Vibration and flutter of unstiffened and orthogonally stiffened circular cylindrical shells

The problem of vibration and flutter analysis of simply-supported unstiffened and orthogonally stiffened circular cylindrical shells which are typical of missile bodies has been developed and programmed for digital computer solution. An extensive review of the existing literature covering various aspects of the shell flutter problem is given with a critical appraisal of the assumptions made, results obtained, etc. A comprehensive chronological bibliography is also included. The analysis and the programme which have been developed are capable of handling shells of arbitrary geometrical, modal and flow parameters. In the case of stiffened shells, the stiffener effects may be treated as 'averaged' ('smeared') or 'discrete' and in each case the influence of eccentricity, in-plane and rotary inertias may be studied. The aerodynamic generalised forces may be calculated using the linear piston theory, the linear piston theory with a correction for curvature, and the exact potential flow solution. By combining the invacuo-natural vibration analysis and the aerodynamic generalised forces the cylindrical shell flutter problem may be solved and the flutter boundaries may be obtained in each of the above cases. The procedures have been illustrated with typical examples in each of the above cases and the results discussed. A few shells have been tested using an experimental vibration rig designed and built for the purpose and compared with the theoretically predicted invacuo-natural frequencies and mode shapes

Vibration analysis of multi-supported curved panel using the periodic structure approach

This papers deals with the radial vibration of a row of cylindrical panels of finite length using the concept of wave propagation in periodic structures. For this study, the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element. For a given geometry dispersion curves of the propagation constant versus (non-dimensional) natural frequency have been drawn corresponding to the circumferential wave propagation. New conclusions that have emerged from this study are as follows. It is shown that by a proper choice of the periodic element the bounding frequencies and the corresponding modes in all the propagation bands can be determined. These have been shown to correspond to a single curved panel with all its edges simply supported. It is noted that there are no attenuation gaps in the entire frequency spectrum beyond the lowest bounding frequency. This is a unique feature of circumferential wave propagation around circular cylindrical shells and panels, as opposed to the wave propagation of periodically supported beams and rectangular panels without curvature. The natural frequency corresponding to every circumferential mode of the complete shell has been identified on the propagation constant curve. It has been observed that the natural frequencies of a cylindrically curved panel of a given curvature and length but of different circumferential arc length (corresponding to different angles subtended at the centre of any circular cross-section) may also be identified on the same propagation constant curve. Finally, it is shown that the same propagation constant curve may also be used to determine all the natural frequencies of a finite row of curved panels with the extreme edges simply supported. Wherever possible the numerical results have been compared with those obtained independently from finite element13; analysis and=or results available in the literature. Flutter analysis of multi-span curved panels using a wave13; approach is the ultimate objective of this work

Free Vibration Characteristics of Cylindrical Shells Using a Wave Propagation Method

In the present paper, concept of a periodic structure is used to study the characteristics of the natural frequencies of a complete unstiffened cylindrical shell. A segment of the shell between two consecutive nodal points is chosen to be a periodic structural element. The present effort is to modify Mead and Bardell's approach to study the free vibration characteristics of unstiffened cylindrical shell. The Love-Timoshenko formulation for the strain energy is used in conjunction with Hamilton's principle to compute the natural propagation constants for two shell geometries and different circumferential nodal patterns employing Floquet's principle. The natural frequencies were obtained using Sengupta's method and were compared with those obtained from classical Arnold-Warburton's method. The results from the wave propagation method were found to compare identically with the classical methods, since both the methods lead to the exact solution of the same problem. Thus consideration of the shell segment between two consecutive nodal points as a periodic structure is validated. The variations of the phase constants at the lower bounding frequency for the first propagation band for different nodal patterns have been computed. The method is highly computationally efficient