2020
DOI: 10.5267/j.esm.2020.1.004
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Numerical modeling of nonlinear vibrations of viscoelastic shallow shells

Abstract: This paper presents a mathematical model of nonlinear supersonic flutter of viscoelastic shells. To describe the strain processes in shallow shells, the Boltzmann-Volterra integral model is used. Based on linear integral models in geometrically nonlinear formulations, equations of nonlinear oscillations of shallow shells are derived. The Koltunov-Rzhanitsyn kernel is used as a relaxation kernel. The equations of motion of shallow shells after applying the Bubnov-Galerkin method in axial coordinates are reduced… Show more

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Cited by 16 publications
(6 citation statements)
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“…Therefore, first-order finite differences eliminate the linear trend (Table 3). Using Table 3, the formulas from the literature [1][2][3][4][5] determine the values of the autocorrelation coefficients 𝑅 𝐿 π‘œπ‘’π‘‘ π‘œπ‘“ 𝐿 = 1,2,3,4,5 (where: 𝐿 π‘Ž , time shift, i.e. the time interval of one phenomenon lagging behind the other associated with it):…”
Section: Resultsmentioning
confidence: 99%
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“…Therefore, first-order finite differences eliminate the linear trend (Table 3). Using Table 3, the formulas from the literature [1][2][3][4][5] determine the values of the autocorrelation coefficients 𝑅 𝐿 π‘œπ‘’π‘‘ π‘œπ‘“ 𝐿 = 1,2,3,4,5 (where: 𝐿 π‘Ž , time shift, i.e. the time interval of one phenomenon lagging behind the other associated with it):…”
Section: Resultsmentioning
confidence: 99%
“…The above mentioned tasks were solved using various methods: 1) The study of the yield of agricultural processes, as a discrete dynamic series and forecasting their yield based on experimental data, play an important role in determining the economic efficiency of farming, dekhkan farms; 2) In this work, the processing and analysis of cotton yield for the observation period 1991-2020 in the Kashkadarya region of the Republic of Uzbekistan was carried out as a discrete time series; 3) Using the methods of statistical analysis of time series, point and interval estimates for the average yield of cotton were constructed , explicit types of trends were determined and the yield was predicted for subsequent years, and various statistical hypotheses were tested [1][2][3][4][5][6][7].…”
Section: Methodsmentioning
confidence: 99%
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“…Depending on the needs, the client can include weed presence, yield, nitrogen supply maps, differential application recommendations, potential yield estimates and more. Automated data collection and analysis enables timely informed decision-making [7,8].…”
Section: Introductionmentioning
confidence: 99%
“…The problems of bending, strength and dynamics of viscoelastic thin-walled structural elements were studied by B.A. Khudayarov and his students [13][14][15][16][17][18][19][20][21][22][23][24][25], [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”
Section: Introductionmentioning
confidence: 99%