We demonstrate the existence of solutions to Signorini’s problem for the Timoshenko’s beam by using a hybrid disturbance. This disturbance enables the use of semigroup theory to show the existence and asymptotic stability. We show that stability is exponential, when the waves speed of propagation is equal. When the waves speed is different, we show that the solution decays polynomially. This result is new. We perform numerical experiments to visualize the asymptotic properties.

中文翻译：

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季莫申科梁的边界接触问题的稳定性

我们通过使用混合扰动证明了蒂莫申科光束的Signorini问题的解的存在。这种干扰使得能够使用半群理论来显示存在性和渐近稳定性。我们表明，当波的传播速度相等时，稳定性是指数级的。当波速不同时，我们表明解是多项式衰减的。这个结果是新的。我们执行数值实验以可视化渐近性质。