scholarly journals Non-Stationary Random Vibration of FE Structures Subjected to Moving Loads

2009 ◽  
Vol 16 (3) ◽  
pp. 291-305 ◽  
Author(s):  
F. Lu ◽  
D. Kennedy ◽  
F.W. Williams ◽  
J.H. Lin
Keyword(s):  
Random Vibration ◽  
High Efficiency ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Mean Value ◽  
Statistical Characteristics ◽  
Moving Loads ◽  
Precise Integration ◽  
Power Spectral ◽  
Decomposition Procedure

An efficient and accurate FEM based method is proposed for studying non-stationary random vibration of structures subjected to moving loads. The loads are assumed to be a stationary process with constant mean value. The non-stationary power spectral densities (PSD) and the time dependent standard deviations of dynamic response are derived by using the pseudo excitation method (PEM) to transform this random excitation problem into a deterministic harmonic excitation one. The precise integration method (PIM) is extended to solve the equation of motion of beams under moving harmonic loads by enhancing the very recent consistent decomposition procedure, in order to simulate the movement of the loads. Six numerical examples are given to show the very high efficiency and accuracy of the method and also to deduce some useful preliminary conclusions from investigation of the dynamic statistical characteristics of a simply supported beam and of a symmetrical three span beam with its centre span unequal to the outer ones.

An efficient method for non-stationary random vibration analysis of beams

2011 ◽  
Vol 17 (13) ◽  
pp. 2015-2022 ◽  
Author(s):  
Jie Yang ◽  
De-you Zhao ◽  
Ming Hong
Keyword(s):  
Efficient Method ◽  
Random Vibration ◽  
High Efficiency ◽  
Theoretical Method ◽  
Random Excitation ◽  
The Finite Element Method ◽  
Euler Beam ◽  
Time Step ◽  
Random Loads ◽  
Pseudo Excitation

An efficient method is presented to investigate the non-stationary random vibration response of structures. This method has the advantage of the accuracy of theoretical method in dealing with random loads and the versatility of the finite element method (FEM) in dealing with structures. In this paper, the Euler beam is adopted in the derivation of the governing equation. The uncoupled approach of the frequency-dependent system matrices is presented for solving the motion equation of forced vibration. The time-variance random dynamic response of the beam is analyzed by the precise integral method, meanwhile, the pseudo-excitation is applied to transform the non-stationary random excitation into deterministic pseudo one to simplify the solution of the dynamic equation. Solutions calculated by the FEM with different time step and theoretical analysis are also obtained for comparison. Numerical examples demonstrate the accuracy and high efficiency of the proposed method.

Non-Linear Model of Rubber Bearings under Random Excitation

2012 ◽  
Vol 452-453 ◽  
pp. 602-606
Author(s):  
Hai Yan Jing ◽  
Yan Ping Zheng ◽  
Ming Xia Fang
Keyword(s):  
Past Research ◽  
Random Excitation ◽  
Mean Value ◽  
Statistical Characteristics ◽  
The Past ◽  
Non Linear ◽  
The Mean ◽  
Rubber Bearings ◽  
Force Displacement ◽  
Sinusoidal Excitation

Through dynamics test and theoretical analysis about rubber bearings in Auto body’s sub-frame, and the past research results of sinusoidal excitation, a hysteretic non-linear mathematical model of the rubber bearings is established under the condition of random excitation. The model shows that the hysteretic renewed force of the rubber bearings under random excitation can be expressed with the mean value and variance of random excitation’s statistical characteristics and speed. Finally curves of the hysteretic renewed force - displacement are reconstructed with the model built, which match the test’s results well.

scholarly journals Random Vibration Model in Linear and Non Linear Structure, Application in Engineering Structure

2015 ◽  
Vol 26 (2) ◽  
pp. 40-45
Author(s):  
Anwar Dolu ◽  
Amrinsyah Nasution
Keyword(s):  
Random Vibration ◽  
Time History ◽  
Linear Structure ◽  
Mean Value ◽  
Characteristic Functions ◽  
Linear Stochastic Differential Equation ◽  
Power Spectral ◽  
Non Linear ◽  
Non Linear System ◽  
External Loads

Response of linear or complex nonlinear structures takes form in a characteristic functions and in the deterministic or stochastic external loads. Non linear model with non linear structure stiffness is a type of Duffing equation. Stochastic external loads system is referred to a random signal white noise with a constant power spectral density (So), while non linear system identification of deterministic system's is based on time history, phase plane and Poincare map. Methods of Galerkin and Runge-Kutta are used to solve the partial non linear governing diferential equations. Mean value , Standard deviation and Probability Density Function (PDF) is stated as statistical responses due to stochastic response of random variables. The analysis of random vibration in the solution of non linear stochastic differential equation is solved

scholarly journals Power Spectral Density Response of Bridge-Like Structures Loaded by Stochastic Moving Forces

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Silvio Sorrentino
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Spectral Density Function ◽  
Mean Value ◽  
Moving Loads ◽  
Mean Values ◽  
Power Spectral ◽  
Potential Applications ◽  
Spectral Density Functions ◽  
The Mean

In this study, simple and manageable closed form expressions are obtained for the mean value, the spectral density function, and the standard deviation of the deflection induced by stochastic moving loads on bridge-like structures. As a basic case, a simply supported beam is considered, loaded by a sequence of concentrated forces moving in the same direction, with random instants of arrival, constant random crossing speeds, and constant random amplitudes. The loads are described by three stochastic processes, representing an idealization of vehicular traffic on a bridge in case of negligible inertial coupling effects between moving masses and structure. System’s responses are analytically determined in terms of mean values and power spectral density functions, yielding standard deviations, with the possibility to easily extend the results to more refined models of single span bridge-like structures. Potential applications regard structural analysis, vibration control, and condition monitoring of traffic excited bridges.

