A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

在平面应力设置的框架内考虑了放置在 Winkler 基础上的薄弹性条的二维混合问题。地基的相对刚度应该很小，以确保低频振动。更高阶的渐近分析导致弯曲运动的一维方程从铁木辛哥型梁方程开始细化许多特别的发展。对于相速度和群速度以及移动载荷的临界速度，通过基础刚度进行了两项扩展。此外，推导了梁由于横向压缩引起的纵向位移的公式。