Stationary Random Vibration Research Articles

Seismic Effectiveness of Tuned Mass Dampers

Time history analysis of 1DOF systems with and without a tuned mass damper, subjected to a set of historical earthquakes, shows that the peak response ratio (ratio between the peak responses with and without damper) depends primarily on damping constants and on earthquake duration. The same analysis reveals that response ratio values are widely scattered and that the mean response ratio in underestimated by conventional stationary random vibration calculations. Improvement is obtained by considering response movement and broadening of the response spectral density function caused by the damper. Based on these considerations, a probabilistic model is developed that gives the distribution of peak response of buildings modified by addition of a tuned mass damper in terms of the same distribution for the unmodified structures. For elastic systems tuned mass dampers have small antiseismic effectiveness.

Small Strain Stationary Random Vibrations of Polymeric Liquids

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A response spectrum method for random vibration analysis of mdf systems

AbstractA response spectrum method for stationary random vibration analysis of linear, multi‐degree‐of‐freedom systems is developed. The method is based on the assumption that the input excitation is a wide‐band, stationary Gaussian process and the response is stationary. However, it can also be used as a good approximation for the response to a transient stationary Gaussian input with a duration several times longer than the fundamental period of the system. Various response quantities, including the mean‐squares of the response and its time derivative, the response mean frequency, and the cumulative distribution and the mean and variance of the peak response are obtained in terms of the ordinates of the mean response spectrum of the input excitation and the modal properties of the system. The formulation includes the cross‐correlation between modal responses, which is shown to be significant for modes with closely spaced natural frequencies.The proposed procedure is demonstrated for an example structure that is subjected to an ensemble of earthquake‐induced base excitations. Computed results based on the response spectrum method are in close agreement with simulation results obtained from time‐history dynamic analysis. The significance of closely spaced modes and the error associated with a conventional method that neglects the modal correlations are also demonstrated.

Stationary Random Vibration of a Nonlinear System with Collision

This paper deals with the response of a nonlinear system with collision subjected to a stationary random excitation. The system consists of an oscillator and reflectors at both sides. Various stochastic properties of the response are determined analytically, including the joint probability density function and the root-mean-square values for the displacement and the velocity of the oscillator, the average number of collisions per unit time, and the probability density functions, the mean values and the standard deviations of the impact velocity, the impulse and the impact acceleration. Experiments are also carried out to examine the analytical results, and good agreement between the analytical and the experimental results is obtained. Numerical results are presented to show effects of the clearance gap between the oscillator and each of the reflectors on the stochastic properties of the response. The width of the gap for snubbers is evaluated, employing the average number of collisions whose impact velocities are beyond a certain level.

重量選別機基礎の振動外乱が選別精度に及ぼす影響

In weight-checking, packages to be checked, even though they may have the same mass value, are not clearly assigned to a certain group but there exists a zone within which the assignment is determined according to a certain probability. The zone of indecision is sometimes referred to as Gray Zone and the weight-checking accuracy depends on the characteristic in probability of the zone. Gray Zone can be divided into two portions; one is the zone due to the inherent characteristics of the checkweigher, while the other is the zone due to the disturbance. In this paper, assuming the disturbance to be stationary random vibration from a foundation of a checkweigher, the characteristic in probability of Gray Zone, namely, the characteristic of the weight-checking accuracy is analysed theoretically and is investigated on computer simulation. As the result, it is clarified that the weight-checking accuracy can be calculated from the spectral density of the disturbance assumed above.

Stationary Random Vibration of a Nonlinear System with Collision

本論文では,振動子と両側反射体とからなる衝突振動系の定常不規則加振について,振動子の変位と速度の結合確率密度や衝突速度,力積,衝突加速度の確率密度,衝突回数の期待値など,衝突振動と衝撃特性の確率統計的性質が解析的な方法により明らかにされ,実験によってその妥当性が検証されている.また,これら諸性質の,間隔による変化が調べられ,制振用ストッパなどの間隔が衝撃特性の観点から評価されている.

Stationary Random Vibration of Hysteretic Systems

A more rigorous derivation of the modified power balance method is given for general yielding systems. It is demonstrated that the physical meaning of the equivalent linearization criteria derived by the mean-square minimization (Krylov-Bogoliubov) method are the equivalency of the dissipative and potential energies of the linear and nonlinear systems. Thus, linearization by power balance can be the same as by mean-square minimization. Simple gradient-stiffness approximations for the amplitude-dependent average frequency of hysteresis cycles and the overall average frequency of random response are presented for systems of Masing's type. In addition to the previously studied bilinear hysteretic system, the method is applied to compute rms response levels of trilinear hysteretic and Ramberg-Osgood type systems.

Synthesis of multivariate random vibration systems: A two-stage least squares AR-MA model approach

A parametric time series model procedure for the synthesis of multivariate stationary time series random vibrations is shown. The vibrations are assumed to be the outputs of a regularly sampled, random noise excited, differential equation model of a vivration system. The procedure is a two-stage least squares method for realizing a multivariate disrcrete time mixed autoregressive-moving average (AR-MA) model from a given stationary process matrix covariance function. The synthesis procedure and the problem of the minimal representation of multivariate output systems and the overparameterization of AR-MA models are discussed and illustrated.

