Random Excitation of a Loaded Nonlinear String

1960 ◽  
Vol 27 (3) ◽  
pp. 575-578 ◽  
Author(s):  
T. K. Caughey
Keyword(s):  
Linear Problem ◽  
Random Excitation ◽  
Additional Stress ◽  
Elastic String ◽  
Equivalent Linear ◽  
The Mean ◽  
A Chain ◽  
Nonlinear String

This paper is devoted to the study of a chain of particles connected by a massless elastic string subjected to random excitation. It is shown that, as a result of the additional stress induced by the stretching of the string, the mean squared deflection of every particle is reduced compared with that for the equivalent linear problem.

scholarly journals Response of a Nonlinear String to Random Loading

1959 ◽  
Vol 26 (3) ◽  
pp. 341-344
Author(s):  
T. K. Caughey
Keyword(s):  
Random Excitation ◽  
Additional Stress ◽  
Random Loading ◽  
Equivalent Linear ◽  
Linear String ◽  
The Mean ◽  
Nonlinear String

Abstract This paper considers the response of a nonlinear string to random excitation. It is shown that, owing to the additional stress induced by the stretching of the string, the mean squared deflection at every point is smaller than that for the equivalent linear string.

scholarly journals Random Excitation of a System With Bilinear Hysteresis

1960 ◽  
Vol 27 (4) ◽  
pp. 649-652 ◽  
Author(s):  
T. K. Caughey
Keyword(s):  
Linear System ◽  
Random Excitation ◽  
Viscous Damping ◽  
Equivalent Linear ◽  
The Mean ◽  
Equivalent Linear System

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system.

Response of a Loaded Nonlinear String to Random Excitation

1962 ◽  
Vol 29 (3) ◽  
pp. 483-485 ◽  
Author(s):  
S. T. Ariaratnam
Keyword(s):  
Planck Equation ◽  
Nonlinear Effects ◽  
String Tension ◽  
Random Excitation ◽  
Markov Random ◽  
Fokker Planck Equation ◽  
Markov Random Process ◽  
The Mean ◽  
Nonlinear String ◽  
Fokker Planck

The response to white noise excitation of a light elastic string loaded at equal intervals by a number of equal masses is examined using the theory of the Markov random process and the associated Fokker-Planck equation. Taking nonlinear effects due to variation in string tension into account, an exact solution of the Fokker-Planck equation is obtained and used in an approximate analytical evaluation of the mean squared response of the system.

scholarly journals Handling Associated with Drenching Does Not Impact Survival and General Health of Low Birth Weight Piglets

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 404
Author(s):  
Kevin Van Tichelen ◽  
Sara Prims ◽  
Miriam Ayuso ◽  
Céline Van Kerschaver ◽  
Mario Vandaele ◽  
...  
Keyword(s):  
Birth Weight ◽  
Low Birth Weight ◽  
Significant Risk ◽  
Skin Lesions ◽  
Additional Stress ◽  
Bioactive Substances ◽  
Blood Samples ◽  
Panel Test ◽  
Esterified Fatty Acids ◽  
The Mean

The increase in litter sizes in recent years has resulted in more low birth weight (LBW) piglets, accompanied by a higher mortality. A potential intervention to overcome this is drenching bioactive substances. However, if the act of drenching provokes additional stress in LBW piglets, it might counteract the supplement’s effect and be detrimental for the piglet’s survival. To study the effect of the drenching act, piglets from 67 sows were weighed within 4 h after birth. The mean litter birth weight (MLBW) and standard deviation (SD) were calculated. LBW piglets (n = 76) were defined as weighing between (MLBW-1*SD) and (MLBW-2.5*SD). They were randomly allocated to two treatments: “sham” (conducting the act of drenching by inserting an empty 2.5 mL syringe in the mouth during 20 s, once a day, d1 till d7; n = 37) or “no treatment” (no handling; n = 39). On day 1, 3, 9, 24 and 38, piglets were weighed and scored for skin lesions. Blood samples were collected on day 9 and 38 and analyzed to determine glucose, non-esterified fatty acids (NEFA), urea, immunoglobulin G (IgG), insulin-like growth factor 1 (IGF-1) and a standard blood panel test. There was no difference between sham drenched and untreated piglets regarding any of the parameters. In conclusion, this study showed that drenching does not impose a significant risk to LBW piglets and can be applied safely during the first 7 days after birth.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

