scholarly journals A CONDITIONAL STOCHASTIC PROJECTION METHOD APPLIED TO A PARAMETRIC VIBRATIONS PROBLEM

2014 ◽  
Vol 20 (6) ◽  
pp. 810-818 ◽  
Author(s):  
Wlodzimierz Brzakala ◽  
Aneta Herbut
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Polynomial Chaos ◽  
Excitation Frequency ◽  
Finite Sequence ◽  
Excitation Amplitude ◽  
Random Excitation ◽  
Parametric Vibrations ◽  
Representative Points ◽  
Cable Stayed Bridges

Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.

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.

Some Observations on the Random Response of an Elasto-Plastic System

1988 ◽  
Vol 55 (4) ◽  
pp. 911-917 ◽  
Author(s):  
L. G. Paparizos ◽  
W. D. Iwan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Markov Process ◽  
Practical Interest ◽  
Random Excitation ◽  
Process Models ◽  
Mean Square ◽  
Random Response ◽  
Monte Carlo Simulation Study

The nature of the response of strongly yielding systems subjected to random excitation, is examined. Special attention is given to the drift response, defined as the sum of yield increments associated with inelastic response. Based on the properties of discrete Markov process models of the yield increment process, it is suggested that for many cases of practical interest, the drift can be considered as a Brownian motion. The approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is accomplished by means of a Monte Carlo simulation study.

scholarly journals Experimental Study of a Variable Stiffness Seat Suspension Installed With a Compact Rotary MR Damper

2021 ◽  
Vol 8 ◽  
Author(s):  
Shuaishuai Sun ◽  
Jian Yang ◽  
Penghui Wang ◽  
Masami Nakano ◽  
Longjiang Shen ◽  
...  
Keyword(s):  
Ride Comfort ◽  
Excitation Frequency ◽  
Mr Damper ◽  
Variable Stiffness ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Shaking Table ◽  
Seat Suspension ◽  
Vibration Attenuation Performance

Traditional MR seat suspension without stiffness control is not able to avoid the resonance between the excitation and the seat, though it can dampen the vibration energy. To solve this problem, this paper proposed a variable stiffness (VS) magnetorheological (MR) damper to implement an advanced seat suspension. Its natural frequency can be shifted away from the excitation frequency through the variations of stiffness, thereby realizing the non-resonance control. The new seat suspension is designed and prototyped first, and then its dynamic property under different energizing current, excitation amplitude, and excitation frequency was tested using an MTS machine. The testing results verified its stiffness controllability. The vibration attenuation performance of the seat suspension was also evaluated on a vibration shaking table. The vibration reduction performance of the seat suspension was evaluated under two kinds of excitations, i.e., harmonic excitation and random excitation; the experimental results indicate that the new seat suspension outperforms passive seat suspensions regarding their ride comfort.

A polynomial chaos meta‐model for non‐linear stochastic magnet variations

2013 ◽  
Vol 32 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Flux Density ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Element Model ◽  
State Function ◽  
Content Type ◽  
Meta Model

PurposeDue to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model.Design/methodology/approachIn this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface.FindingsThe used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten.Research limitations/implicationsDue to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed.Originality/valueThe comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.

Exceedance Probabilities of MDOF-Systems Under Stochastic Excitation

1997 ◽  
Vol 50 (11S) ◽  
pp. S168-S173 ◽  
Author(s):  
H. J. Pradlwarter ◽  
G. I. Schue¨ller
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Procedure ◽  
Random Excitation ◽  
Stochastic Excitation ◽  
First Passage ◽  
Simulation Procedure ◽  
Mdof Systems ◽  
Low Probability ◽  
Probability Domain

A numerical procedure of evaluating the exceedance probabilities of MDOF-systems under non-stationary random excitation is presented. The method is based on a newly developed Controlled Monte Carlo simulation procedure applicable to dynamical systems. It uses “Double and Clump” to assess the low probability domain and employs further intermediate thresholds to increase the efficiency of MCS for estimating first passage probabilities. Applied to a hysteretic type of MDOF-system, the method shows good results when compared with direct MCS.

Sign in / Sign up

Export Citation Format

Share Document