Mathematical Model and Method of Determination of Amplitude-Frequency Characteristics of Corrugated Cylindrical Shells for Geometrically Nonlinear Vibrations

Q4 Engineering
M. Marchuk, T. Goriachko, Bohdan Kindratskyy, V. Pakosh
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引用次数: 0

Abstract

On the basis of spatial geometrically nonlinear theory of elasticity by using quadratic approximations for components of the vector of displacements along the normal coordinate to the median surface is developed a new mathematical model of nonlinear dynamics of cylindrical shells with corrugated configuration for median surface. The perturbation method for the solution of systems of nonlinear differential equations for problems of determination of amplitude-frequency characteristics is generalized. In a combination of finite element and generalized perturbations methods, a new methodology for solving problems of free geometrically nonlinear vibrations of shells with complex guide geometry was developed and verified. With its help the influence of geometrical parameters of corrugating at circular coordinate on the main frequency of the elongated cylindrical panel is investigated.
几何非线性振动下波纹圆柱壳幅频特性的数学模型及确定方法
在空间几何非线性弹性理论的基础上,利用中面位移矢量沿法坐标方向分量的二次逼近,建立了波纹形圆柱壳中面非线性动力学的数学模型。推广了求解非线性微分方程组的幅频特性确定问题的摄动法。将有限元法与广义摄动法相结合,提出并验证了一种求解复杂导向结构壳体自由几何非线性振动问题的新方法。在此基础上,研究了圆坐标处波纹几何参数对细长圆柱板主频率的影响。
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来源期刊
Vibrations in Physical Systems
Vibrations in Physical Systems Engineering-Mechanics of Materials
CiteScore
0.70
自引率
0.00%
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0
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