Least squares estimates of structural system parameters using covariance function data

A statistically efficient and computationally economical two-stage least squares procedure for the estimation of the natural frequencies and damping parameters of structural systems under stationary random vibration conditions is considered. The structural system is represented by the system of ordinary differential equations that is characteristic of lumped mass-spring-damper systems with a random forcing function. Emphasis is placed on the problem corresponding to the observation of the top story vibrations of a tall building under random wind excitation. In that case, the random excitation can be approximated by a white noise and the regularly sampled vibration record can be represented as a mixed autoregressive-moving average (ARMA) time series. The ARMA time series parameters are estimated by a two-stage least squares method using only the covariance function of the top story vibrations. The natural frequency and damping parameters of the structural system can be expressed in terms of the AR parameters. Estimates of the coefficient of variation of the structural system parameter estimates are expressed in terms of the ARMA parameter estimates. The numerical results of the least squares and maximum likelihood parameter estimation procedures worked on a real vibration data example are shown.

Stochastic prediction of maximum seismic response of light secondary systems

A stochastic model is presented for predicting the elastic response of light multi-degree-of-freedom secondary systems to strong motion earthquakes. Secondary systems may include light mechanical or electrical equipment, piping, or other light systems attached at one or several points to walls or floors of the supporting or primary structures. The critical functions of these secondary systems in nuclear power plants make the accurate prediction of their maximum responses important. The response of such secondary structures may be obtained by a direct time-history analysis, or more approximately, by the response spectrum method. The time-history solution is, of course, expensive; moreover, there is no single representative earthquake and thus a number of possible earthquake ground motions have to be considered. On the other hand, the response spectrum method applied to secondary systems can lead to unreliable results. Within the framework of the normal mode method, a decoupled stationary random vibration model is developed based on the assumption of Gaussian response process and Poisson barrier crossings. The accuracy of the proposed model is verified by comparing the calculated responses, at the 10 and 50% probability of exceedance level, with the second highest and average of the time-history responses from eight normalized accelerograms. The influence of decoupling, i.e. ignoring the dynamic interaction between the primary and the secondary systems, on the response is examined. The influence of nonstationarity is also evaluated. It is observed that nonstationarity is unimportant for earthquakes of relatively long duration, and that for a given damping most of the error can be accounted for by a simple scaling. It is also shown that one aspect of the proposed method constitutes the basis for some of the approximations in the response spectrum method; however, the proposed method yields results that are consistently more reliable than the response spectrum method. Moreover, results obtained with the proposed method represent maximum response statistics from an ensemble of earthquakes rather than a single earthquake.

Experimental Fatigue Results under Stationary and Nonstationary Random Vibration

There is a steadily increasing supply of interesting fatigue test result for materials under the action of random processes, especially in the area of stationary random loading. In the strictest sense, nonstationary random processes in fatigue should be considered quasistationary processes since the fatigue loading is nominally stationary over the long run to failure. It is possible to imagine nonstationary loading s over a complete fatigue life (such as the action of wear or steadily increasing damping in a fatigue test), but actual tests of this nature are not yet available. This paper surveys the field of stationary and quasistationary random loading subsequent to the author's 1968 state of the art paper on this topic. One of the most significant findings from this survey is the widespread use of repeated random loading sequences by research groups and working professional committees in interlaboratory test programs. The necessity to analyze service loadings carefully, to separate random and nonrandom aspects, is also dealt with in detail.

Statistical Parameters under Stationary Random Excitation

Fundamental statistical parameters used to describe stationary random vibrations are viewed with emphasis on those parameters of special concern in structural response and failure prediction problems. Included in the review are correlation and spectral density functions, instantaneous and peak value probability density functions, arbitrary level crossing statistics, and elementary considerations in the first passage problem. The relevance of the various statistical parameters to the prediction of structural fatigue and extreme value failures, assuming simple failure mechanism models, is introduced in qualitative terms. Both theoretical and experimental results are displayed to illustrate important relationships. Special attention is given to the importance of underlying assumptions inherent in classical applications, in particular, the excitation normality and system underlying assumptions. Data are presented to demonstrate the impact of common nonlinearities on such response parameters as the instantaneous and peak value probability density functions. Finally, the importance of the stationarity and associated constant parameter system assumptions are discussed from a practical viewpoint. Illustrations are included to clarify the types of errors that result when nonstationary random excitations and responses are analyzed as if they were stationary.

On the First-Excursion Probability in Stationary Narrow-Band Random Vibration, II

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.

The first passage problem for stationary random structural vibration

This paper presents an analysis of the first passage time problem. A lumped parameter model for a structural system is considered, and the excitation is limited to white noise. The response of this type of system is a Markov process on a multi-dimensional position-velocity space (for a damped harmonic oscillator the position-velocity space is two-dimensional). The Markov property is used to develop an integral equation for the first passage time density function. Numerical results are presented for the damped harmonic oscillator. A one-sided position boundary is considered as the region of safe operation, and a stationary start condition is analyzed. The results are compared to several previous studies of the first passage time problem.

Closure to “Discussion of ‘On the First Excursion Probability in Stationary Narrow-Band Random Vibration’” (1972, ASME J. Appl. Mech., 39, p. 632)

Closure to “Discussion of ‘On the First Excursion Probability in Stationary Narrow-Band Random Vibration’” (1972, ASME J. Appl. Mech., 39, p. 632)

On the First Excursion Probability in Stationary Narrow-Band Random Vibration

Dealing with a stationary narrow-band Gaussian process X(t) with mean zero, this paper derives a number of approximate solutions on the basis of the point-process approach. In particular, upper and lower bounds sharper than those presently available are established, an approximation based on the Markov point process is obtained, and the clump size approach is also used for approximation. These approximations are checked with the result of the semisimulation performed by Crandall, et al. [11]. Some remarks are also made on the use of the principle of maximum entropy.