Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method

Free vibrations of oval and elliptic laminated composite cylinders.Comparison between experimental and numerical modeling of elliptic cylinders.Geometric description via differential geometry of oval and elliptic structures.General higher-order layer-wise and equivalent single layer theories.Generalized Differential Quadrature method applied in curvilinear principal coordinates.

We use the generalized differential quadrature method (GDQ) and shell theories of different order to study free vibrations of laminated cylinders of oval and elliptic cross-sections. In the GDQ method partial derivatives of a function at a point are expressed as weighted sums of values of the function at several neighboring points. Thus, strong forms of equations of motion are analyzed. It is found that the computed frequencies rapidly converge with an increase in the number of grid points along the oval or elliptic circumference defining the cross-section of the mid-surface of the cylinder. For a clamped-free elliptic cylinder the converged frequencies match well with the corresponding experimental ones available in the literature. Furthermore, the lowest ten frequencies computed with either an equivalent single layer theory or a layer wise theory of first order and using shear correction factor are accurate.