This paper is determined to study the forced vibration response of doubly-curved shells including different shape panels. A power-full higher-order shear-deformation theory in curvilinear coordinate is developed to model the doubly-curved nano-size shell. Furthermore, a general nonlocal strain gradient theory is employed in order to catch up with both phenomena of small-scale behaves. The nanoshell is made of advanced composite materials whose effective material properties vary continuously through the z-axis. After estimating the effective material properties utilizing a modified power-law, a virtual work of Hamilton statement is applied over the theories to obtain both governing equations as well as boundary conditions. Afterwards, an analytical technique based upon double Fourier series is exploited to satisfy conditions in edges. The numerical examples are presented to reveal the effect of the power-law index, porosity coefficient, elastic medium, aspect and length-to-thickness ratios and small-scale parameters, highlighted by loading time interval, on the dynamic response (i.e., transverse deflection and stresses) of spherical- elliptical, hyperbolic as well as cylindrical nano-panels.

本文旨在研究包括不同形状面板的双曲面壳的受迫振动响应。开发了曲线坐标中的强大高阶剪切变形理论来模拟双弯曲纳米尺寸的壳。此外，采用一般的非局部应变梯度理论来赶上小规模行为的两种现象。纳米壳由先进的复合材料制成，其有效材料特性在整个z-轴。在使用修正的幂律估计有效材料属性后，将 Hamilton 陈述的虚拟功应用于理论以获得控制方程和边界条件。然后，利用基于双傅立叶级数的分析技术来满足边缘条件。数值例子揭示了幂律指数、孔隙度系数、弹性介质、纵横比和长厚比以及加载时间间隔突出的小尺度参数对动态响应（即横向偏转和应力）的球形-椭圆形、双曲线形以及圆柱形纳米板。