Abstract—

In this article, we consider flexural (bending) waves propagating in a homogeneous beam fixed on a nonlinear elastic foundation. The dynamic behavior of the beam is determined by Timoshenko’s theory. The system of equations describing the bending vibrations of the beam is reduced to a single nonlinear fourth-order equation for the transverse displacements of the beam median line particles. We state that if the beam stiffness is small compared to the linear stiffness of the foundation, the evolutionary equation is a modified Ostrovsky equation with an additional third-order nonlinear term. For the evolutionary equation, exact soliton solutions are found from the class of stationary waves in the form of a kink and an antikink.

中文翻译：

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非线性弹性基底上铁木辛柯梁中传播的弯曲波的色散和空间定位

摘要-

在本文中，我们考虑在固定在非线性弹性基础上的均匀梁中传播的弯曲（弯曲）波。梁的动态行为由 Timoshenko 的理论决定。描述梁弯曲振动的方程组被简化为梁中线粒子横向位移的单个非线性四阶方程。我们声明，如果梁刚度与基础的线性刚度相比较小，则演化方程是带有附加三阶非线性项的修正 Ostrovsky 方程。对于演化方程，可以从扭结和反扭结形式的驻波类中找到精确的孤子解。