Shi Dongyan, He Dongze, Wang Qingshan, Ma Chunlong, Shu Haisheng
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China.
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China.
Materials (Basel). 2019 Nov 20;12(23):3808. doi: 10.3390/ma12233808.
In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed.
本文采用一种半解析方法来分析一般边界条件下复合材料层合扁壳的自由振动特性。结合两种壳体理论，即一阶剪切变形壳体理论（FSDT）和经典壳体理论（CST），来描述位移合力与力矢量之间的动力学关系，建立了理论公式。根据所提出的工作，将位移和横向旋转变量转换为波函数形式以满足理论公式。针对不同的边界条件，建立了复合材料扁壳的总矩阵。使用二分法搜索总矩阵的行列式，得到复合材料层合扁壳的固有频率。通过几个经典数值例子，证明了本文方法计算结果更准确可靠。此外，为了讨论几何参数和材料常数对复合材料层合扁壳固有频率的影响，计算了一些数值例子进行分析。同时，还讨论了边界弹性约束刚度的影响。
