Abstract

Initial value problems with various boundary conditions at the ends are studied for the beam vibration equation taking into account the beam rotational motion under bending. An energy inequality is established, which implies the uniqueness of the solution of the four initial–boundary value problems posed. In the case of hinged ends, theorems on the existence and stability of the solution of the problem in the classes of regular and generalized solutions are proved.

中文翻译：

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梁振动方程在弯曲下允许旋转运动的初边值问题

摘要

考虑梁在弯曲下的旋转运动，研究了梁两端具有各种边界条件的初值问题。建立了能量不平等，这意味着所提出的四个初始-边值问题的解的唯一性。在铰接端的情况下，证明了正则解和广义解中有关问题解的存在性和稳定性的定理。