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本文利用特征方程根的性质,研究了开口圆柱薄壳精确微分方程的特征方程的渐近解。分析证明:二级近似项只有参考价值,而一级近似则是完全正确的。本文应用按量级分析得到的几个近似计算公式,对工程实践中广泛应用的各种不同长度的圆柱薄壳,作了比较详细的分析和计算,并且,还给出了各个公式的渐近误差。提出了在通常情况下,按精确理论求解常用的各向同性圆柱薄壳的一种方法。
In this paper, the asymptotic solution of the eigenvalue equation of the exact differential equation of an open cylindrical shell is studied by using the properties of the root of the eigenvalue equation. The analysis proves that the second-level approximation has only reference value, while the first-order approximation is completely correct. In this paper, several approximate calculation formulas obtained by means of the order of magnitude analysis are applied to analyze and calculate various kinds of cylindrical shells with different lengths widely used in engineering practice. In addition, the asymptotic error. A method to solve commonly used isotropic cylindrical shells according to exact theory is proposed.