Abstract

The p-version of the finite element method based on the first-order shear deformation theory (FSDT) is applied, to the free vibration of symmetric variable stiffness composite laminated (VSCL) elliptical plates, with curvilinear fibers. A curved hierarchical rectangular finite element is developed and used to model the elliptical plate. The geometry is described accurately by the blending function method. The element stiffness and mass matrices are integrated numerically using the Gauss-Legendre quadrature. The equations of motion are derived employing Lagrange’s method. The numerical results are validated by means of convergence tests and compared with available data in the literature, for isotropic and constant stiffness composite laminated (CSCL) circular and elliptical plates. The contour plots of the fundamental frequency as a function of the fiber orientation angles are presented for clamped and soft simply supported symmetric VSCL elliptical plates. The effect of thickness ratio, aspect ratio, boundary conditions, and mechanical parameters on the frequencies of the lowest five modes is investigated and discussed. The mode shapes are examined by considering the effect of the fiber orientation angles and stacking sequences.

摘要

p _-基于一阶剪切变形理论 (FSDT) 的有限元方法的版本应用于具有曲线纤维的对称变刚度复合层压 (VSCL) 椭圆板的自由振动。开发了一种弯曲的分层矩形有限元并用于对椭圆板进行建模。几何形状通过混合函数方法准确描述。使用 Gauss-Legendre 求积法对单元刚度和质量矩阵进行数值积分。运动方程是使用拉格朗日方法导出的。对于各向同性和恒定刚度复合层压 (CSCL) 圆形和椭圆板，数值结果通过收敛性测试得到验证，并与文献中的可用数据进行了比较。给出了夹紧和软简支对称 VSCL 椭圆板的基频随纤维取向角变化的等值线图。研究和讨论了厚度比、纵横比、边界条件和力学参数对最低五种模式频率的影响。通过考虑纤维取向角和堆叠顺序的影响来检查振型。