1988 ◽  
Vol 110 (2) ◽  
pp. 205-209
Author(s):  
A. V. Singh
Keyword(s):  
Transient Response ◽  
Random Vibration ◽  
Time History ◽  
Wide Band ◽  
Random Excitation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
History Of ◽  
The Mean ◽  
Random Vibration Analysis

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

Effects of Elevated Atmospheric CO2 and its Interaction with Temperature and Nitrogen on Yield of Barley (Hordeum vulgare L.): A Meta-analysis

2021 ◽  
Author(s):  
Mekides Woldegiorgis Gardi ◽  
Bettina I.G Haussmann ◽  
Waqas Ahmed Malik ◽  
Petra Högy
Keyword(s):  
Grain Yield ◽  
Nitrogen Fertilizer ◽  
Meta Analysis ◽  
N Fertilization ◽  
Additional Stress ◽  
Hordeum Vulgare L ◽  
Grain Number ◽  
Experimental Conditions ◽  
Elevated Atmospheric Co2 ◽  
The Mean

Abstract AimsThe general aim of this meta-analysis is to synthesize and summarise the mean response of barley yield variables to elevated CO2 (eCO2) and its interaction with temperature and N fertilization. Methods The present study quantitatively synthesized the response of barley to eCO2 and its interaction with temperature, and Nitrogen (N). A meta-analysis procedure was used to analyse five yield variables of barley extracted from 76 articles to determine the effect size and the magnitude in relation to eCO2 and its interaction with temperature and N. Results CO2 enrichment increased biomass (23.8%), grain number (24.8%), grain yield (27.4%), and thousand-grain weight (5.6%). However, responses to eCO2 were affected by genotype, additional stress, and experimental conditions. In comparison, genotype “Anakin” shows the highest response of biomass (47.1%), while “Genebank accessions” had a higher grain number (46.1%) and grain yield (57.1%) under eCO2. The maximal enhancement of barley yield was observed when plants grow under a combination of eCO2 and higher nitrogen fertilizer (>100 kg ha-1). Nevertheless, biomass (-12%), and grain yield (-17%) responses were lower when eCO2 is combined with high temperature (>25 °C). It was further noted the response of barley yield to eCO2 was higher in the growth chamber than in other CO2 exposure methods. Moreover, comparing pot-rooted versus field-rooted barley plants, a higher response of biomass and grain yield was observed for pot-rooted plants. ConclusionsOverall, results suggest that the maximal barley production under eCO2 will be obtained in combination with high nitrogen fertilizer and optimal temperature (21-25 °C).

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.

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.

Contribution of the Torsional Modes to the Equilibrium Distribution of Vibrational States and to the Specific Heat of a Chain Molecule

1983 ◽  
Vol 38 (12) ◽  
pp. 1285-1292 ◽  
Author(s):  
J. A. Borges da Costa ◽  
C. Scherer ◽  
A. Holz ◽  
J. Naghizadeh
Keyword(s):  
Specific Heat ◽  
Equilibrium Distribution ◽  
Spatial Configuration ◽  
Low Frequency ◽  
Chain Molecule ◽  
Vibrational States ◽  
Polymer Molecules ◽  
The Mean ◽  
A Chain ◽  
Increasing Temperature

Abstract The torsional modes of a chain molecule were studied recently under the assumption that it has a well defined spatial configuration at any time. Here we show how the averages over the possible configurations, for a distribution in thermal equilibrium, should be performed in the calculation of the thermodynamical properties. Our results show that the mean density of torsional states increases in the low frequency region with increasing temperature. The specific heat behaviour shows a considerable difference from the result obtained in the previous paper, where only the lowest energetic configuration was considered. The consequences of this result with respect to the configurational properties of polymer molecules near the θ temperature are discussed.

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