The Stability of a Moving Elastic Strip Subjected to Random Parametric Excitation

1979 ◽  
Vol 46 (2) ◽  
pp. 404-410 ◽  
Author(s):  
F. Kozin ◽  
R. M. Milstead
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Equations Of Motion ◽  
Stochastic Equations ◽  
Thin Strip ◽  
Elastic Strip ◽  
Moving Strip ◽  
The Stability ◽  
Sufficiency Conditions

The dynamic stability of a thin strip, traveling axially, at a constant speed between two roller supports is investigated for the case of zero mean random in-plane loading. Galerkin’s method is used to reduce the equations of motion to a set of fourth-order stochastic equations. An extention of the method first proposed by Wu and Kozin is developed which allows determination of the sufficiency conditions to guarantee Almost Sure Asymptotic Stability of stochastic systems of order greater than two. Using this method, results in terms of the variance of the random loadings on the moving strip are derived. It is found that the critical noise level to guarantee stability of the strip decreases with increasing mode, approaching asymptotically a level determined solely by the strip stiffness.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS WITH DAMPING

2004 ◽  
Vol 14 (11) ◽  
pp. 3931-3947 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability

A system that consists of two impacting oscillators with damping has been considered in this paper. In the first part, a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions are presented. The results of the computations carried out by these methods have been illustrated with a few examples. In the second part of the paper, the results of some numerical investigations are presented. The goal of these studies is to determine, in which regions of parameters characterizing the system, the periodic motion with one impact per period exists and is stable.

scholarly journals ДИНАМІЧНА РЕАКЦІЯ ТА СТІЙКІСТЬ ПОШКОДЖЕНОЇ КОНСТРУКЦІЇ ТРАНСПОРТНОГО ЛІТАКА

2020 ◽  
pp. 173-180
Author(s):  
Є. Ю. Іленко ◽  
В. М. Онищенко
Keyword(s):  
Dynamic Stability ◽  
Equations Of Motion ◽  
Initial Perturbation ◽  
Aerodynamic Characteristics ◽  
Operating Conditions ◽  
Ultimate State ◽  
Main Method ◽  
Operating Load ◽  
The Stability

In the process of designing and operating the aircraft, it is important to determine the ultimate state of the structure, taking into account the dynamic load of the structure and its stability. The ultimate state of the structure is characterized by damage, in which the structure still retains the ability to withstand without catastrophic destruction of the maximum operating load. The main method of studying the stability of the structure is the dynamic method. It allows us to investigate the perturbed motion of a structure as a nonconservative system for some initial perturbation. The monotonic departure of the system from the equilibrium position or its oscillations with increasing amplitudes indicate the instability of the structure. The paper analyzes the effect of damage to the aircraft structure on its dynamic stability based on the determination of the dynamic response of the aircraft to some non-stationary perturbation, for example, on the action of a turbulent atmosphere. The method of computational analysis is used to study the dynamic stability of the structure. The basis of this method is mathematical modeling (MM) of the operation of the aircraft in the form of a system of equations of motion and deformation of the structure. The problem of dynamic aeroelasticity is considered - the behavior of the elastic damaged structure of the aircraft in the air flow to the initial perturbation. On the basis of computer simulation, the dynamic stability of the elastic structure, its oscillating or quasi-static (aperiodic) deformation motion within the flight range of the aircraft is estimated. On the basis of parametric researches the limits of instability of a design at the set damages for typical operating conditions are estimated. The relevance of the direction focused on the creation and advanced operation of MM aircraft - their mathematical backups in the process of design and operation of aircraft due to the complexity and limited capabilities of ground experimental installations and flight experiment. It is noted that the condition for the application of this method is the formed MM operation of the aircraft and the availability of information on the mass-inertial, stiffness and aerodynamic characteristics of the aircraft.

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF AN IMPACTING OSCILLATOR WITH TWO FENDERS

2004 ◽  
Vol 14 (09) ◽  
pp. 3115-3134 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Damped Oscillator

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable.

