. Multiple time scales have helped in acquiring (getting) the four-dimensional averaged equations for measuring the primary and 1:2 internal resonances. This article’s controlled assessment is useful for controlling the nonlinear vibrations of the considered framework. Likewise, the controller dispenses with the framework’s oscillations in a brief time frame. The demonstrations of the numerous coefficients and the framework directed at the examined resonance case have been determined. Using MATLAB 7.0 programs has aided in completing the simulation results. At last, the numerical outcomes displayed an admirable concurrence with the methodical ones. A comparison with recently available articles has also indicated good results through using the presented controller.

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