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Nonhomogeneous Boundary Value Problem for a Semi-strip Clamped at the End: Exact Solution

机译：半条形夹在末端的非齐次边值问题：精确解

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摘要

In the paper, on the basis of the solution of the biharmonic problem for a smooth semi-strip and the method of the integral Fourier transform, is constructed the exact solution of a nonhomogeneous boundary value problem for a semi-strip clamped at the end (a concentrated force is applied inside the domain along the horizontal axis). The solution is constructed on the superposition principle in the form of the sum of integrals and series in trigonometric functions and Papkovich–Fadle eigenfunctions. The coefficients of these expansions are determined by simple formulas as the Fourier integrals of given boundary functions.
机译：本文基于光滑半条带双调和问题的解和积分傅里叶变换的方法，构造了最后夹紧的半条带非齐次边值问题的精确解（沿水平轴在区域内部施加集中力）。该解决方案以叠加函数的形式构造，形式为三角函数和Papkovich-Fadle本征函数的积分和级数之和。这些展开系数通过简单的公式确定为给定边界函数的傅立叶积分。

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