Mean-square response of an infinite Bernoulli-Euler beam to nonstationary random excitation

AIAA Journal ◽  
1987 ◽  
Vol 25 (6) ◽  
pp. 864-870 ◽  
Author(s):  
M. K. Maceyko ◽  
R. D. McGhie
Keyword(s):  
Random Excitation ◽  
Mean Square ◽  
Euler Beam ◽  
Mean Square Response

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.

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.

Mean-Square Response of Thermoviscoelastic Medium to Nonstationary Random Excitation

1976 ◽  
Vol 43 (1) ◽  
pp. 150-158 ◽  
Author(s):  
W. Mosberg ◽  
M. Yildiz
Keyword(s):  
Random Excitation ◽  
Irreversible Thermodynamics ◽  
Envelope Function ◽  
Statistical Characteristics ◽  
Mean Square ◽  
Statistical Property ◽  
Step Functions ◽  
Mean Square Response ◽  
The Mean ◽  
Thermoviscoelastic Medium

The mean-square wave response of a lightly damped thermoviscoelastic medium to a special type of nonstationary random excitation is determined. The excitation function on the thermoviscoelastic medium is taken in the form of a product of a well-defined, slowly varying envelope function, and a part which prescribes the statistical characteristics of the excitation. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. By taking into consideration the slow variation envelope function and the wave characteristics of the lightly damped thermoviscoelastic medium, the mean-square response (as a function of temperature, excitation, and damping parameters with the aid of reversible and irreversible thermodynamics) is evaluated.

Mean-Square Response of Simple Mechanical Systems to Nonstationary Random Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 221-227 ◽  
Author(s):  
R. L. Barnoski ◽  
J. R. Maurer
Keyword(s):  
White Noise ◽  
Random Noise ◽  
Random Excitation ◽  
Correlated Noise ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Step Functions ◽  
Unit Step ◽  
Mean Square Response ◽  
The Mean

This paper concerns the mean-square response of a single-degree-of-freedom system to amplitude modulated random noise. The formulation is developed in terms of the frequency-response function of the system and generalized spectra of the nonstationary random excitation. Both the unit step and rectangular step functions are used for the amplitude modulation, and both white noise and noise with an exponentially decaying harmonic correlation function are considered. The time-varying mean-square response is shown not to exceed its stationary value for white noise. For correlated noise, however, it is shown that the system mean-square response may exceed its stationary value.

Response of a Rotating Shaft to Uniaxial Random Excitation

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
M. F. Dimentberg ◽  
A. Naess ◽  
L. Sperling
Keyword(s):  
Exact Analytical Solution ◽  
Quantitative Description ◽  
Stability Margin ◽  
Lateral Force ◽  
Random Excitation ◽  
Mean Square ◽  
Rotating Shaft ◽  
Simple Processing ◽  
Mean Square Response ◽  
On Line

Random vibrations are considered for a Jeffcott rotor subject to uniaxial broadband random excitation by a lateral force along one of its transverse axes. Exact analytical solution for mean square responses is obtained which provide quantitative description of two effects: the magnification of mean square whirl radius due to rotation; and the increasing mean square response along the nonexcited direction with increasing rotation speed, that is, the spread of vibration to all directions around the shaft. The latter effect clearly corresponds to the approaching forward whirl of the shaft approaching its instability threshold; it can be used for the on-line evaluation of the rotor’s stability margin from the simple processing of its measured response signals as demonstrated by direct numerical simulation.

The Random Vibration Response of a System Having Many Degrees of Freedom

1966 ◽  
Vol 17 (1) ◽  
pp. 21-30 ◽  
Author(s):  
J. D. Robson
Keyword(s):  
Density Matrix ◽  
Random Vibration ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Random Excitation ◽  
Mean Square ◽  
Spectral Density Matrix ◽  
Mean Square Response ◽  
Cross Correlations ◽  
Generalised Coordinates

SummaryThe paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square response.

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.

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