Calculating the forced response of cylinders and cylindrical shells using the wave and finite element method

The dynamic response of circular cylinders can be obtained analytically in very few (and simple) cases. For complicated (thick or anisotropic) circular cylinders, researchers often resort to the finite element (FE) method. This can lead to large models, especially at higher frequencies, which translates into high computational costs and memory requirements. In this paper, the response of axially homogenous circular cylinders (that can be arbitrarily complex through the thickness) is obtained using the wave and finite element (WFE) method. Here, the homogeneity of the cylinder around the circumference and along the axis are exploited to post-process the FE model of a small rectangular segment of the cylinder using periodic structure theory and obtain the wave characteristics of the cylinder. The full power of FE methods can be utilised to obtain the FE model of the small segment. Then, the forced response of the cylinder is posed as an inverse Fourier transform. However, since there are an integer number of wavelengths around the circumference of a closed circular cylinder, one of the integrals in the inverse Fourier transform becomes a simple summation, whereas the other can be resolved analytically using contour integration and the residue theorem. The result is a computationally efficient technique for obtaining the response to time harmonic, arbitrarily distributed loads of axially homogenous, circular cylinders with arbitrary complexity across the thickness.