On the stability of compressed plate

Kolpak, Eugeny P.; Federation, Russian; Ivanov, Sergei Evgenievich

doi:10.12988/ces.2015.57213

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…For the solution of nonlinear differential equations is applied various analytical methods [5][6][7][8][9][10]: the harmonic balance method, van der Pol method, the small parameter method, the averaging method, Krylov-Bogolyubov method, the Poincare perturbation method and the polynomial transformations method. The exact solution of the nonlinear system of equations is obtained numerically by the method of Runge-Kutta fourth order with the following parameters: The analytical solution is obtained by the modified method of polynomial transformations [11][12][13].…”

Section: Fig3 the Kinematic Scheme Of Truck Cranementioning

confidence: 99%

Mathematical modeling of nonlinear dynamic system of the truck crane

Ivanov¹

2016

ces

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The mathematical model of the mechanical system of truck crane with three degrees of freedom is considered. The truck crane includes the mechanisms of bridge and electric hoist, which are modeled by translational kinematic pairs. For the automation of handling operations are determined the position of cargo, speed and acceleration of cargo in the initial coordinates system. The device for soft start-stop of the truck crane is simulated by nonlinear polynomial with generalized coordinates. By modified method of polynomial transformations we obtain the analytical solution of nonlinear mathematical model of truck crane. For control the accuracy of analytical results we carried out calculation of mathematical model by the method Runge-Kutta fourth order. The power of devices necessary for lift and move the cargo is defined.

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Section: Fig3 the Kinematic Scheme Of Truck Cranementioning

confidence: 99%

Mathematical modeling of nonlinear dynamic system of the truck crane

Ivanov¹

2016

ces

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“…The solution of nonlinear differential equations [18][19][20][21][22][23][24][25] can be carried out various approximate analytical methods [26][27][28][29][30][31][32][33][34][35]: the method of Van der Pol, the harmonic balance method, the averaging method, the small parameter method, the method of Krylov-Bogolyubov, method of harmonic linearization, the method of Poincare. We obtained an approximate analytical solution of the modified method of harmonic linearization with Chebyshev polynomials [36][37][38][39][40][41][42] 2 2 4 2 4 2 2 2 2 3 3 3 3 11 11 11 22 3 15 3 1 2 3 3 3 3 3 Figure 15 shows graphs of the vertical oscillations of mobile satellite antenna obtained by analytical method (blue), a numerical method (yellow) and the graph the oscillation without vibration protection devices (green).…”

Section: Fig14 the Scheme Vibration Protection Devicementioning

confidence: 99%

Mathematical modeling of the guidance system of satellite antenna

Ivanov¹,

Kolpak²

2016

ces

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The present paper develops a mathematical model of mobile satellite antenna elliptical shape which is under the influence of wind loads. The wind load is calculated in the framework of a hydrodynamic model for the mathematical package freeFEM++. To reduce the external impact, a model of vibration protection device is developed. The solution of developed mathematical model is constructed using numerical and analytical methods.

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“…Accordingly, from the condition of incompressibility is sought the multiplicity of deformation change of membrane, the thickness 31…”

Section: The Equations Of Motionmentioning

confidence: 99%

“…For large deformations of shells and membranes to calculate such characteristics are not simply [22][23][24][25][26]. This is due to not only to the difficulties of constructing solutions of nonlinear boundary value problems, but also to the fact that they can have more than one solution [27][28][29][30][31][32][33][34][35]. If the problem has several solutions, there are difficulties in the numerical solution of boundary value problems [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%