Abstract This paper is devoted to the construction of asymptotically correct simplified models of nonlinear beam equations for various boundary conditions. V.V. Bolotin mentioned that in some cases (e.g., if compressed load is near the buckling value), the so-called “nonlinear inertia” must be taken into account. The effect of nonlinear inertia on the oscillations of the clamped-free beam is investigated in many papers. Bolotin used some physical assumption and did not compare the order of nonlinear terms in original equations. Below we propose our method for deriving those, which we will named “Bolotin's equations”. This approach is based on fractional analysis of original boundary value problems.

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关于 Bolotin 的简化梁模型与各种边界条件

摘要 本文致力于构建各种边界条件下非线性梁方程的渐近修正简化模型。VV Bolotin 提到，在某些情况下（例如，如果压缩载荷接近屈曲值），必须考虑所谓的“非线性惯性”。许多论文研究了非线性惯性对自由夹紧梁的振荡的影响。Bolotin 使用了一些物理假设并且没有比较原始方程中非线性项的阶数。下面我们提出我们的推导方法，我们将其命名为“Bolotin 方程”。这种方法基于对原始边值问题的分数分析。