Nonstationary Response Analysis Research Articles

Non-stationary response analysis for sandwich panels with corrugated cores under moving random loads

In this work, a recursion reverberation-ray matrix method (RRRM) is presented to formulate an exact and unified solution for the non-stationary responses analysis of the sandwich panels with corrugated cores (SPCC) subjected to the moving random loads. The governing equations for the basic units are obtained by employing the simple first-order shear deformation theory (S-FSDT) and Hamilton's principle. Then, based on the traditional reverberation ray matrix method (MRRM), the RRRM is established by incorporating a bidirectional recursion technique to effectively calculate the exact solutions of the whole model. Thereinto, the kinematic relation matrix between the cell units can be constructed to facilitate the coupling of various desired numbers of elements by employing the virtual coupling spring. In addition, a unified loading mechanism for multi-scenario loads is proposed by integrating the pseudo-excitation method (PEM) with the load stage division technique. The applicability and accuracy of the current method to non-stationary response behaviors of the SPCC are clarified by carrying out sufficient comparative studies between the calculated results with reference solutions from FEM and Monte Carlo simulation method. Furthermore, several meaningful conclusions are drawn regarding the effects of structural and load parameters on the vibration characteristic, non-stationary displacement response, power spectrum density (PSD), and time-varying root mean square (RMS).

Fast Convolution Integration–Based Nonstationary Response Analysis of Linear and Nonlinear Structures with Nonproportional Damping

AbstractThe frequency domain approach (FDA) based on the power spectral description of input and output has been widely applied in the random vibration analysis of structures because of its high ef...

DIMENSION REDUCTION OF FPK EQUATION FOR VELOCITY RESPONSE ANALYSIS OF STRUCTURES SUBJECTED TO ADDITIVE NONSTATIONARY EXCITATIONS1)

The nonlinear response analysis of structures subjected to random excitation is a highly challenging problem. The solution of FPK equation provides exact solutions to these problems. However, for nonlinear multi-degree-of-freedom systems, the direct solutions of the FPK equation is prohibitively difficult. Actually, the numerical solutions are strictly limited by the dimension of the equation, while the analytical solutions are available only for very few specific systems, and most of them are steady-state solution. Therefore, reducing the dimension of the FPK equation is an important way to solve the high-dimensional nonlinear dynamic response analysis problem. In the present paper, for the nonstationary response analysis of multi-degree-of-freedom nonlinear structures subjected to amplitude-modulated additive white noise, the high-dimensional FPK equation in terms of the joint probability density function is reduced in dimension. For the probability density function of velocity response, it is converted to a one-dimensional FPK-like equation through introducing the equivalent drift coefficient. The method of conditional mean function estimate is suggested to construct the equivalent drift coefficient. Afterwards, the numerical results of probability density function of velocity can be obtained by applying the path integration method to solve the dimension-reduced FPK-like equation. The accuracy and efficiency of the proposed method are discussed and verified through the numerical examples, including the non-stationary response analysis of velocity of a single-degree-of-freedom Rayleigh oscillator, a ten-story linear shear frame structure and a nonlinear shear frame structure subjected to amplitude-modulated additive white noise.

Nonstationary Response Analysis of Long Span Bridges under Spatially Varying Differential Support Motions Using Continuous Wavelet Transform

An input-output relation for the nonstationary response of long-span bridges subjected to random differential support motions is proposed in the present study. The proposed methodology is more general than the existing ones, in the sense that it can evaluate nonstationarity in both the intensity and frequency content of the response statistics for spatially correlated multipoint random excitations. Furthermore, because the input-output relation is established through the transfer functions of dynamic systems, the proposed wavelet-based methodology can easily be used to predict the stochastic response of any structural systems in conjunction with available finite-element software. The input-output formulation is also not restricted to a particular wavelet basis function, since it has been derived by following a general wavelet-based description of input nonstationary processes. The bridge has been modeled as a simply supported beam with multispans in a finite-element framework to obtain the dynamic propert...

Equivalent Linearization for the Nonstationary Response Analysis of Nonlinear Systems with Random Parameters

This paper presents an approach for analyzing nonlinear systems with parameter uncertainty subjected to stochastic excitation. The uncertain parameters are modeled as time-independent random variables. A general solution procedure based on equivalent linearization is presented. The set of orthogonal polynomials associated with the probability density function is used as the solution basis for the response moments. In addition, the instantaneous equivalent stiffness and damping matrices are approximated as quadratic random functions. The resulting Liapunov system with explicit random coefficients can then be converted into a deterministic system using the method of weighted residuals. Applications to single-degree-of-freedom uncertain systems are given and the accuracy of the results is validated.

Wavelet-based non-stationary response analysis of a friction base-isolated structure

A wavelet-based stochastic formulation has been presented in this paper for the seismic analysis of a base-isolated structural system which is modelled as a two-degree-of-freedom (2-DOF) system. The ground motion has been modelled as a non-stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non-linear system by an equivalent linear system with time-dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non-stationarity on the non-linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non-stationarity in the ground motion leads to inaccurate non-linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.

