Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis

1995 ◽  
Author(s):  
Muhammad R. Hajj ◽  
Ali H. Nayfeh ◽  
Pavol Popovic
Keyword(s):  
Experimental Study ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Analytical Techniques ◽  
Modal Interactions ◽  
Unknown Parameters ◽  
Nonlinear Parameters ◽  
The Subject ◽  
Beam Frame ◽  
Subharmonic Resonances

Abstract Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.

scholarly journals Experimental study of isolas in nonlinear systems featuring modal interactions

PLoS ONE ◽  
2018 ◽  
Vol 13 (3) ◽  
pp. e0194452 ◽  
Author(s):  
Thibaut Detroux ◽  
Jean-Philippe Noël ◽  
Lawrence N. Virgin ◽  
Gaëtan Kerschen
Keyword(s):  
Experimental Study ◽  
Nonlinear Systems ◽  
Modal Interactions

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

Study on the working state of the five hundred-meter aperture spherical telescope using step-wise assignment method

2014 ◽  
Vol 229 (2) ◽  
pp. 316-324 ◽  
Author(s):  
Yu Liu ◽  
Feng Gao
Keyword(s):  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Driving Mechanism ◽  
Initial Value ◽  
Unknown Parameters ◽  
Support Structure ◽  
Assignment Method ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model

The working state of the five hundred-meter aperture spherical telescope (FAST) is solved using the step-wise assignment method. In this paper, the mathematical model of the cable-net support structure of the FAST is set up by the catenary equation. There are a large number of nonlinear equations and unknown parameters of the model. The nonlinear equations are solved by using the step-wise assignment method. The method is using the analytical solutions of the cable-net equations of one working state as the initial value for the next working state, from which the analytical solutions of the nonlinear equations of the cable-net for each working state of the FAST and the tension and length of each driving cable can be obtained. The suggested algorithm is quite practically well suited to study the working state of the cable-net structures of the FAST. Also, the working state analysis result of the cable-net support structure of a reduced model of the cable-net structure reflector for the FAST is given to verify the reliability of the method. In order to show the validity of the method, comparisons with another algorithm to set the initial value are presented. This method has an important guiding significance to the further study on the control of the new type of flexible cable driving mechanism, especially the FAST.

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

Two-dimensional buoyant plumes in a uniform co-flow

2021 ◽  
Vol 932 ◽  
Author(s):  
Gary R. Hunt ◽  
Jamie P. Webb
Keyword(s):  
Theoretical Investigation ◽  
Analytical Solutions ◽  
Richardson Number ◽  
Relative Magnitude ◽  
Dynamical Behaviour ◽  
Finite Width ◽  
Two Dimensional ◽  
Buoyant Plumes ◽  
The Subject ◽  
Flow Case

The behaviour of turbulent, buoyant, planar plumes is fundamentally coupled to the environment within which they develop. The effect of a background stratification directly influences a plumes buoyancy and has been the subject of numerous studies. Conversely, the effect of an ambient co-flow, which directly influences the vertical momentum of a plume, has not previously been the subject of theoretical investigation. The governing conservation equations for the case of a uniform co-flow are derived and the local dynamical behaviour of the plume is shown to be characterised by the scaled source Richardson number and the relative magnitude of the co-flow and plume source velocities. For forced, pure and lazy plume release conditions the co-flow acts to narrow the plume and reduce both the dilution and the asymptotic Richardson number relative to the classic zero co-flow case. Analytical solutions are developed for pure plumes from line sources, and for highly forced and highly lazy releases from sources of finite width in a weak co-flow. Contrary to releases in quiescent surroundings, our solutions show that all classes of release can exhibit plume contraction and the associated necking. For entraining plumes, a dynamical invariance spatially only occurs for pure and forced releases and we derive the co-flow strengths that lead to this invariance.

scholarly journals THE EFFECT OF DEFINITIONS TOWARD STUDENTS’ VOCABULARY

2018 ◽  
Vol 6 (1) ◽  
pp. 34
Author(s):  
Tawali Tawali
Keyword(s):  
Experimental Study ◽  
Alternative Hypothesis ◽  
T Test ◽  
Second Grade ◽  
Control Group ◽  
Second Grade Students ◽  
Post Test ◽  
The Subject ◽  
And Control ◽  
Experimental Group

This research is aimed to find out the effect of definitions toward students’ vocabulary mastery: it was an experimental study at the second grade student of MTs NW Haqqul Yaqin Sayang- sayang. The subject of this research was the second grade of MTs NW Haqqul Yaqin Sayang- sayang.The research was used experimental method with quantitative approach. The population of this research consist of 55 students, and the sample is 29 for experimental group while 26 for control group. The technique of collecting data was used definition for experimental group and matching word with antonym for control group. The data was collected by using post-test only and the data was analyzed by t-test formula. Based on data analysis the mean score of experimental group was 76,4 and control group was 69,23, beside of that standard deviation for experimental group was 114,28 and for control group was 113,09 and the value of t-test was 2,44 and t-table was 2,000. Degree of freedom is 53 with significant level 0,05. It means that the value of t-test was higher than t-table (t-test ˃ t-table). The alternative hypothesis (Ha) was accepted and null hypothesis (Ho) was rejected. Thus, the conclusion of this research was there was an effect of definition toward students’ vocabulary mastery: an experimental study at the second grade students of MTs NW Haqqul Yaqin Sayang-sayang.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Teaching Vocabulary through Fly Swatter Game

2019 ◽  
Vol 2 (1) ◽  
pp. 17
Author(s):  
Hikmah Noerqori Saputra ◽  
Muhamad Sofian Hadi
Keyword(s):  
Experimental Study ◽  
Test Scores ◽  
Quantitative Method ◽  
T Test ◽  
Significant Difference ◽  
Post Test ◽  
The Subject ◽  
Academic Year ◽  
Experimental Group

The study aimed to find out whether fly swatter game can give influence toward students’ vocabulary mastery. The subject of this study was grade VII-2 of SMPN 9 Tangerang Selatan in the academic year of 2018/2019, which consisted of 42 students. The method used in this study is a quantitative method with the design of the pre-experimental study. The data from pre-test and post-test were analyzed statistically using spss 16. The result of this study showed; the students’ pre-test mean score was 45.4 and the students’ post-test mean score was 86.6. The result of t-test was 21.55 and significant (2-tailed) was 0.00 < p (0.05). The hypothesis (H1) was accepted, which means there is a significant difference between pre-test and post-test scores of the experimental group. It can be concluded that applying fly swatter game in teaching vocabulary to 7th grade students of SMPN 9 Tangerang Selatan is effective.

scholarly journals Mandelbrot, Fama and the emergence of econophysics

2016 ◽  
Vol 35 (69) ◽  
pp. 637-662
Author(s):  
Boris Salazar Trujillo
Keyword(s):  
Analytical Solutions ◽  
Financial Economics ◽  
Analytical Techniques ◽  
Infinite Variance ◽  
Pareto Distributions

It is argued that Mandelbrot's stable Lévy-Pareto distributions were not accepted into the emerging field of financial economics due to their incompatibility with the analytical techniques and properties of equilibrium economics, and to the absence -both in physics and in economics- of analytical solutions to the infinite variance associated with those distributions. Whilst physicists made stable Lévy distributions plausible, creating Econophysics in the meantime, economists just forgot about them, suggesting their strong bias towards desirable properties and against established facts.

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