In this paper, the effects of plane pre-stresses on the free vibration and static analyses of circular and annular sandwich panels are examined based on an accurate formulation, as first time. It is assumed that initially pre-stresses consist of in-plane normal (tensile/compressive) and pure bending stresses. New first-order shear deformation theory together with a layerwise approach for sandwich panel is utilized. The sandwich panels are made up of either orthotropic or heterogeneous polar orthotropic materials. Furthermore, piecewise-defined linear local in-plane displacements are adopted based on zigzag theory. The governing partial differential equations are extracted by implementing principle of minimum total potential energy. A unified analytical solution procedure is developed based on power series method for the analysis of heterogeneous initially stressed annular and circular sandwich panels with arbitrary boundary conditions. The transverse shear stress is precisely calculated by considering three-dimensional theory of elasticity. To validate the proposed formulation, the obtained results are compared with those of finite element method. After numerically demonstrating the accuracy of the method, the effects of different geometrical and material parameters, boundary conditions and in-plane pre-stresses on the free vibration and static behavior of circular and annular sandwich panels are investigated.

本文首次以精确的公式为基础，研究了平面预应力对圆形和环形夹芯板的自由振动和静力分析的影响。假定最初的预应力包括平面法向应力（拉力/压缩应力）和纯弯曲应力。利用了新的一阶剪切变形理论以及层合方法来制作夹芯板。夹心板由正交各向异性材料或非均质极性正交各向异性材料组成。此外，基于之字形理论采用分段定义的线性局部面内位移。通过实现最小总势能原理提取控制偏微分方程。基于幂级数方法开发了统一的解析解程序，用于分析任意边界条件下的异质初始受力环形和圆形夹芯板。考虑到三维弹性理论，可以精确计算出横向剪切应力。为了验证所提出的公式，将所得结果与有限元方法进行了比较。在数值上证明了该方法的准确性之后，研究了不同的几何和材料参数，边界条件和平面内预应力对圆形和环形夹芯板的自由振动和静态行为的影响。考虑到三维弹性理论，可以精确计算出横向剪切应力。为了验证所提出的公式，将所得结果与有限元方法进行了比较。在数值上证明了该方法的准确性之后，研究了不同的几何和材料参数，边界条件和平面内预应力对圆形和环形夹芯板的自由振动和静态行为的影响。考虑到三维弹性理论，可以精确计算出横向剪切应力。为了验证所提出的公式，将获得的结果与有限元方法的结果进行比较。在数值上证明了该方法的准确性之后，研究了不同的几何和材料参数，边界条件和平面内预应力对圆形和环形夹芯板的自由振动和静态行为的影响。