Nonstationary response analysis of offshore guyed tower subjected to earthquake loading

A method for nonstationary seismic response analysis of an offshore guyed tower is presented. The equation of motion is formulated for the horizontal motion of the guyed tower using a multi-degrees-of-freedom model. The nonlinear hydrodamping and the nonlinear restoring force of the guyline system are included in analysis with the aid of the equivalent linearizations. The nonstationarity of the earthquake excitation is modelled by imposing a time varying envelope function onto a stationary random component. The nonstationary responses are obtained in terms of time dependent variance functions. By taking the autocorrelation function of the nonstationary ground acceleration in terms of sinusoidal and exponential functions of time, an analytical procedure is developed for computing time varying variances of the tower responses. Expected maximum responses are evaluated thereafter. Example analysis indicates that the nonstationary method gives consistent estimates for the maximum responses, if the earthquake duration is taken to be longer than the duration of strong excitation. Comparison is made with the results obtained by the conventional spectral method based on the stationary assumption.

Recursive response analysis of structures subjected to nonwhite random excitation

Based on the Newmark time stepping formulas a direct numerical integration procedure is developed for the nonstationary response analysis of structures subjected to nonwhite random exitations. The derived formulas for the computation of the nonstationary response variance are recursive and easy to implement. The stability of the proposed procedure is discussed. It is shown that the stability conditions are the same as that for deterministic cases. The example given in this paper shows that the introduced procedure is computationally quite efficient as compared to the conventional one.

Direct integration variance prediction of random response of nonlinear systems

This paper describes a study to develop a direct integration procedure for the nonstationary response analysis of nonlinear systems which is suitable for both white and nonwhite random exitation. The developed procedure is recursive and computationally quite efficient. The example given in this paper shows that the results obtained with the direct integration procedure are in close agreement with the digitally simulated data and are not sensitive to the choice of time step, which is vital to the application of the procedure.

A computer-assisted learning system for random vibrations

The computer-assisted learning system described in this paper is based on the idea that solutions to problems in random vibrations consist of sequences of well-defined logical steps each requiring a certain amount of routine calculations. The student is engaged in the solution of the problem by selecting the proper sequence of steps, and the computer facilitates the solution by carrying out the routine calculations necessary for each step. The system enhances the learning process by (a) freeing the student from routine calculations that are not central to a fundamental understanding of the subject, (b) providing the means for application of the theory to realistic problems, thus helping the student gain experience and confidence, (c) providing the means for immediate visualization and interpretation of data at all levels, and (d) facilitating experimentation and exploration with the results of the theory. The system described includes capabilities for stationary and nonstationary response analysis as well as analysis of crossings and local and extreme peaks of processes.

Nonstationary response analysis of suspension bridges for multiple support excitations

A method for the nonstationary response analysis of suspension bridges subjected to earthquake ground excitations at multiple supports is developed. The equation of motion is formulated for the vertical motion of the bridge girder using a continuous co-ordinate system. The nonstationarity of the earthquake excitation is modeled by utilizing a time-varying envelope function. The correlation effects between ground excitations at different supports are investigated, for various cases of traveling seismic waves with different wave propagation velocities. The non-stationary responses are obtained in terms of time-dependent variance functions. Expected peak responses are also evaluated, thereafter. Numerical results from the example analysis indicate that the correlation effects between different support excitations are very significant on the response of the suspension bridge.

Nonstationary response analysis of a nonsymmetric nonlinear multi-degree-of freedom system to nonwhite random excitation.

An approximate analytical technique is developed for obtaining the nonstationary responses of a multi-degree-of-freedom mechanical system with nonsymmetric non-linearities subjected to nonwhite random excitations with arbitrary covariance functions. The method consists of a modification of the equivalent linearization technique, in which the equivalent linear system is subjected to the equivalent forcing function with shifted mean, and the use of moment equations of the system. Numerical examples are given for single and two degree-of-freedom systems whose restoring force characteristics have both quadratic and cubic nonlinearities. In the first case, the results are compared with those of the corresponding digital simulation in order to demonstrate the validity of the present method.

An iterative method for non-stationary response analysis of non-linear random systems

A method for calculating the non-stationary response of non-linear systems subjected to random excitations is formulated. The time-dependent equivalent linear system is considered and an iterative procedure for evaluating the non-stationary mean-square responses is developed. Several examples are presented and applicability of the technique is illustrated.

Nonstationary Response Analysis of a Duffing Oscillator by the Wiener-Hermite Expansion Method

The Wiener-Hermite functional series expansion method is used to analyze the nonstationary response of a Duffing oscillator under random excitations. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite kernel functions is described. The first three terms in the series are retained. The nonstationary response of a damped Duffing oscillator subjected to a modulated white noise is studied. For several values of nonlinearity strength and different damping coefficients the nonstationary mean-square responses are obtained. The results are compared with those found by a single-term expansion and other methods. It is shown that mean-square responses obtained by the three-term expansion agree with the exact stationary variances and the simulation results.

NON-STATIONARY RESPONSE ANALYSIS OF DYNAMIC STRUCTURAL SYSTEMS

NON-STATIONARY RESPONSE ANALYSIS OF DYNAMIC STRUCTURAL SYSTEMS

Non-stationary response analysis of non-symmetric non-linear single-degree-of-freedom systems subjected to random excitation.

Non-stationary response analysis of non-symmetric non-linear single-degree-of-freedom systems subjected to random excitation.