Parametric Excitation Under Multiple Excitation Parameters: Asymmetric Plates Under a Rotating Spring

1991 ◽  
Author(s):  
I. Y. Shen ◽  
C. D. Mote
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
System Stability ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Matrix Eigenvalue Problem ◽  
Secondary Resonances ◽  
Nonlinear Matrix ◽  
Perturbation Parameters ◽  
Floquet Theorem

Abstract A perturbation method is developed to predict stability of parametrically excited dynamic systems containing multiple perturbation parameters. This method, based on the Floquet theorem and the method of successive approximations, results in a nonlinear matrix eigenvalue problem whose eigenvalues are used to predict the system stability. The method is applied to a classical circular plate, containing elastic or viscoelastic inclusions, excited by a linear transverse spring rotating at constant speed. Primary and secondary resonances are predicted. The transition to instability predicted by the perturbation analysis agrees with predictions obtained by numerical integration of the equations of motion.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

Geometrically nonlinear calculation of trailing rod designs. Part 2. Matrix calculation of trailing systems

10.12737/336 ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 18-27 ◽  
Author(s):  
Андрей Свентиков
Keyword(s):  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Geometrically Nonlinear ◽  
Matrix Algorithms ◽  
Nonlinear Matrix ◽  
Matrix Calculation ◽  
Good Agreement

Is treated geometrically nonlinear matrix calculation of core construction with the use of flexible threads. The second part of the article is devoted to the study of matrix algorithms nonlinear calculation of hanging systems. For the geometrically nonlinear calculation was applied the method of elastic solutions, and for the constructive nonlinear basis of the method of successive approximations. The proposed methods have been tested on the well-known plane examples of the calculation, as well as on the example of study of the spatial hanging rod cover. The results found on the proposed methods have shown good agreement with the corresponding data of other authors. Also it is established that the greatest imbalance nodes in the cantilevered system is observed in the nodes of a fle­xible bearing thread, as well as in the nodes of the greatest intensity of the load.

scholarly journals Some Kinds of the Controllable Problems for Fuzzy Control Dynamic Systems

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
N. D. Phu ◽  
P. V. Tri ◽  
A. Ahmadian ◽  
S. Salahshour ◽  
D. Baleanu
Keyword(s):  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Fuzzy Systems ◽  
Local Existence ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Global Existence And Uniqueness ◽  
Control Dynamic ◽  
Generalized Lipschitz Condition ◽  
Fuzzy Solutions

In this work, we have discussed the fuzzy solutions for fuzzy controllable problem, fuzzy feedback problem, and fuzzy global controllable (GC) problems. We use the method of successive approximations under the generalized Lipschitz condition for the local existence and furthermore, we have described the contraction principle under suitable conditions for global existence and uniqueness of fuzzy solutions. We have too the GC results for fuzzy systems. Some examples and computer simulation illustrating our approach are also given for these controllable problems.

Flow Near the Stagnation Point of a Body Which Undergoes a Sudden Change in a Steady Stream

1973 ◽  
Vol 40 (1) ◽  
pp. 37-42 ◽  
Author(s):  
K. Nanbu
Keyword(s):  
Stagnation Point ◽  
Equations Of Motion ◽  
Sudden Change ◽  
Order Theory ◽  
Small Time ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order Theory ◽  
Time Solution

Unsteady laminar boundary layers near the stagnation point of a body which undergoes a sudden change in a steady stream are analyzed by the method of successive approximations. It is shown that the second approximation which includes the effect of nonlinear convective terms of the equations of motion improves remarkably the first-order theory by the earlier investigators. Also, it seems that when the body is started with velocity increasing gradually with increasing time, the small-time solution obtained thus connects smoothly with the existing large-time solution.

scholarly journals Curvilinear Squeeze Film Bearing Lubricated with a Dehaven Fluid or with Similar Fluids

2017 ◽  
Vol 22 (3) ◽  
pp. 697-715
Author(s):  
A. Walicka ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Reynolds Equation ◽  
Equations Of Motion ◽  
Unified Model ◽  
Squeeze Film ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Shear Stresses ◽  
Strain Rates ◽  
Load Carrying Capacity ◽  
Load Carrying

AbstractIn the paper, the model of a DeHaven fluid and some other models of non-Newtonian fluids, in which the shear strain rates are known functions of the powers of shear stresses, are considered. It was demonstrated that these models for small values of material constants can be presented in a form similar to the form of a DeHaven fluid. This common form, called a unified model of the DeHaven fluid, was used to consider a curvilinear squeeze film bearing. The equations of motion of the unified model, given in a specific coordinate system are used to derive the Reynolds equation. The solution to the Reynolds equation is obtained by a method of successive approximations. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of flows of the unified DeHaven fluid in gaps of two simple squeeze film bearings are presented.

PERTURBATION PARAMETERS TUNING OF MULTI-OBJECTIVE OPTIMIZATION DIFFERENTIAL EVOLUTION AND ITS APPLICATION TO DYNAMIC SYSTEM MODELING

2015 ◽  
Vol 75 (11) ◽  
Author(s):  
Mohd Zakimi Zakaria ◽  
Hishamuddin Jamaluddin ◽  
Robiah Ahmad ◽  
Azmi Harun ◽  
Radhwan Hussin ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Dynamic System ◽  
Dynamic Systems ◽  
System Modeling ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Structure Selection ◽  
Dynamic System Modeling ◽  
Perturbation Parameters ◽  
Model Structure Selection

This paper presents perturbation parameters for tuning of multi-objective optimization differential evolution and its application to dynamic system modeling. The perturbation of the proposed algorithm was composed of crossover and mutation operators.  Initially, a set of parameter values was tuned vigorously by executing multiple runs of algorithm for each proposed parameter variation. A set of values for crossover and mutation rates were proposed in executing the algorithm for model structure selection in dynamic system modeling. The model structure selection was one of the procedures in the system identification technique. Most researchers focused on the problem in selecting the parsimony model as the best represented the dynamic systems. Therefore, this problem needed two objective functions to overcome it, i.e. minimum predictive error and model complexity.  One of the main problems in identification of dynamic systems is to select the minimal model from the huge possible models that need to be considered. Hence, the important concepts in selecting good and adequate model used in the proposed algorithm were elaborated, including the implementation of the algorithm for modeling dynamic systems. Besides, the results showed that multi-objective optimization differential evolution performed better with tuned perturbation parameters.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

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