Monte Carlo Simulation of Coupled Nonlinear Oscillators Under Random Excitations

1990 ◽  
Vol 57 (4) ◽  
pp. 1097-1099 ◽  
Author(s):  
Wenlung Li ◽  
R. A. Ibrahim
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Nonlinear Interaction ◽  
Internal Resonance ◽  
Initial Conditions ◽  
Non Gaussian ◽  
Energy Absorbing ◽  
Three Degree Of Freedom ◽  
Gaussian Closure

The main objectives of this note are to examine the random response of nonlinear three degree-of-freedom systems in the neighborhood of combination internal resonance by using Monte Carlo simulation and to compare the results with those obtained by first-order non-Gaussian closure. The numerical simulation is found to support the main features of the nonlinear interaction in the neighborhood of internal resonance conditions. For example, the nonlinear interaction takes place in the form of a randomly continuous energy exchange between the modes involved. In addition, the results verify the existence of energy absorbing effect as predicted by the non-Gaussian closure method. While the non-Gaussian closure exhibits regions of multiple solutions in the neighborhood of exact internal resonance, the numerical simulation gives only one solution depending on the assigned initial conditions. This observation requires further investigation to establish the domains of attraction in stochastic nonlinear dynamics.

Structural Modal Multifurcation With Internal Resonance: Part 2—Stochastic Approach

1993 ◽  
Vol 115 (2) ◽  
pp. 193-201 ◽  
Author(s):  
R. A. Ibrahim ◽  
B. H. Lee ◽  
A. A. Afaneh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Axial Load ◽  
Random Excitation ◽  
Stochastic Bifurcation ◽  
Density Level ◽  
Analytical Treatment ◽  
Asymmetric Mode ◽  
Non Gaussian ◽  
Gaussian Closure

Stochastic bifurcation in moments of a clamped-clamped beam response to a wide band random excitation is investigated analytically, numerically, and experimentally. The nonlinear response is represented by the first three normal modes. The response statistics are examined in the neighborhood of a critical static axial load where the normal mode frequencies are commensurable. The analytical treatment includes Gaussian and non-Gaussian closures. The Gaussian closure fails to predict bifurcation of asymmetric modes. Both non-Gaussian closure and numerical simulation yield bifurcation boundaries in terms of the axial load, excitation spectral density level, and damping ratios. The results of both methods are in good agreement only for symmetric response characteristics. In the neighborhood of the critical bifurcation parameter the Monte Carlo simulation yields strong nonstationary mean square response for the asymmetric mode which is not directly excited. Experimental and Monte Carlo simulation exhibit nonlinear features including a shift of the resonance peak in the response spectra as the excitation level increases. The observed shift is associated with a widening effect in the response bandwidth.

Driver Differentiation With Seat Settings: Part II—Feasibility Study for US Household

2010 ◽  
Author(s):  
Carol Flannagan ◽  
Shih-Ken Chen ◽  
Bakhtiar Litkouhi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Feasibility Study ◽  
Initial Conditions ◽  
Population Variability ◽  
Driver Identification

The addition of user-customizable features to automobiles increases the need to differentiate among drivers so that each driver’s custom settings can be automatically applied. Part 1 of this study modeled driver component positioning as a function of the stature difference between sharing drivers. To fully understand the feasibility of this approach to driver identification, we need to model the distribution of stature differences in the population of sharing drivers. Monte Carlo simulation is used to simulate both population variability in stature and positioning and the effect of initial conditions on positioning are included. The simulation of 10,000 households showed that for 87% of target pairs, differentiation performance of fewer than 2% errors can be achieved, even when the drivers share a vehicle equally (the most difficult differentiation scenario).

NUMERICAL SIMULATION OF THE FORMATION AND PROPAGATION OF STREAMER

2007 ◽  
Vol 18 (06) ◽  
pp. 957-971 ◽  
Author(s):  
A. SETTAOUTI ◽  
L. SETTAOUTI
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Electric Fields ◽  
Sulfur Hexafluoride ◽  
Industrial Applications ◽  
Negative Ion ◽  
The Past ◽  
Ion Distributions ◽  
Streamer Propagation

There has been considerable interest in non-thermal discharges over the past decade due to the increased number of industrial applications. The properties of discharges in electronegative gases are most frequently used for technological applications. For the improvement of performance in these applications, it is necessary to understand discharge dynamics experimentally and numerically. In this paper, a Monte Carlo simulation is carried out in sulfur hexafluoride (SF6) in uniform electric fields. The streamer propagation, electron, positive and negative ion distributions and space charge fields are studied in detail as time increases.

Monte Carlo simulation of asteroid collisions

1974 ◽  
Vol 22 ◽  
pp. 107-110
Author(s):  
W. McD. Napier ◽  
R. J. Dodd
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Solar System ◽  
Mass Distribution ◽  
Related Question ◽  
Monte Carlo Technique ◽  
Small Bodies ◽  
Collision Processes ◽  
Analytical Complexity

Derivation of the mass distribution resulting from the fragmentation of mutually colliding bodies is a problem of some analytical-complexity, even in the asymptotic case (see, for example, Safronov, 1963, Hellyer 1970). A related question is that of the mass distributionn(m) expected at any time if small bodies stick on impact, so coagulating into large ones. This latter problem might be relevant to the growth of planetesimals in the early stages of Solar System evolution. At Edinburgh, a Monte Carlo technique is being used to simulate these collision processes directly. Numerical simulation has advantages over and above the avoidance of analytical complexities. For example the physical assumptions can be easily changed, and the random variations which occur in reality are automatically incorporated, that is, the problem is treated stochastically rather than deterministically.

scholarly journals Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation

2002 ◽  
Vol 298 (5-6) ◽  
pp. 325-329 ◽  
Author(s):  
Roberto da Silva ◽  
Nelson A Alves ◽  
J.R Drugowich de Felı́cio
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Exponent ◽  
Initial Conditions ◽  
Short Time

Correlation of Steel Yield Stress and Ultimate Strength - Monte Carlo Simulation via Non-Gaussian Random Variables

2017 ◽  
Vol 893 ◽  
pp. 223-228 ◽  
Author(s):  
Petr Konečný
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Yield Stress ◽  
Ultimate Strength ◽  
Joint Distribution ◽  
Assessment Method ◽  
Joint Distributions ◽  
Steel Strength ◽  
Simulation Based ◽  
Non Gaussian

This paper describes a Monte Carlo simulation of the correlated steel characteristics of yield stress and ultimate strength of steel S235 grade from Northern Moravia region in the Czech Republic. Their joint distribution is described by a correlation index and frequency histograms. The paper step-by-step describes simulation process of the transformation of a correlated Gaussian joint distribution to a general joint distribution, because the yield stress as well as ultimate steel strength random parameters do not follow a Gaussian distribution. Their marginal distribution can be easily described by a suitable parametric distribution or frequency histogram suitable for use with the Simulation-based Reliability Assessment method (SBRA). Describing joint distributions of non-Gaussian processes is overcome by application of fractile correlation.

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