Phase Difference in Lateral Synchronization of Pedestrian Floors Using a Modified Hybrid Van der pol/Rayleigh Oscillator

2016 ◽  
Vol 16 (08) ◽  
pp. 1550042 ◽  
Author(s):  
Anil Kumar ◽  
Silvano Erlicher ◽  
Pierre Argoul
Keyword(s):  
Experimental Data ◽  
Phase Difference ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Lateral Motion ◽  
Periodic Excitation ◽  
External Excitation ◽  
Van Der Pol ◽  
Autonomous Case ◽  
The Given

The modified hybrid Van der Pol/Rayleigh (MHVR) oscillator was originally proposed by the authors to model the lateral oscillations of a pedestrian walking on a rigid floor and it was shown that for the autonomous case, the MHVR oscillator can correctly fit the experimental data. The case of a pedestrian walking on a laterally moving floor is modeled by a nonautonomous oscillator. The case of a floor subjected to a harmonic lateral motion has been then studied by the authors, with focus on the amplitude and stability of the entrained response, i.e. the response having the same frequency as that of the given periodic excitation. For the nonautonomous (moving floor) case, the main focus of this paper is on the analysis of the phase difference between the oscillator entrained response and the external excitation. Both analytical and numerical calculations have been performed. The approximate analytical method is the harmonic balance method. Then, the model is used to represent the experimental results for the pedestrian lateral oscillations during walking. Comparison is made for the examples along with discussions.

scholarly journals Frequency characteristics of the fractional oscillator Van der Pol

2019 ◽  
Vol 127 ◽  
pp. 02010
Author(s):  
Roman Parovik
Keyword(s):  
Quality Factor ◽  
Harmonic Balance ◽  
Fractional Derivatives ◽  
Harmonic Balance Method ◽  
Oscillatory System ◽  
Frequency Characteristics ◽  
Van Der Pol ◽  
Fractional Oscillator ◽  
Analytical Formulas ◽  
Frequency Phase

Into this paper, the amplitude-frequency and phase-frequency characteristics of the Van der Polar fractional oscillator are studied in order to establish their relationship with the orders of fractional derivatives included in the model equation. Using the harmonic balance method, analytical formulas were obtained for the amplitude-frequency, phase-frequency characteristics, as well as the quality factor – the energy characteristic of the oscillatory system. It was shown that the quality factor depends on the orders of fractional derivatives, and change in their values can lead to both an increase and a decrease in the quality factor.

The Residue Harmonic Balance Method for Duffing-Van Der Pol Oscillator with Fractional Derivative

2013 ◽  
Vol 774-776 ◽  
pp. 103-106
Author(s):  
Xin Xue ◽  
Lian Zhong Li ◽  
Dan Sun
Keyword(s):  
Fractional Derivative ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Balance Method ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Fractional Orders

Duffing-van der Pol oscillator with fractional derivative was constructed in this paper. The solution procedure was proposed with the residue harmonic balance method. The effect of different fractional orders on resonance responses of the system in steady state were analyzed for an example without parameters. The approximate solutions were contrasted with numerical solutions. The results show that the residue harmonic balance method to Duffing-van der Pol differential equation with fractional derivative is very valid.

NEIMARK BIFURCATIONS OF A GENERALIZED DUFFING–VAN DER POL OSCILLATOR WITH NONLINEAR FRACTIONAL ORDER DAMPING

2013 ◽  
Vol 23 (11) ◽  
pp. 1350177 ◽  
Author(s):  
A. Y. T. LEUNG ◽  
H. X. YANG ◽  
P. ZHU
Keyword(s):  
Fractional Order ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Viscoelastic Behavior ◽  
Higher Order ◽  
Balance Method ◽  
Van Der Pol Oscillator ◽  
Homotopy Continuation ◽  
Van Der Pol ◽  
Steady State Responses

A generalized Duffing–van der Pol oscillator with nonlinear fractional order damping is introduced and investigated by the residue harmonic homotopy. The cubic displacement involved in fractional operator is used to describe the higher-order viscoelastic behavior of materials and of aerodynamic damping. The residue harmonic balance method is employed to analytically generate higher-order approximations for the steady state responses of an autonomous system. Nonlinear dynamic behaviors of the harmonically forced oscillator are further explored by the harmonic balance method along with the polynomial homotopy continuation technique. A parametric investigation is carried out to analyze the effects of fractional order of damping and the effect of the magnitude of imposed excitation on the system using amplitude-frequency curves. Jump avoidance conditions are addressed. Neimark bifurcations are captured to delineate regions of instability. The existence of even harmonics in the Fourier expansions implies symmetry-breaking bifurcation in certain combinations of system parameters. Numerical simulations are given by comparing with analytical solutions for validation purpose. We find that all Neimark bifurcation points in the response diagram always exist along a straight line.

scholarly journals Calculating periodic vibrations of nonlinear autonomous multi-degree-of-freedom systems by the incremental harmonic balance method

2004 ◽  
Vol 26 (3) ◽  
pp. 157-166
Author(s):  
Nguyen Van Khang ◽  
Thai Manh Cau
Keyword(s):  
Harmonic Balance ◽  
Floquet Theory ◽  
Monodromy Matrix ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Van Der Pol ◽  
Incremental Harmonic Balance ◽  
The Stability

In this paper the incremental harmonic balance method is used to calculate periodic vibrations of nonlinear autonomous multip-degree-of-freedom systems. According to Floquet theory, the stability of a periodic solution is checked by evaluating the eigenvalues of the monodromy matrix. Using the programme MAPLE, the authors have studied the periodic vibrations of the system multi-degree van der Pol form.

The Incremental Harmonic Balance Method Applied to Coupled Van der Pol Oscillators

2010 ◽  
Author(s):  
Wei Zhang ◽  
Hailiang Hu ◽  
Youhua Qian
Keyword(s):  
Numerical Method ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Van Der Pol ◽  
Van Der Pol Oscillators ◽  
Incremental Harmonic Balance ◽  
Ihb Method ◽  
Good Agreement

The incremental harmonic balance (IHB) method is used to investigate coupled Van der Pol oscillators. An effective way for calculating the coefficient matrices and selecting the appropriate initial values is presented. The results of the IHB method are in good agreement with the results of the numerical method.

scholarly journals Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems

2014 ◽  
Vol 63 (4) ◽  
pp. 591-600
Author(s):  
René Plasser ◽  
Oszkár Bíró
Keyword(s):  
Finite Element ◽  
Eddy Current ◽  
Harmonic Balance ◽  
Eddy Currents ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Periodic Excitation ◽  
The Finite Element Method ◽  
Element Analysis ◽  
3 Dimensional

Abstract An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.

The substantiation of the formalized estimation of effectiveness of technological and production systems

2018 ◽  
Vol 15 (1) ◽  
pp. 169-181
Author(s):  
M. I. Sidorov ◽  
М. Е. Stavrovsky ◽  
V. V. Irogov ◽  
E. S. Yurtsev
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Production Systems ◽  
Van Der Pol

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

Sign in / Sign up

Export Citation Format

Share Document