Abstract For the beam vibration equation, we study the inverse problems of finding the right-hand side (the source of vibrations) and the initial conditions. The solutions of the problems are constructed in closed form as sums of series, and the corresponding existence and uniqueness theorems are proved. The problem of small denominators arises when justifying the convergence of the series. In this connection, we establish estimates for the denominators that guarantee their boundedness away from zero and indicate the corresponding asymptotics. Based on these estimates, we prove the convergence of the series in the class of regular solutions of the beam vibration equation.

中文翻译：

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确定梁振动方程右手边和初始条件的反问题

摘要 对于梁振动方程，我们研究了求右手边（振动源）和初始条件的反问题。问题的解被构造为级数和的封闭形式，并证明了相应的存在唯一性定理。在证明级数的收敛性时会出现小分母的问题。在这方面，我们建立分母的估计，以保证它们的有界远离零并指示相应的渐近性。基于这些估计，我们证明了该系列在梁振动方程的正则解类中的收敛性。