中文摘要：

加速盘子的向轴的方向的动态稳定性被调查。由于加速和 nonhomogeneous 边界条件改变紧张的纵被加亮。与粘弹性相结合的板的一个模型被使用。在粘弹性的组成的关系中，材料衍生物被用来代替部分时间衍生物。分析、数字的方法被用来分别地调查求和和主要参量的回声。由为在小排水量政体的横向的行为的线性模型的使用，板被粘滞的抑制力量限制。概括哈密尔顿原则被用来导出管理方程，起始的条件，和联合平面颤动的边界条件。解决之可能性条件被直接使用多重规模的方法建立。Routh-Hurwitz 标准被用来获得稳定性的必要、足够的条件。数字例子被给在稳定性边界上显示出相关参数的效果。改变紧张和 nonhomogeneous 边界条件的纵的有效性被一个微分照计划把多重规模的方法的结果与那些作比较加亮。

英文摘要：

The dynamic stability of axially accelerating plates is investigated. Longitudi- nally varying tensions due to the acceleration and nonhomogeneous boundary conditions are highlighted. A model of the plate combined with viscoelasticity is applied. In the viscoelastic constitutive relationship, the material derivative is used to take the place of the partial time derivative. Analytical and numerical methods are used to investigate summation and principal parametric resonances, respectively. By use of linear models for the transverse behavior in the small displacement regime, the plate is confined by a viscous damping force. The generalized Hamilton principle is used to derive the govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple scales. The Routh-Hurwitz criterion is used to obtain the necessary and sufficient condition of the stability. Numerical examples are given to show the effects of related parameters on the stability boundaries. The validity of longitudinally varying tensions and nonhomogeneous boundary conditions is highlighted by comparing the results of the method of multiple scales with those of a differential quadrature scheme.