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.

Geometrically Nonlinear Calculation of Trailing rod designs. Part 1. Calculation of flexible threads

10.12737/335 ◽  
2013 ◽  
Vol 1 (1) ◽  
pp. 7-17
Author(s):  
Андрей Свентиков
Keyword(s):  
Linear Model ◽  
Geometric Nonlinearity ◽  
Geometrical Nonlinearity ◽  
Constant Load ◽  
Geometrically Nonlinear ◽  
Flexible Rods ◽  
Nonlinear Matrix ◽  
Current Value ◽  
Special Case ◽  
Matrix Calculation

Is treated geometrically nonlinear matrix calculation core construction with the use of flexible threads. The first part is devoted to the study the major calculation dependencies of flexible threads. It is established that the geometric nonlinearity of flexible rods depends on the cube of the ratio of the calculation in a zero-offsets end stabilize relations to its current value. Also found that the constructive nonlinearity is a special case of geometrical nonlinearity and depends on the degree of impact on the VDS of flexible thread load on its own weight. It is found that the preliminary adjustment of the length of flexible rods leads to the increase of the share of the stresses of constant load and, accordingly, to the approximation of the nature of the work of these elements into a linear model.

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.

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.

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.

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.

scholarly journals A new method of successive approximations when calculating elements of electromechanical machines

2020 ◽  
Vol 5 (2) ◽  
pp. 168-172
Author(s):  
K. Ismayilov ◽  
◽  
S.T. Suleymanov ◽  
S.T. Ruziev ◽  
M.B. Aripjanova ◽  
...  
Keyword(s):  
New Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

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