<p>This article presents adaptation of the Wittrick-Williams algorithm to calculate the natural vibration frequencies of cylindrical shells. Initially, the “algorithm” was proposed and used to find the natural frequencies of branched piping systems (trusses) in structural mechanics problems. We expanded it for shells, where a more difficult system of main differential equations is solved, with increasing calculation effort. The Wittrick-Williams algorithm was chosen to find vibration frequencies, because it is the only one exact solution for the transcendental eigenvalue problem. The “algorithm” gives the number of natural frequencies below a trial value of frequency, therefore, using bisection method, as the simplest, it is possible to find frequencies with sufficient accuracy. It can been used, for example, in a dynamic analysis, where it is important to find accurately the lower frequencies, and to distinguish between coupled frequencies. For solution the shell must been divided into a certain number of parts; convergence graphs are given, according to which the optimal number of partitions is selected. Obtained results show good convergence with experimental and literature data for different boundary conditions.&nbsp; Several special cases have been considered for shells with different values of elastic boundary conditions. The method has proven to be practical and can been used for modal, harmonic and seismic analysis.</p>

Application of the Williams-Wittrick Algorithm for Thin Shell Vibrations Problems

Paper Proceedings: https://asmedigitalcollection.asme.org/PVP/PVP2021/volume/85314

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