Bifurcation Analysis of Piezoelectric Bi-Stable Plates

2014 ◽  
Author(s):  
Lihua Chen ◽  
Ma Yepeng ◽  
Wei Zhang
Keyword(s):  
Numerical Simulations ◽  
Phase Portrait ◽  
Bifurcation Analysis ◽  
Nonlinear Dynamic ◽  
Piezoelectric Effect ◽  
Kutta Method ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamic Model ◽  
Piezoelectric Patch ◽  
Runge Kutta Method

The complex nonlinear dynamic behaviors of the composite bi-stable plates with piezoelectric patch are analyzed. Based on the Vo n Karman hypothesis and Hamilton’s principle, the nonlinear dynamic model is derived. Temperature and piezoelectric effect are also considered in the model. Numerical simulations are performed to study the nonlinear vibration response of the composite bi-stable plate using the Runge-Kutta method. The analysis of the phase portrait, waveforms and bifurcation diagrams of numerical simulations shows that the period, multi-period and chaotic responses can be observed with the variation of the excitation in frequency and amplitude.

The Effects of Bearing Stiffness on Nonlinear Dynamic Behaviors of Multi-Mesh Gear Train

2012 ◽  
Author(s):  
T. N. Shiau ◽  
T. H. Young ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. R. Wang
Keyword(s):  
Chaotic Motion ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Time Varying ◽  
Kutta Method ◽  
Dynamic Behaviors ◽  
Runge Kutta Method ◽  
Bearing Stiffness

In this study, the nonlinear dynamic analysis of the multi-mesh gear train with elastic bearing effect is investigated. The gear system includes the three rigid shafts, two gear pairs and elastic bearings. The stiffness and damper coefficient of elastic bearing are considered. The equations of motion of nonlinear time-varying system are derived using Lagrangian approach. The Runge-Kutta Method is employed to determine the system dynamic behaviors including the bifurcation and chaotic motion. The results show that the periodic motion, quasi-periodical motion and chaos can be excited with the elastic bearing effect. Especially, the results also indicate the dynamic response will go from periodic to quasi-periodical before the chaotic motion when the bearing stiffness is increased.

Nonlinear Dynamics Analysis of Gear System Considering Unbalance and Loosening Faults

2014 ◽  
Vol 875-877 ◽  
pp. 1976-1981 ◽  
Author(s):  
Li Cui ◽  
Da Fang Shi ◽  
Jian Rong Zheng ◽  
Xiao Guang Song
Keyword(s):  
Nonlinear Dynamic ◽  
Gear System ◽  
Dynamic Equations ◽  
Radial Clearance ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Diverse Range ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Equations ◽  
Chaos Motion

Considering backlash, radial clearance of bearing and time-varying mesh stiffness, nonlinear dynamic model of gear bearing rotor system is established considering unbalance and loosening fault. Nonlinear dynamic equations are solved using Runge-Kutta method and Newton-Raphson method. Numerical simulations of the dynamic equations and the affection of the depth of crack and length of wear to the nonlinear dynamic behavior are studied. The results shows that tooth off, bilateral impact phenomenon are occurred, with increasing gear failure when unbalance occurs, and the gear system exhibits a diverse range of periodic, quasi-periodic and chaotic motion. When loosening fault occurs, the range of chaos motion is increased, and gear burnishing is also intensified.

Accuracy and Reliability of Piecewise-Constant Method in Studying the Responses of Nonlinear Dynamic Systems

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Liming Dai ◽  
Xiaojie Wang ◽  
Changping Chen
Keyword(s):  
Numerical Methods ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamic Systems ◽  
Processing Unit ◽  
Kutta Method ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Accuracy and reliability of the numerical simulations for nonlinear dynamical systems are investigated with fourth-order Runge–Kutta method and a newly developed piecewise-constant (P-T) method. Nonlinear dynamic systems with external excitations are studied and compared with the two numerical approaches. Semianalytical solutions for the dynamic systems are developed by the P-T approach. With employment of a periodicity-ratio (PR) method, the regions of regular and irregular motions are determined and graphically presented corresponding to the system parameters, for the comparison of accuracy and reliability of the numerical methods considered. Central processing unit (CPU) time executed in the numerical calculations with the two numerical methods are quantitatively investigated and compared under the same computational conditions. Due to its inherent drawbacks, as found in the research, Runge–Kutta method may cause information missing and lead to incorrect conclusions in comparing with the P-T method.