Random Vibration Analysis of Heavy-Duty Truck Based on Pseudo Excitation

2011 ◽  
Vol 299-300 ◽  
pp. 1244-1247
Author(s):  
Yu Ying Qin ◽  
Jing Qian Wang ◽  
Guo Hong Tian
Keyword(s):  
Random Vibration ◽  
Statistical Characteristics ◽  
Heavy Duty ◽  
Pseudo Excitation Method ◽  
Heavy Duty Truck ◽  
Power Spectral ◽  
Vibration Model ◽  
Vibration Responses ◽  
Pseudo Excitation ◽  
Excitation Method

This paper discusses pseudo excitation method and constructs pseudo six-wheel pseudo excitation. For the complexity of heavy-duty truck, construction of vibration model is difficult for real structures; thirteen-degree-of-freedom full model is constructed for heavy-duty truck. Taken frequency response function as a bridge, pseudo excitation method is applied and a new method is gained for statistical characteristics of heavy-duty truck. The result shows that the method for random vibration of heavy-duty truck is feasible and convenient by constructing six-wheel road pseudo excitation and obtaining power spectral densities of vibration responses.

Exact Solutions of Fully Nonstationary Random Vibration for Rectangular Kirchhoff Plates Using Discrete Analytical Method

2017 ◽  
Vol 17 (10) ◽  
pp. 1750126 ◽  
Author(s):  
Dixiong Yang ◽  
Guohai Chen ◽  
Jilei Zhou
Keyword(s):  
Exact Solutions ◽  
Analytical Method ◽  
Vibration Analysis ◽  
Random Vibration ◽  
High Efficiency ◽  
Noise Model ◽  
Thin Plates ◽  
Precise Integration ◽  
Kirchhoff Plates ◽  
Random Vibration Analysis

This paper proposes the discrete analytical method (DAM) to determine exactly and efficiently the fully nonstationary random responses of rectangular Kirchhoff plates under temporally and spectrally nonstationary acceleration excitation of earthquake ground motions. First, the fully nonstationary power spectral density (PSD) model is suggested by replacing the filtered frequency and damping of Gaussian filtered white-noise model with the time-variant ones. The exact solutions of free vibration of thin plates with two opposite edges simply supported boundary conditions are introduced. Then, the full analytical procedure for random vibration analysis of the plate is established by using a pseudo excitation method (PEM) that can consider all modal auto-correlation and cross-correlation terms. Owing to involving a series of Duhamel time integrals of single degree of freedom systems, it is difficult to fully analytically evaluate the PSD of time-variant responses such as the transverse deflection, velocity, acceleration and stress components. Thus, DAM that combines the PEM with precise integration technique is developed to enhance the computational efficiency. Finally, comparison of the results by the DAM with Monte Carlo simulations and the analytical stationary random vibration analysis demonstrates the high efficiency and accuracy of DAM. Moreover, the fully nonstationary excitation imposes a remarkable effect on the response PSD of rectangular Kirchhoff plates.

scholarly journals Power spectral density analysis for nonlinear systems based on Volterra series

2021 ◽  
Author(s):  
Penghui Wu ◽  
Yan Zhao ◽  
Xianghong Xu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Random Vibration ◽  
Volterra Series ◽  
Harmonic Excitation ◽  
Random Load ◽  
Vibration Prediction ◽  
Power Spectral

AbstractA consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

1988 ◽  
Vol 110 (2) ◽  
pp. 205-209
Author(s):  
A. V. Singh
Keyword(s):  
Transient Response ◽  
Random Vibration ◽  
Time History ◽  
Wide Band ◽  
Random Excitation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
History Of ◽  
The Mean ◽  
Random Vibration Analysis

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

2013 ◽  
Author(s):  
Giuseppe Muscolino ◽  
Roberta Santoro ◽  
Alba Sofi
Keyword(s):  
Sensitivity Analysis ◽  
Series Expansion ◽  
Neumann Series ◽  
Mean Value ◽  
Frame Structure ◽  
Young’S Moduli ◽  
Rational Series ◽  
Power Spectral ◽  
Stochastic Sensitivity Analysis ◽  
Neumann Series Expansion

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

scholarly journals Experimental Design and Validation of an Accelerated Random Vibration Fatigue Testing Methodology

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yu Jiang ◽  
Gun Jin Yun ◽  
Li Zhao ◽  
Junyong Tao
Keyword(s):  
Fatigue Life ◽  
Stress Responses ◽  
Life Prediction ◽  
Random Vibration ◽  
Fatigue Testing ◽  
Fatigue Tests ◽  
Fatigue Life Prediction ◽  
Power Spectral ◽  
Vibration Fatigue ◽  
Non Gaussian

Novel accelerated random vibration fatigue test methodology and strategy are proposed, which can generate a design of the experimental test plan significantly reducing the test time and the sample size. Based on theoretical analysis and fatigue damage model, several groups of random vibration fatigue tests were designed and conducted with the aim of investigating effects of both Gaussian and non-Gaussian random excitation on the vibration fatigue. First, stress responses at a weak point of a notched specimen structure were measured under different base random excitations. According to the measured stress responses, the structural fatigue lives corresponding to the different vibrational excitations were predicted by using the WAFO simulation technique. Second, a couple of destructive vibration fatigue tests were carried out to validate the accuracy of the WAFO fatigue life prediction method. After applying the proposed experimental and numerical simulation methods, various factors that affect the vibration fatigue life of structures were systematically studied, including root mean squares of acceleration, power spectral density, power spectral bandwidth, and kurtosis. The feasibility of WAFO for non-Gaussian vibration fatigue life prediction and the use of non-Gaussian vibration excitation for accelerated fatigue testing were experimentally verified.

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