Abstract—

Differential equations for potentials are considered that ensure the fulfillment of the basic vector differential equation of the linear theory of elasticity in the case of a harmonic dependence of the displacement field on time. An alternative scheme for splitting the vector differential equation of the linear theory of elasticity into unrelated equations is developed. It is based on the concept of a gamma vector that satisfies a screw equation. As a result, the problem of finding the vortex component of the displacement field is reduced to the sequential solution of unrelated screw first-order partial differential equations. A theorem on the completeness of the representation of the displacement field using two screw vortex vector fields is formulated and proved.

中文翻译：

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用两个螺钉矢量表示弹性理论中空间协调问题中的位移

摘要-

在位移场对时间的谐波依赖性的情况下，可以考虑电位微分方程，以确保满足线性弹性理论的基本矢量微分方程。提出了将线性弹性理论的矢量微分方程分解为不相关方程的替代方案。它基于满足螺丝方程的伽马矢量的概念。结果，找到位移场的涡旋分量的问题被简化为无关的螺杆一阶偏微分方程的顺序解。提出并证明了利用两个螺旋涡旋矢量场表示位移场的完备性的定理。