Axisymmetric and non-axisymmetric flows of a non-newtonian fluid between coaxial rotating discs

1991 ◽  
Vol 337 (1648) ◽  
pp. 467-495 ◽  
Keyword(s):  
Newtonian Fluid ◽  
Flow Problem ◽  
Equations Of Motion ◽  
Body Motion ◽  
Rotating Discs ◽  
Infinite Extent ◽  
Torsional Flow ◽  
The Stability ◽  
Fluid Behaviour

The axisymmetric and non-axisymmetric motions of a viscoelastic fluid driven by the steady rotations of a pair of coaxial, parallel discs, each of infinite extent, are studied analytically and numerically. The constitutive equation and the equations of motion depend altogether on four parameters and the numerical scheme used is robust and is capable of discovering regular and limit point bifurcations as well as folds arising from the changes in the values of the parameters. First and foremost, the work reported here is an exhaustive collection of old and new results in the above flow problem, including the stability of the axisymmetric flows. Non-existence of bifurcations from the rigid body motion and their appearance from the torsional flow and other flows are found under a variety of conditions, extending from the newtonian to the non-newtonian fluid behaviour. Secondly, the use of a scaling lemma permits the determination of the solutions to the problem over the entire range of parameters from the known solutions obtained for a finite range of the parameters. Thirdly, the type of non-axisymmetric flows likely to occur in the two-disc problem are determined numerically and they show that slip-layers may exist in the flow regime. These findings seem to confirm the experimental observations in the coaxial flow of a non-newtonian fluid.

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

Synthesis and solvatochromic studies of 2- amino-3-phenolazo1-(4-sulfophenyl)-3-methyi-5-pyrozolone and use it for the determination of trace amount of Nickel (II) in blood samples

2016 ◽  
Vol 5 (10) ◽  
pp. 4920
Author(s):  
Amar M. Ali ◽  
Hussain. J. Mohammed*
Keyword(s):  
Stability Constant ◽  
Trace Amount ◽  
Benzenesulfonic Acid ◽  
Determination Method ◽  
Blood Samples ◽  
Determination Of Nickel ◽  
Normal Human ◽  
The Stability ◽  
Normal Human Blood

A new, simple, sensitive and rapid spectrophotometric method is proposed for the determination of trace amount of Nickel (II). The method is based on the formation of a 1:2 complex with 4-(4-((2-hydroxy-6-nitrophenyl) diazenyl) -3-methyl-5-oxo-2, 5-dihydro-1H-pyrazol-1-yl) benzenesulfonic acid (2-ANASP) as a new reagent is developed. The complex has a maximum absorption at 516 nm and εmax of 1. 84 X 105 L. mol-1. cm-1. A linear correlation (0. 25 – 4. 0μg. ml-1) was found between absorbance at λmax and concentration. The accuracy and reproducibility of the determination method for various known amounts of Nickel (II) were tested. The results obtained are both precise (RSD was 1. 2 %) and accurate (relative error was 0. 787 %). The effect of diverse ions on the determination of Nickel (II) to investigate the selectivity of the method were also studied. The stability constant of the product was 0. 399 X 106 L. mol-1. The proposed method was successfully applied to the analysis of diabetes blood and normal human blood. 

scholarly journals Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC)

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 525 ◽  
Author(s):  
Mehdi Keshavarz-Ghorabaee ◽  
Maghsoud Amiri ◽  
Edmundas Kazimieras Zavadskas ◽  
Zenonas Turskis ◽  
Jurgita Antucheviciene
Keyword(s):  
Essential Elements ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Analysis Of Means ◽  
Simulation Based ◽  
Criteria Weights ◽  
The Stability ◽  
Computational Analyses ◽  
Weighting Methods

The weights of criteria in multi-criteria decision-making (MCDM) problems are essential elements that can significantly affect the results. Accordingly, researchers developed and presented several methods to determine criteria weights. Weighting methods could be objective, subjective, and integrated. This study introduces a new method, called MEREC (MEthod based on the Removal Effects of Criteria), to determine criteria’ objective weights. This method uses a novel idea for weighting criteria. After systematically introducing the method, we present some computational analyses to confirm the efficiency of the MEREC. Firstly, an illustrative example demonstrates the procedure of the MEREC for calculation of the weights of criteria. Secondly, a comparative analysis is presented through an example for validation of the introduced method’s results. Additionally, we perform a simulation-based analysis to verify the reliability of MEREC and the stability of its results. The data of the MCDM problems generated for making this analysis follow a prevalent symmetric distribution (normal distribution). We compare the results of the MEREC with some other objective weighting methods in this analysis, and the analysis of means (ANOM) for variances shows the stability of its results. The conducted analyses demonstrate that the MEREC is efficient to determine objective weights of criteria.

scholarly journals Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1976
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
The Finite Element Method ◽  
Homogenization Procedure ◽  
Plate Structures ◽  
Corrugated Board ◽  
Energy Equivalence ◽  
The Stability ◽  
Global Stiffness Matrix

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

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