The boundary value problem for forced rod vibrations is considered. The rod is assumed to be made of complex material incorporating oscillating inclusions. The equations of motion of the rod consist of two coupled PDEs one describing the carrying medium and the other describing the behavior of the oscillating inclusions. The resonant vibrations in the weakly nonlinear case are studied. Applying the method of small parameter, the stationary solutions of two types depending on the number of frequencies are constructed. The stability of solutions and their coexistence are also discussed therein.

中文翻译：

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由带有振荡夹杂物的材料制成的棒的非线性共振

考虑了受迫杆振动的边界值问题。假定杆由包含振荡夹杂物的复杂材料制成。杆的运动方程由两个耦合的偏微分方程组成，一个描述承载介质，另一个描述振荡夹杂物的行为。研究了弱非线性情况下的共振。应用小参数方法，构造了两种取决于频率数的平稳解。其中还讨论了溶液的稳定性及其共存。