Hybrid Optimization and Anti-Optimization of a Stochastically Excited Beam

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Isaac Elishakoff ◽  
Kévin Dujat ◽  
Maurice Lemaire ◽  
Guy Gadiot
Keyword(s):  
Cross Section ◽  
Mean Square Displacement ◽  
Random Excitation ◽  
Hybrid Optimization ◽  
Maximum Response ◽  
Mean Square ◽  
Euler Beam ◽  
Middle Cross Section ◽  
The Mean ◽  
Probabilistic Response

Random vibrations of the damped Bernoulli–Euler beam with two supports and subjected to a stationary random excitation are studied. The supports are symmetrically placed with respect to the middle cross-section of the beam. We investigate the mean square displacement of the beam with the goal of determining the optimum location of supports in order to minimize the maximum probabilistic response. This study falls in the category of hybrid optimization and anti-optimization, since we are looking for the worst maximum response, constituting the anti-optimization process; subsequently, we are looking for optimization of the structure to make the maximum response minimal by properly the spacing supports.

Random Vibration of Beams

1962 ◽  
Vol 29 (2) ◽  
pp. 267-275 ◽  
Author(s):  
S. H. Crandall ◽  
Asim Yildiz
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Models ◽  
Random Excitation ◽  
Viscous Damping ◽  
Mean Square ◽  
Euler Beam ◽  
Rayleigh Beam ◽  
Mean Square Response ◽  
The Mean ◽  
Band Limited

The calculated response of a uniform beam to stationary random excitation depends greatly on the dynamical model postulated, on the damping mechanism assumed, and on the nature of the random excitation process. To illustrate this, the mean square deflections, slopes, bending moments, and shear forces have been compared for four different dynamical models, with three different damping mechanisms, subjected to a distributed transverse loading process which is uncorrelated spacewise and which is either ideally “white” timewise or band-limited with an upper cut-off frequency. The dynamic models are the Bernoulli-Euler beam, the Timoshenko beam, and two intermediate models, the Rayleigh beam, and a beam which has the shear flexibility of the Timoshenko beam but not the rotatory inertia. The damping mechanisms are transverse viscous damping, rotatory viscous damping, and Voigt viscoelasticity. It is found that many of the mean-square response quantities are finite when the excitation is ideally white (i.e., when the input has infinite mean square); however, some of the responses are unbounded. For these cases the rate of growth of the response as the cut-off frequency of the excitation is increased is obtained.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

Molecular Dynamics Study of Microscopic Mechanism of Diffusion in Li2SiO3 System

1991 ◽  
Vol 46 (7) ◽  
pp. 616-620 ◽  
Author(s):  
Junko Habasaki
Keyword(s):  
Molecular Dynamics ◽  
Coordination Number ◽  
Md Simulation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Lithium Ions ◽  
Microscopic Mechanism ◽  
Trapping Model ◽  
The Mean

MD simulation has been performed to learn the microscopic mechanism of diffusion of ions in the Li2SiO3 system. The motion of lithium ions can be explained by the trapping model, where lithium is trapped in the polyhedron and moves with fluctuation of the coordination number. The mean square displacement of lithium was found to correlate well with the net changes in coordination number.

THE EFFECT OF PREMELTING: STUDY FOR SEMI-INFINITE CRYSTALS AND NANO-SYSTEMS

1994 ◽  
Vol 08 (24) ◽  
pp. 3411-3422 ◽  
Author(s):  
W. SCHOMMERS
Keyword(s):  
Pair Correlation ◽  
Mean Square Displacement ◽  
Phonon Density ◽  
Mean Square ◽  
Phonon Density Of States ◽  
Molecular Dynamics Calculations ◽  
Theory Of Melting ◽  
The Mean ◽  
Dynamical Properties ◽  
Reliable Interaction

The effect of premelting is of particular interest in connection with the theory of melting. In this paper, we discuss the structural and dynamical properties of the surfaces of semi-infinite crystals as well as of nano-clusters, which show the effect of premelting. The investigations are based on molecular-dynamics calculations: different models are used for the systematic study of the effect of premelting. In particular, the behaviour of the following functions have been studied: pair correlation function, generalized phonon density of states, and the mean-square displacement as a function of time. The calculations have been done for krypton since for this substance a reliable interaction potential is available.

scholarly journals On an extension of the stochastic linearization

1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Equation ◽  
Random Excitation ◽  
Linearization Method ◽  
Mean Square ◽  
Fundamental Idea ◽  
Stochastic Linearization ◽  
The Mean ◽  
The Difference

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Non-Markovian effect of the fractional damping environment and Newton’s second law of motion

2018 ◽  
Vol 32 (19) ◽  
pp. 1850210
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qin ◽  
Yu-Qing Xu ◽  
Shu-Qin Lv ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Mean Square Displacement ◽  
Dynamical Analysis ◽  
Second Law ◽  
Mean Square ◽  
Fractional Damping ◽  
Dynamical Mechanism ◽  
Brownian Particles ◽  
The Mean ◽  
Dissipative Environments

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

Stationary random vibration of a viscoelastic Timoshenko cantilever beam under diverse random processes

2019 ◽  
Vol 234 (4) ◽  
pp. 849-861
Author(s):  
Qingzhao Zhou ◽  
David He ◽  
Yaping Zhao
Keyword(s):  
White Noise ◽  
Cantilever Beam ◽  
Time Correlation ◽  
Random Excitation ◽  
Transverse Displacement ◽  
Mean Square ◽  
Concentrated Force ◽  
The Mean ◽  
Definite Integration ◽  
Band Limited

In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

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