We address the stability of solutions corresponding to weakly damped two-layered Timoshenko beams with space variable coefficients. The mathematical model is composed of a system of coupled wave equations and describes the slip effect produced by a thin adhesive layer joining the beams. For the considered PDE system, combined with different boundary conditions, the main result is that the decay rates for the energy depend on local equality of the wave propagation velocity. The latter is achieved by introducing new observability estimates for the present model. We also study the problem with constant coefficients. Here, two main results are obtained: (i) for mixed boundary condition type, we characterize the exponential decay rate by assuming the equality of the wave propagation velocity and (ii) without imposing this assumption, we establish optimal rational decay rates.

我们讨论了具有空间可变系数的弱阻尼两层Timoshenko梁对应的解的稳定性。该数学模型由耦合波动方程组组成，描述了连接梁的薄粘合剂层产生的滑移效应。对于考虑的PDE系统，结合不同的边界条件，主要结果是能量的衰减率取决于波传播速度的局部均等。通过为当前模型引入新的可观察性估计来实现后者。我们还研究了系数恒定的问题。在这里，获得了两个主要结果：（i）对于混合边界条件类型，我们通过假设波传播速度相等来表征指数衰减率，以及（ii）不加此假设，