Axial Wave Propagation in Infinitely Long Periodic Curved Panels

Abstract

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.

Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions

“…It has been reported that fiber orientation has a significant impact on the dynamic behavior of panels. Vibration of a cylindrical multi-supported shell has been investigated [14] A high-precision triangular arbitrary shell FE of Cowper, Lindberg and Olson [15,16] is successfully applied to stiffened shell [17], orthogonally supported curved panels [18,19], and curved panels with axially periodic support [20] for free vibration analysis. In the present work, the same high precision triangular shell FE [15,16] is extended to include the supersonic flow based on linear piston theory for the flutter analysis of isotropic flat (square and rectangular) and cylindrically curved panels for different edge boundary conditions.…”

A metamaterial cylindrical shell with multiple graded resonators for broadband longitudinal wave attenuation

“…Therefore, researchers have extensively studied wave propagation in cylindrical shells using analytical and numerical methods. The propagation of axis waves in cylindrically curved panels of infinite length was studied by Pany et al, and their natural frequencies of bending vibration were determined [21]. Recently, the Wave Finite Element Method was utilized by Manconi et al to analyze wave dispersion in isotropic and orthotropic cylindrical panels and closed cylindrical shells [22].…”

Editorial: Application of periodic structure theory with finite element approach

“…The theory of wave propagation in the periodic structure with FEM (PSFEM) is the goal of the study topic, and the numerical solution is based on the FE analysis of the unit cell of the structure. This numerical FE method enables high accuracy with very little computational effort and is a recommended option for predicting waves in one-dimensional and twodimensional single waveguides (Orris and Petyt, 1974;Pany et al, 2002;Pany and Parthan, 2003a;Pany et al, 2003;Pany and Parthan, 2003b;Pany, 2022). The majority of published works on periodic structures used in engineering try to create theoretical and numerical techniques to understand wave propagation behavior and its attributes, even though the fact that these phenomena are widely known.…”