We are concerned with asymptotic stability of energy for plate equations with vanishing viscoelastic dampings and complementary frictional dampings, where the internal viscoelastic dampings are assumed to be time-dependent. In terms of the relaxation function \(\theta (t)\) and the coefficient \(\gamma (t)\) of viscoelastic term, we obtain the decay rates for the plate equations’ energies. Since we do not need the viscoelastic damping coefficient to be bigger than a fixed positive number, which is required in previous investigations of the asymptotic stability of the plate equations’ energies, our decay theorems extend and improve essentially the existing decay results for the plate equations in both viscoelastic damping case and mixed-type damping case.

我们关注具有消失的粘弹性阻尼和互补摩擦阻尼的板方程的能量渐近稳定性，其中内部粘弹性阻尼被认为是时间相关的。根据松弛函数\（\ theta（t）\）和粘弹性项的系数\（\ gamma（t）\），我们获得了板方程能量的衰减率。由于我们不需要粘弹性阻尼系数大于固定的正数（这是以前对板式方程能量渐近稳定性的研究所要求的），因此我们的衰减定理得以扩展并实质上改善了板式方程的现有衰减结果无论是粘弹性阻尼箱还是混合型阻尼箱。