Bifurcation Analysis About a Mathematical Model of Somitogenesis Based on the Runge–Kutta Method

2018 ◽  
Vol 103 (1) ◽  
pp. 221-230
Author(s):  
Linan Guan ◽  
Jianwei Shen
Keyword(s):  
Mathematical Model ◽  
Bifurcation Analysis ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Nonlinear analysis of high accuracy and reliability in traffic flow prediction

2020 ◽  
Vol 9 (1) ◽  
pp. 290-298
Author(s):  
Liming Dai ◽  
Luyao Wang
Keyword(s):  
Traffic Flow ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
High Accuracy ◽  
Kutta Method ◽  
Duffing System ◽  
Traffic Flow Prediction ◽  
Runge Kutta Method ◽  
Flow Prediction ◽  
Nonlinear Dynamic Behavior

AbstractFor quantitatively identifying the chaotic patterns in traffic flow prediction, certain types of Duffing systems can be used. The accuracy and reliability of numerical results of the system’s solution have significant influence on the traffic flow prediction. The nonlinear dynamic behavior of Duffing system used for the traffic flow prediction is investigated in this research. The solutions of the system are developed and solved numerically by using the P-T method. The regular and irregular responses of the system considered are graphically illustrated with the newly developed P-R method. Based on the results of the research, the frequency and amplitude of the external excitations applied on the system significantly affecting the nonlinear dynamic behavior therefore the traffic flow prediction in transferring the results by Wigner-Ville transform. Additionally, a comparison between the P-T and Runge-Kutta method is conducted in regarding the accuracy and reliability of the methods.

Nonlinear Dynamic Buckling for Truncated Sandwich Shallow Conical Shell Structure Subjected to Pulse Impact

2012 ◽  
Vol 252 ◽  
pp. 93-97 ◽  
Author(s):  
Ming Qiao Tang ◽  
Jia Chu Xu
Keyword(s):  
Shell Structure ◽  
Conical Shell ◽  
Nonlinear Dynamic ◽  
Dynamic Buckling ◽  
Physical Parameters ◽  
Kutta Method ◽  
Spherical Shells ◽  
Nonlinear Dynamic Response ◽  
Shallow Conical Shell ◽  
Runge Kutta Method

Nonlinear dynamic buckling for sandwich shallow conical shell structure under uniform triangular pulse is investigated. Based on the Reissner’s assumption and Hamiton’s principle, the nonlinear dynamic governing equation of sandwich shallow spherical shells is derived. The corresponding nonlinear dynamic response equations are obtained by Galerkin method and solved by Runge-Kutta method. Budiansky-Roth criterion expressed by displacements of rigid center is employed to determine the critical impact bucking load. The effects of geometric parameters and physical parameters on impact buckling are discussed.

Transitions of flow past a row of square bars

2000 ◽  
Vol 405 ◽  
pp. 305-323 ◽  
Author(s):  
J. MIZUSHIMA ◽  
Y. KAWAGUCHI
Keyword(s):  
Numerical Simulations ◽  
Flow Pattern ◽  
Bifurcation Analysis ◽  
Pitchfork Bifurcation ◽  
Side Length ◽  
Length Ratio ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Flow Past ◽  
Flow Visualizations

Transitions of flow past a row of square bars placed across a uniform flow are investigated by numerical simulations and the bifurcation analysis of the numerical results. The flow is assumed two-dimensional and incompressible. It is already known that jets coming through gaps between square bars are independent of each other when the pitch-to-side-length ratio of the row is large, whereas the confluence of two or three jets occurs due to a first pitchfork bifurcation from the flow with independent jets when the pitch-to-side-length ratio is small. It is found that confluence of four jets occurs in consequence of the second pitchfork bifurcation from the flow with pairs of jets joined to each other. Bifurcation diagrams of the flow are obtained, which include confluences of double, triple and quadruple jets. Lengths of the twin vortices are evaluated for each flow pattern. The confluences of two, three and four jets are qualitatively confirmed experimentally by flow visualizations.

scholarly journals Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Youhua Qian ◽  
Danjin Zhang ◽  
Bingwen Lin
Keyword(s):  
Numerical Simulations ◽  
Phase Portrait ◽  
Time Scales ◽  
Bifurcation Analysis ◽  
Hot Spot ◽  
Periodic Excitation ◽  
Fast Subsystem ◽  
Van Der Pol ◽  
Bursting Oscillations ◽  
Bursting Oscillation

The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing–Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow-varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow-varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold/fold bursting, symmetric fold/supHopf bursting, symmetric subHopf/fold cycle bursting, and symmetric subHopf/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.

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