Equivalent Linearization Analysis of Electromagnetic Energy Harvesters Subjected to Gaussian White Noise

2021 ◽  
pp. 409-420
Author(s):  
Wei Wang ◽  
Junyi Cao ◽  
Zon-Han Wei
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Electromagnetic Energy ◽  
Equivalent Linearization ◽  
Energy Harvesters

Probabilistic Solutions of a Nonlinear Plate Excited by Gaussian White Noise Fully Correlated in Space

2017 ◽  
Vol 17 (09) ◽  
pp. 1750097 ◽  
Author(s):  
G. K. Er ◽  
V. P. Iu
Keyword(s):  
White Noise ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Computational Effort ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Nonlinear Random Vibration ◽  
Split Method ◽  
Probabilistic Solution ◽  
Polynomial Closure

This paper addresses the nonlinear random vibration of a rectangular von Kármán plate excited by uniformly distributed Gaussian white noise which is fully correlated in space. The state-space-split method and exponential polynomial closure method are jointly utilized to analyze the probabilistic solutions of the plate. The computational efficiency and numerical accuracy of the methodology for analyzing the nonlinear random vibration of the plate are verified by comparing the computational effort and numerical results with those obtained by Monte Carlo simulation and equivalent linearization, respectively. Meanwhile, the convergence of the probabilistic solution in the sense of Galerkin’s approximation is examined by analyzing the plate modeled as single-degree-of-freedom and multi-degree-of-freedom systems. Some phenomena are discussed after numerically studying the behaviors of probabilistic solutions of the deflection at different locations of the plate.

Probabilistic Solutions of the In-Plane Nonlinear Random Vibrations of Shallow Cables Under Filtered Gaussian White Noise

2018 ◽  
Vol 18 (04) ◽  
pp. 1850062 ◽  
Author(s):  
G. K. Er ◽  
K. Wang ◽  
V. P. Iu
Keyword(s):  
White Noise ◽  
Computational Efficiency ◽  
Gaussian White Noise ◽  
Peak Frequency ◽  
Seismic Intensity ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Seismic Force ◽  
Cable Systems ◽  
Polynomial Closure

The probabilistic solutions of the responses of shallow cable are studied when the cable is excited by filtered Gaussian white noise. The nonlinear multi-degree-of-freedom system is formulated which governs the random vibration of cable. The state-space-split (SSS) method and exponential polynomial closure (EPC) method are adopted to analyze the probabilistic solutions of cable systems in order to study the effectiveness and computational efficiency of SSS-EPC procedure in analyzing the probabilistic solutions of the cable systems under the excitation of filtered Gaussian white noise. Numerical results obtained by SSS-EPC method, Monte Carlo simulation, and equivalent linearization method are compared to examine the computational efficiency and numerical accuracy of SSS-EPC method in this case. Thereafter, the behaviors of probabilistic solutions of the cable systems are studied with different values of peak frequency and seismic intensity of excitation when the cable is excited by Kanai–Tajimi seismic force. Some observations and discussions are given by introducing a probabilistic quantity to show the influence of excitations on the probabilistic solutions.

scholarly journals Friction Damping of Random Vibration in Gas Turbine Engine Airfoils

1987 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Gas Turbine ◽  
Turbine Blade ◽  
Random Vibration ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Equivalent Linearization ◽  
Turbine Engine ◽  
Optimal Value

The optimal value of slip load is calculated for a frictionally damped turbine blade subjected to random excitation. The nature of excitation is assumed to be Gaussian white noise and the statistics of response are obtained using equivalent linearization approach. The results from this technique are compared with those from numerical simulations.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

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