Axial Wave Propagation in Infinitely Long Periodic Curved Panels

Propagation of waves along the axis of the cylindrically curved panels of infinite length, supported at regular intervals is considered in this paper to determine their natural frequencies in bending vibration. Two approximate methods of analysis are presented. In the first, bending deflections in the form of beam functions and sinusoidal modes are used to obtain the propagation constant curves. In the second method high precision triangular finite elements is used combined with a wave approach to determine the natural frequencies. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effect. Curves of propagation constant versus natural frequencies have been obtained for axial wave propagation of a multi supported curved panel of infinite length. From these curves, frequencies of a finite multi supported curved panel of k segments may be obtained by simply reading off the frequencies corresponding to $jπ/kj=1,2…k.$ Bounding frequencies and bounding modes of the multi supported curved panels have been identified. It reveals that the bounding modes are similar to periodic flat panel case. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature.