A numerical method is proposed to calculate the first excursion probability that the linear system response to non-stationary random excitation exceeds in magnitude its respective threshold level ...within a specified time interval. Its derivation is carried through three steps. First, the numerical expression for the first excursion probability, based on the modification of the level crossing rates, is developed. Secondly, the time domain expressions for the first three order spectral moments of the response are given, from which the level crossing rates can be computed. Thirdly, it is then demonstrated how Simpson’s rule of numerical integration can be applied to the approximate computation of the first three order spectral moments. It is shown by examples that both numerical accuracy and efficiency of this method are apparently very high.
This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The ...uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.
In this paper, a study was conducted regarding the stability of a binary airfoil under stochastic disturbances with feedback control. A new stochastic controller has been developed and investigated ...via Monte Carlo simulation. In order to design the new controller, the original system is transformed to the second-order moment one. Then the optimal control parameters can be obtained by searching for the effectual control parameters in the second-order moment system. Finally, the numerical simulations are included to visualize the good performances in flutter suppression.
Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random ...vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testing of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.
The new type of passive tuned liquid damper (TLD), which relies on the motion of liquid inside a movable rectangular tank with two degrees of freedom (horizontal displacement and rotation), is ...investigated, including the influence of a vessel's horizontal motion and rotation on the damping of the vertical and horizontal vibrations of footbridges. Experimental solution consists in the determination of the magnitude of the excitation force of the shaking table required under resonance during the excitation of the vessel.
A statistical approach based on the interval analysis (IA) is proposed for the analysis of the effects, on the radiation patterns radiated by phased arrays, of random errors and tolerances in the ...amplitudes and phases of the array-elements excitations. Starting from the efficient, reliable, and inclusive computation of the bounds of the complex-valued interval array pattern function by means of IA, an analytic method is presented to yield closed-form expressions for the probability of occurrence of a user-chosen value of the power pattern or of its features within the corresponding IA-derived bounds. A set of numerical examples is reported and discussed to assess the reliability of the proposed probabilistic interval analysis (PIA) method with the results from Monte Carlo simulations as well as to point out its effectiveness and potentialities/advantages/efficiency in real applications of great industrial interest.
The aim of this paper is to continue our previous investigations on beam–beam interaction models in particle accelerators by considering these models under narrow-band random excitation. In this ...investigation the multiple scale and the moment methods are used. The equations of modulation of the amplitude and the phase are derived and perturbation techniques are used to seek approximate steady-state solutions. Two special cases are considered to illustrate this study and excellent agreement is found between analytical and numerical results. Other cases can be similarly studied. The effects of noise and detuning parameters are examined numerically and theoretically and we find that the system demonstrates a diffused limit cycle as the intensity of noise increases. The numerical results show that the multiple scale method is effective for these stochastic systems.
Although a great deal of work has been carried out on structural dynamic systems under random excitation, there has been a comparatively small amount of this work concentrating on the calculation of ...the quantities commonly measured in structural dynamic tests. Among the existing work, the Volterra series, a means of predicting nonlinear system response for weakly nonlinear systems, has allowed the computation of various measurable quantities of interest for structural dynamics, including: auto- and cross-spectra, FRFs, coherences and higher-order spectra. These calculations are quite intensive and are typically only possible using computer algebra. A previous calculation by the authors for the coherence for a Duffing oscillator yielded results which showed some qualitatitive disagreement with numerical simulation; the object of the current paper is simply to extend the calculation in order to see if better agreement can be achieved.
For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of ...submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.
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