Study on the Topology Structure and Evolvement Analysis of Nonlinear Model under Superharmonic Resonance

2011 ◽  
Vol 58-60 ◽  
pp. 73-78
Author(s):  
Jun Hai Ma ◽  
Qi Zhang
Keyword(s):  
Approximate Solution ◽  
Nonlinear Model ◽  
Oscillation Amplitude ◽  
Driving Frequency ◽  
System Quality ◽  
System Complexity ◽  
First Order ◽  
Complex Systems Theory ◽  
Inherent Frequency ◽  
Research Findings

Based on the work of domestic and foreign scholars and the application of complex systems theory, we study the first-order approximate solution of a category nonlinear model, and the intrinsic complex relationship among oscillation amplitude, phase, the system inherent damping parameters, driven amplitudeand driving frequency of approximate solution under the circumstances of system quality resonance that incentive frequency of nonlinear model which is far away from system inherent frequency when . We also study the evolution process of system complexity with different combination of factors , and have got some useful research findings.

Nonlinear dynamics of a shell encapsulated microbubble near solid boundary in an ultrasonic field

2020 ◽  
Vol 14 (3) ◽  
pp. 7235-7243
Author(s):  
N.M. Ali ◽  
F. Dzaharudin ◽  
E.A. Alias
Keyword(s):  
Oscillation Amplitude ◽  
Ultrasonic Field ◽  
Dynamical Behaviour ◽  
Ultrasound Contrast Agents ◽  
Chaotic Behaviour ◽  
Solid Boundary ◽  
Driving Frequency ◽  
Pressure Amplitude ◽  
Radial Expansion ◽  
Therapeutic Delivery

Microbubbles have the potential to be used for diagnostic imaging and therapeutic delivery. However, the transition from microbubbles currently being used as ultrasound contrast agents to achieve its’ potentials in the biomedical field requires more in depth understanding. Of particular importance is the influence of microbubble encapsulation of a microbubble near a vessel wall on the dynamical behaviour as it stabilizes the bubble. However, many bubble studies do not consider shell encapsulation in their studies. In this work, the dynamics of an encapsulated microbubble near a boundary was studied by numerically solving the governing equations for microbubble oscillation. In order to elucidate the effects of a boundary to the non-linear microbubble oscillation the separation distances between microbubble will be varied along with the acoustic driving. The complex nonlinear vibration response was studied in terms of bifurcation diagrams and the maximum radial expansion. It was found that the increase in distance between the boundary and the encapsulated bubble will increase the oscillation amplitude. When the value of pressure amplitude increased the single bubble is more likely to exhibit the chaotic behaviour and maximum radius also increase as the inter wall-bubble distance is gradually increased. While, with higher driving frequency the maximum radial expansion decreases and suppress the chaotic behaviour.

scholarly journals Perturbation Solution for One-Dimensional Flow to a Constant-Pressure Boundary in a Stress-Sensitive Reservoir

2021 ◽  
Author(s):  
Amarjot Singh Bhullar ◽  
Gospel Ezekiel Stewart ◽  
Robert W. Zimmerman
Keyword(s):  
Approximate Solution ◽  
Pore Pressure ◽  
Constant Pressure ◽  
Initial Permeability ◽  
Order Perturbation ◽  
Zeroth Order ◽  
One Dimensional ◽  
First Order ◽  
Outflow Boundary ◽  
Perturbation Solutions

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.

scholarly journals Direct solution of uncertain bratu initial value problem

2019 ◽  
Vol 9 (6) ◽  
pp. 5075
Author(s):  
N. R. Anakira ◽  
A. H. Shather ◽  
A. F. Jameel ◽  
A. K. Alomari ◽  
A. Saaban
Keyword(s):  
Approximate Solution ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Approximate Analytical Solution ◽  
Order System ◽  
Direct Solution ◽  
Initial Value ◽  
First Order ◽  
Bratu Equation ◽  
Variation Iteration Method

<span>In this paper, an approximate analytical solution for solving the fuzzy Bratu equation based on variation iteration method (VIM) is analyzed and modified without needed of any discretization by taking the benefits of fuzzy set theory. VIM is applied directly, without being reduced to a first order system, to obtain an approximate solution of the uncertain Bratu equation. An example in this regard have been solved to show the capacity and convenience of VIM.</span>

A Perturbation Analysis of the Wavemaking of a Ship, with an Interpretation of Guilloton’s Method

1975 ◽  
Vol 19 (03) ◽  
pp. 140-148
Author(s):  
F. Noblesse
Keyword(s):  
Approximate Solution ◽  
Free Surface ◽  
Perturbation Analysis ◽  
Order Approximation ◽  
Second Order ◽  
Regular Perturbation ◽  
First Order ◽  
Perturbation Problem ◽  
Sinkage And Trim ◽  
Basic Ideas

A thin-ship perturbation analysis, suggested by Guilloton's basic ideas, is presented. The analysis may be regarded as an application of Lighthill's method of strained coordinates to a regular perturbation problem. An inconsistent second-order approximation in which the Laplace equation is satisfied to first order, and the boundary conditions both at the free surface and on the ship hull are satisfied to second order, is derived. When sinkage and trim, incorporated into the present analysis, are ignored, this approximate solution is shown to be essentially equivalent to the method of Guilloton.

scholarly journals An Evolutionary Analytic Method of Multi-DOF Nonlinear Coupling Dynamic Model for Controllable Close-Chain Linkage Mechanism System

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Ru-Gui Wang ◽  
Gan-Wei Cai ◽  
Xiao-Rong Zhou
Keyword(s):  
Approximate Solution ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Dynamic Responses ◽  
Analytic Method ◽  
Nonlinear Coupling ◽  
Linkage Mechanism ◽  
First Order ◽  
Coupling System ◽  
Coupling Dynamic

The 2-DOF controllable close-chain linkage mechanism is investigated in this paper. Based on the characteristics of the multi-DOF nonlinear coupling dynamic equation of the system established by the finite element method, an analytic method of multiple-scales Newmark is presented after thinking about the method of perturbation and the method of numerical analysis. Firstly, the first-order approximate solution of the dynamic responses of the system at the time of t is calculated by the multiple scales method. Then, taken the first-order approximate solution as the initialization of the generalized coordinate of the system, the stable dynamic response of the system is obtained by the implicit Newmark method. The simulation and experimental results are given in the end. The studies indicate that the method of multiple-scales Newmark is correct and practicable to study the dynamic characteristics of such kind of multi-DOF nonlinear coupling system.

Diagnostics on nonlinear model with scale mixtures of skew-normal and first-order autoregressive errors

Statistics ◽  
2013 ◽  
Vol 48 (5) ◽  
pp. 1033-1047 ◽  
Author(s):  
Chun-Zheng Cao ◽  
Jin-Guan Lin ◽  
Jian-Qing Shi
Keyword(s):  
Nonlinear Model ◽  
First Order ◽  
Scale Mixtures ◽  
Autoregressive Errors ◽  
Skew Normal
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