Integrated orthogonal polynomials based spectral collocation method for vibration analysis of coupled laminated shell structures

• An integral approach is presented to study vibrations of laminated coupled shells.
• Arbitrary elastic-support boundary conditions can be easily modeled.
• The present formulation makes the choice of basis function quite flexible.
• Advantages of present method lie in its simplicity, fast convergence and accuracy.

In this paper, the spectral collocation method based on integrated orthogonal polynomials is applied to the free vibration analysis of coupled axisymmetric laminated shell structures with arbitrary elastic-support boundary conditions (BCs). The coupled shell structure is firstly divided into its multiple components (i.e. the cone, cylinder, sphere and annular plate) at the location of junction in the meridional direction. Then by applying Hamilton׳s principle, the equations of motion for all the individual shell segments are derived on the basis of the first-order shear deformation theory. Instead of adopting conventional differentiation scheme, an integration technique is used to each individual segment which leads to a set of algebraic equations. These shell segments are further coupled together by matching all of the required displacement and force continuous conditions at the interface. The remaining elastic-support boundary conditions are employed at the ends of the coupled shells. Accuracy and efficiency of the proposed numerical method are explored through a series of free vibration analysis of joined and stepped shell structures, and the results are compared with those available solutions in open literature. Furthermore, the frequency parameters and mode shapes of selected coupled shell structures including cylindrical–spherical, coupled conical and stepped shells are presented to reveal their geometry- and BC-dependent free vibration characteristics.